Seminar Algebra–Geometrie–Kombinatorik
Deutsch International renommierte Wissenschaftler tragen ihre aktuellen Forschungsresultate in diesem Seminar vor. Die Vortragsreihe wird von Prof. Manuel Bodirsky und Prof. Arno Fehm vom Institut für Algebra sowie von Prof. Uli Kraehmer, Jun.Prof. Mario Kummer und Prof. Andreas Thom vom Institut für Geometrie veranstaltet. Alle Interessenten sind herzlich eingeladen. Um Informationen über bevorstehende Vorträge per EMail zu erhalten, tragen Sie sich bitte auf unserer MailingListe ein. 
English 
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Summer term 2024  
Thursday, 18.07.2024 13.30  14.30 ZOOM 
Kelly Maggs (Lausanne) Contact: Prof. Dr. A. Thom 
Thursday, 11.07.2024 13.30  14.30 WIL C 133 
Dr. Vincenzo Galgano (MPICBG) Secant varieties are among the main protagonists in tensor decomposition, whose study involves both pure and applied mathematical areas. Any generalised Grassmannian G/P is a set of rank1 "tensors" in the corresponding (minimal) irreducible representation, like Grassmannians for skewsymmetric tensors. The geometry of secant varieties to G/P is in general not completely understood. In this talk we discuss the 2nd secant variety to a generalised Grassmannian, and we give results on the identifiability and singularity in the case of Grassmannians. Some results are from a joint work with Reynaldo Staffolani Contact: Jun.Prof. Dr. Mario Kummer 
Thursday, 04.07.2024 13.30  14.30 WIL C 133 
Dr. Tariq Syed The generalized Serre question asks whether algebraic vector bundles over topologically contractible smooth affine complex varieties are always trivial or not. Many examples of topologically contractible smooth affine complex varieties are given by socalled cyclic coverings. In this talk, we present new results on the motivic cohomology of such cyclic coverings which might indicate a positive answer to the generalized Serre question in low dimensions 
Thursday, 27.06.2024 13.30  14.30 WIL C 133 
Prof. Dr. Andreas Thom (TU Dresden) We show that there are 2^{ℵ_0} nonisomorphic universal sofic groups. This proves a conjecture of Simon Thomas. This is joint work with Vadim Alekseev. Contact: Prof. Dr. A. Thom 
Thursday, 20.06.2024 13.30  14.30 WIL C 133 
Dr. Aljaž Zalar (University of Ljubljana) In the talk we will present quantitative estimates for the gap between positive polynomials and sums of squares polynomials in three different vector spaces: 1) the space of biquadratic biforms, 2) the space of biquadratic biforms modulo the ideal of all orthonormal 2frames, 3) the space of even quartic forms.The motivation to study the gap in 1) comes from quantum information theory, in 2) from financial mathematics, and in 3) from matrix theory. In 1) the gap corresponds to the gap between positive maps and completely positive maps between matrix algebras, in 2) to the gap between crosspositive maps and completely crosspositive maps between matrix algebras, and in 3) to the gap between copositive matrices and matrices that are a sum of a positive semidefinite matrix and entrywise nonnegative one. This is joint work with Igor Klep, Scott McCullough, Klemen Šivic and Tea Štrekelj. Contact: Jun.Prof. Dr. Mario Kummer 
Thursday, 30.05.2024 13.30  14.30 WIL C 133 
Prof. Dr. Amador MartinPizarro (AlbertLudwigsUniversität Freiburg) Given an abelian group G, a corner is a a subset of pairs of the form (x,y),(x+d,y),(x,y+d) with d≠0 non trivial. Ajtai and Szemerédi proved that, asymptotically, every dense subset S of Z/NZ×Z/NZ contains a corner. Shkredov gave a quantitative lower bound on the density of the subset S for particular finite abelian groups. In this talk, we will explain how modeltheoretic conditions on the subset S, such as stability, imply the existence of corners and of other configurations for (pseudo)finite abelian groups. No prior knowledge of mathematical logic is necessary for this talk. 
Thursday, 16.05.2024 13.30  14.30 WIL C 133 
Dr. Fabian Ruehle (Northeastern University) Contact: Prof. Dr. A. Thom 
Thursday, 25.04.2024 13.30  14.30 WIL C 133 
Dr. Philip Ditmann (TU Dresden) Contact: Prof. Dr. M. Bodirsky 
Thursday, 18.04.2024 13.30  14.30 WIL C 133 
Dr. Türkü Özlüm Celik (Koc University) Contact: Prof. Dr. A. Thom 
Thursday, 11.04.2024 13.30  14.30 WIL C 133 
Dr. Matthieu Joseph (Laboratoire Mathématique d’Orsay) Contact: Prof. Dr. M. Bodirsky 
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Winter term 2023/24  
Thursday, 01.02.2024 13.30  14.30 WIL A 124 
Colin Jahel Contact: Prof. Dr. M. Bodirsky 
Thursday, 
Andy Zucker (University of Waterloo) 
Thursday, 
Winfried Hochstättler (FernUniversität in Hagen) Tutte's 4flow conjecture if k=5 After giving more details on the above we will report on partial progress concerning the case k=4, which emanated from collaborations with Goddyn, Neudauer, GuzmánPro and Chidiac. Contact: Prof. Dr. M. Bodirsky 
Thursday, 11.01.2024 13.30 – 14.30 Z21/250 
Lukasz Grabowski (Leipzig)

Thursday, 
Matěj Konečný In turn, Fraisse theory tells us that homogeneous structures correspond to classes of finite structures with the socalled amalgamation property. It is thus not that surprising that various dynamical properties of closed subgroups of Sym(N) are equivalent to combinatorial properties of the corresponding classes of finite structures. In this talk, I will outline an example of this: A class C of finite structures has the extension property for partial automorphisms (EPPA, also called the Hrushovski property) for every A in the class there is B in the class containing A as a substructure such that every partial automorphisms of A extends to an automorphism of B. This has, for example, been a key ingredient in the proof of the small index property for the automorphism group of the random graph by Hodges, Hodkinson, Lascar, and Shelah. Contact: Prof. Dr. M. Bodirsky 
Thursday, 
Jan Hubicka (Charles University) 
Thursday, 
Édouard Bonnet (ÉNS Lyon) 
Thursday, 30.11.2023 
 
Thursday, 23.11.2023 13.30 – 14.30 WIL A 124 
Alexey Bufetov (Leipzig)
Hidden symmetries in Hecke algebra and stochastic applications 
Thursday, 
Waltraud Lederle Boomerang subgroups and the NevoStuckZimmer theorem We introduce the notion of boomerang subgroups of a discrete group. Those are subgroups satisfying a strong recurrence property, when we consider them as elements of the space of all subgroups with the conjugation action. We prove that every boomerang subgroup of SL(n,Z) is finite and central or of finite index if n is at least 3. Thus we give a new and simple proof of the NevoStuckZimmer rigidity theorem for SL(n,Z) avoiding almost all measure theory. This is joint work with Yair Glasner. 
Thursday, 09.11.2023 13.30 – 14.30 Z21/250 / link 
Alcides Buss Deformation Quantization of Operator Algebras In this talk we introduce the audience to the basics of deformation quantization theory of Operator Algebras as developed originally by Mark Rieffel in the 90’s in the setting of C*algebras carrying an action of R^n. For locally compact abelian groups this was later generalized by Kasprzak using Landstad duality for crossed products. For nonabelian groups one can replace actions by coactions of groups and develop a similar procedure for deforming C*algebras via 2cocycles on the group. Some difficulties appear if the cocycle is not continuous. We propose a deformation process that works for every Borel 2cocycle and extends previous work by Bhowmick, Neshveyev, and Sangha. This is based on joint work with Siegfried Echterhoff. 
Thursday, 02.11.2023 13.30 – 14.30 Z21/250 / link 
Daniel Plaumann 
Thursday, 26.10.2023 
 
Thursday, 19.10.2023 13.30 – 14.30 Z21/250 / link 
Kıvanç Ersoy 
Thursday, 12.10.2023 13.30 – 14.30 Z21/250 / link 
Simon Telen 
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Summer term 2023  
Thursday, 13.07.2023 13.30 – 14.30 Z21/250 link 
Ivan Bartulović (TU Dresden)
Cyclic objects from string links and surfaces 
Thursday, 29.06.2023 13.30 – 14.30 Z21/250 link 
Santiago Guzmán Pro (TU Dresden) 
Thursday, 
Mark Pengitore (University of Virginia) Characteristic quotients of surface groups and residual finiteness of mapping class groups It is a classical result of Grossman that mapping class groups of finite type surfaces are residually finite. In recent years, residual finiteness growth functions of groups have attracted much interest; these are functions that measure the complexity of the finite quotients needed to separate group elements from the identity. Residual finiteness growth functions detect many subtle properties of groups, including linearity. In this talk, I will discuss some recent joint work with Thomas Koberda on residual finiteness growth for mapping class groups, adapted to nilpotent and solvable quotients of the underlying surface group. 
Thursday, 15.06.2023 13.30 – 14.30 Z21/217 
Sebastian Mentemeier (Universität Hildesheim) Contact: Prof. Dr. A. Behme 
Thursday, 04.05.2023 13.30 – 14.30 Z21/250 link 
Daniel Hoffmann (TU Dresden) Model completeness of SL(2,R) I will try to present results from my joint project with Chieu Minh Tran and Jinhe Ye. Model completeness is a weakening of quantifier elimination.The main task here is to define a field in the structure of the pure group, but in such a way that this definition transfers over some group extensions. I will recall basic facts from the model theory needed here and similar recent results in the field, then  hopefully  I will be able to sketch the idea of the proof, which is quite geometric. 
Thursday, 13.04.2023 13.30 – 14.30 Z21/250 link 
Henry Bradford (University of Cambridge) Hopfian wreath products and the stable finiteness conjecture Motivated by connections with residual finiteness, we study the Hopf property for the wreath product of two finitely generated groups. We show that, if the basegroup is abelian, then there is a strong connection between the Hopf property for the wreath product, and a famous conjecture of Kaplansky concerning units in group algebras. We also produce many examples of Hopfian wreath products with nonabelian base, including some where the acting group is nonHopfian. 
Thursday, 
Konrad Schmüdgen (University of Leipzig) Positivstellensätze for semirings in real algebraic geometry 
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Winter term 2022/23  
Thursday, 2.2.2023 13.30  14.30 WIL A 124 link 
Inna Capdebosq (University of Warwick) 
Thursday, 
Stefan Ludwig (ENS, Paris) An approximate AxKochenErshov principle for valued fields in continuous logic In a paper from 2014, Itaï Ben Yaacov considered complete valued fields, with value group in the reals, as structures in continuous logic. For technical reasons one has to consider the projective line over such a field rather than the field itself. In this talk, after introducing the above setting, I will present two recent results on metric valued fields of residue characteristic 0, namely a complete description of the elementary classes in terms of the residue field and value group (in a sense an approximate AKE principle), and the fact that, contrarily to the situation in discrete logic, the theory of metric valued fields with a distinguished isometric isomorphism does not admit a modelcompanion, answering a question of Ben Yaacov. This is joint work with Martin Hils. 
Thursday, 24.11.2022 13.30  14.30 WIL A 124 link 
Paul Wedrich (Universität Hamburg) 
Thursday, 
Pascal Schweitzer (TU Darmstadt) 
Thursday, 
Moritz Lichter (TU Darmstadt) Separating Rank Logic from Polynomial Time The quest for a logic capturing polynomial time is the question whether there exists a logic that exactly defines all properties decidable in polynomial time. The most promising candidates for such a logic are Choiceless Polynomial Time (CPT) and rank logic. Rank logic extends fixedpoint logic by a rank operator over prime fields. In this talk, I argue that rank logic cannot define the isomorphism problem of a variant of the so called CFI graphs. This isomorphism problem is decidable in polynomial time and actually definable in CPT. Thus, rank logic is separated from CPT and in particular from polynomial time. 
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Summer term 2022  
Thursday, 14.7.2022 13.30  14.30 WIL A 124 Link: https://tudresden.zoom.us/my/mariokummer 
Claus Scheiderer 
Thursday, 7.7.2022 13.30  14.30 WIL A 124 Link: https://tudresden.zoom.us/my/mariokummer 
Mario Kummer 
Thursday, 23.06.2022 13.30  14.30 WIL A 124 Link: https://tudresden.zoom.us/my/mariokummer 
Rafael Oliveira 
Thursday, 02.06.2022 13.30  14.30 WIL A 124 Link: https://tudresden.zoom.us/my/mariokummer 
Thomas Nikolaus 
Thursday, 19.05.2022 
Alexander Mang 
Thursday, 12.05.2022 
Kevin Wolf 
Thursday, 21.04.2022 
Emily Roff This talk will introduce the theory and discuss recent developments, without assuming detailed knowledge of category theory or homological algebra. Leinster and Shulman’s construction suggests a means to build a ‘magnitude nerve’ for any group G equipped with a conjugationinvariant length function L, and this will be our central example. The magnitude homology of (G,L)  the homotopy of its magnitude nerve  captures information about the spectrum of L as well as the traditional group homology of G. To illuminate the picture, we’ll construct a variant on the fundamental group of a subset of the plane and analyse its magnitude homology. 
14.4.2022 (Do.) 13:30 Uhr WIL/A124 online 
Ulrich Krähmer (TU Dresden) 
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Winter term 2021/22  
27.01.2022 (Do) 13:30 Uhr Online 
Wieslaw Kubis Czech Academy of Science Abstract evolution systems, amalgamation and homogeneity An evolution system is just a category with a distinguished class of arrows, called transitions. This concept, in particular, generalizes abstract rewriting system. It turns out that evolution systems with amalgamation provide a good framework for studying homogeneous structures, both finite and infinite. I will present several motivating examples. 
16.12.2021 (Do) 13:30 Uhr Online 
Gil Goffer Weizmann Institute of Science Is invariable generation hereditary? We will discuss the notion of invariably generated groups, with various motivating examples. We will then see how hyperbolic groups and small cancellation theory are used in answering the question in the title, which was asked by Wiegold and by KantorLubotzkyShalev. This is a joint work with Nir Lazarovich. 
09.12.2021 (Do) 13:30 Uhr Online 
Rainer Sinn Universität Leipzig Polypols and their adjoints Polypols were introduced by Emil Wachspress as more general geometric elements than simplices and their adjoints play a key role for generalizing barycentric coordinates. We define these objects, discuss their relation to positive geometries from particle physics, and give an open problem about adjoints of polypols in the plane. 
25.11.2021 (Do) 13:30 Uhr Online 
Damien Gaboriau ENS Lyon On homology torsion growth for SL_{d}(Z), Artin groups and mapping class groups. This is joint work with Miklos Abert, Nicolas Bergeron and Mikolaj Fraczyk. The growth of the sequence of Betti numbers is quite well understood when considering a suitable sequence of finite sheeted covers of a manifold or of finite index subgroups of a countable group. We are interested in other homological invariants, like the growth of the mod p Betti numbers and the growth of the torsion of the homology. We produce new vanishing results on the growth of torsion homologies in higher degrees for SL_{d}(Z), Artin groups and mapping class groups. As a central tool, we introduce a quantitative homotopical method that constructs small classifying spaces of finite index subgroups, at the same time controlling the complexity of the homotopy. Our method easily applies to free abelian groups and then extends recursively to a wide class of residually finite groups. 
18.11.2021 (Do) 13:30 Uhr In Präsenz (WIL/A317) Auch auf Zoom 
Vadim Alekseev Institut für Geometrie What is... a lattice in a Lie group? 
11.11.2021 (Do) 13:30 Uhr In Präsenz (WIL/A317) Auch auf Zoom 
Jens Kaad University of Southern Denmark Group cocycles on loop groups In this talk we start out by reviewing the construction of central extensions of smooth loop groups and their relationship to the tame symbol of a pair of meromorphic functions on a Riemann surface. Our goal is then to introduce higher central extensions of smooth double loop groups. In this process we shall see how to combine operator theoretic techniques relating to perturbations of Fredholm operators on Hilbert spaces with concepts from higher category theory. The talk is based on joint work with Ryszard Nest and Jesse Wolfson. 
04.11.2021 (Do) 13:30 Uhr In Präsenz (WIL/A317) Auch auf Zoom 
Ulrich Krähmer Institut für Geometrie What is... a quantum group? The theory of quantum groups/Hopf algebras can be motivated and approached in many ways. This talk is designed as a survey talk and I wil present the maybe most elementary one that focuses on actions on rings and avoids the use of tensor products. Towards the end I will sketch the results of a series of joint papers with my PhD students Angela Tabiri, Manuel Martins and Blessing Oni in which we study quantum groups acting on the commutative coordinate rings of singular plane curves. 
21.10.2021 (Do) 13:30 Uhr In Präsenz (WIL/A317) Auch auf Zoom 
Daniel Max Hoffmann University of Warsaw Elementary Equivalence Theorem for structures In the case of the theory of fields, there is a special class of fields, pseudoalgebraically closed fields (PAC fields). PAC fields were the core of research in field theory in the second half of the 20th century. Why? Because the theory of a PAC field is controlled by its absolute Galois group, so all the machinery from Galois theory can be invoked and used with success. One of the main results on PAC fields is socalled Elementary Equivalence Theorem  in short: the firstorder theory of a PAC field is determined by (classical algebraic data and by) the isomorphism class of its absolute Galois group. Model theory generalizes the notion of PAC fields to the level of PAC structures and, in the talk, I would like to describe this generalization and a general variant of the Elementary Equivalence Theorem. If time permits, I plan to show some easy applications in the case of PACdifferential fields. 
14.10.2021 (Do) 16:20 Uhr Online 
Slawomir Solecki Cornell University Closed groups generated by generic measure preserving transformations The behavior of a measure preserving transformation, even a generic one, is highly nonuniform. In contrast to this observation, a very different picture of a uniform behavior of the closed group generated by a generic measure preserving transformation has emerged. This picture included substantial evidence that pointed to all these groups being topologically isomorphic to a single group, namely, L^{0}  the topological group of all Lebesgue measurable functions from [0,1] to T. We will describe the background touched on above (including all the relevant definitions) and outline a proof of the following theorem: for a generic measure preserving transformation T, the closed group generated by T is not topologically isomorphic to L^{0}. This result answers a question of Glasner and Weiss. The proof rests on an analysis of unitary representations of L^{0}. 
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Summer term 2021  
22.07.2021 (Do) 13:30 Uhr Online 
Harald Helfgott Universität Göttingen New bounds on growth in SL_{n} Let G be a finite group. For A a set of generators of G, the diameter diam(Γ(G,A)) is the minimal r such that (A U A^{1} U {e})^{r} = G. Define the diameter of G to be the maximum of diam(Γ(G,A)) over all sets of generators A. Babai's conjecture states that, for any finite simple nonabelian group G, the diameter of G is bounded by (logG)^{C} for some absolute constant C. Following work of mine proving the conjecture for G = SL_{2}(F_{p}) and SL_{3}(F_{p}), BreuillardGreenTao and PyberSzabo proved that, for G a finite simple group of Lie type, the diameter of G is bounded by (log G)^{Cn} where C_{n} depends on n. The dependence was not made explicit, but their proofs surely give C_{n} growing faster than exponentially on n (namely, C_{n} = e^{n}^{^O(1)}). We give a proof for G = SL_{n}(F_{p}) giving diam(G)<(log G)^{Cn} with C_{n} polynomial, namely C_{n} = O(n^{4}log(n)). This bound should be compared not just to BGT and PS but also to the bound diam(G)<q^{O(n(log n)²)} (HalasiMarótiPyberQiao, 2019). Our proof is based on an improved escape procedure and on dimensional estimates particular to conjugacy classes and abelian subgroups. 
15.07.2021 (Do) 13:30 Uhr Online 
Manuel Bodirsky Institut für Algebra What do I teach in … Combinatorics? Andreas Thom Institut für Geometrie What do I teach in … Groups and Geometry? 
8.07.2021 (Do) 13:30 Uhr Online 
Mehmet Haluk Sengün University of Sheffield Hecke operators for operator Ktheory Cohomology of arithmetic groups admits the action of a commuting family of endomorphisms, called 'Hecke operators'. These cohomology groups, as 'Hecke modules', play a crucial role in the Langlands program, sitting in the intersection of the theory of automorphic forms, representation theory and differential geometry. In the world of noncommutative geometry, one finds several 'cohomology groups' associated to arithmetic groups; these arise as Kgroups of certain C*algebras. With Bram Mesland (Leiden), we showed that these cohomology groups admit an action of Hecke operators as well. Could these new 'Hecke modules' play a similar role to the ordinary cohomology in the Langlands program? 
1.07.2021 (Do) 13:30 Uhr Online 
Steffen Kionke FernUniversität in Hagen Amenability and profinite completions of finitely generated groups Is it possible to decide whether or not a residually finite group is amenable by looking at its finite quotients only? In general, the answer is negative. In this talk we exhibit an uncountable family of finitely generated counterexamples based on the theory of branch groups. On the other hand, we explain why uniform amenability, a stronger concept introduced in the 70's, can be detected from the finite quotients of residually finite groups. This is based on joint work with Eduard Schesler. 
24.06.2021 (Do) 13:30 Uhr Online 
Holger Kammeyer Karlsruher Institut für Technologie On the profinite rigidity of higher rank lattices If two infinite groups have the same set of finite quotients, are they isomorphic or at least commensurable? This question is particularly intriguing for lattices in simple Lie groups. We show that in most higher rank Lie groups, there exist lattices with the same finite quotients that are not commensurable. But surprisingly, three exceptional Lie groups exhibit profinite rigidity: in the complex groups of type E_{8}, F_{4}, and G_{2}, the set of finite quotients determines the commensurability class of a lattice. Joint work with Steffen Kionke. 
17.06.2021 (Do) 13:30 Uhr Online 
Michael Wibmer Graz University of Technology Solving difference equations in sequences Systems of finite difference equations occur in various models of realworld phenomena. Informally, they can be described as discrete analogs of systems of differential equations. A very simple example of a finite difference equation is a recursion formula, such as the recursion formula defining the Fibonacci sequence. Clearly, a solution to a recursion formula can always be found by iterating the formula. However, when studying systems of general (implicit, nonlinear) finite difference equations, algorithms for deciding the existence of a solution are very hard to come by. In fact, this problem was shown to be decidable only recently by Ovchinnikov, Pogudin and Scanlon. In this talk we will discuss the (un)decidability of some natural computational questions associated with systems of finite difference equations. This is joint work with Thomas Scanlon and Gleb Pogudin. 
10.06.2021 (Do) 13:30 Uhr Online 
Katrin Tent WWU, Münster Simple automorphism groups The automorphism groups of many homogeneous structures (Riemannian symmetric spaces, projective spaces, trees, algebraically closed fields, Urysohn space etc) are abstractly simple groups  or at least are simple after taking an obvious quotient. We present criteria to prove simplicity for a broad range of structures based on the notion of stationary independence. 
6.05.2021 (Do) 13:30 Uhr online 
Christoph Schulze Institute of Geometry Cones of locally nonnegative polynomials 
29.04.2021 (Do) 13:30 Uhr online 
Myriam Mahaman Institute of Geometry What is... a HopfGalois extension of fields? HopfGalois extensions generalize the classical notion of Galois extensions of fields; however, in contrast to the classical notion, a given field extension L/K might have more than one HopfGalois structure on it. In 1987, Greither and Pareigis published a paper on the HopfGalois structures of separable field extensions, in which they show how the classication of those structures reduces to a grouptheoretic problem. Nowadays, this classification problem has grown into its own area of research. In this talk, I will give an introduction to HopfGalois extensions of fields and to the GreitherPareigis theorem. 
22.04.2021 (Do) 13:30 Uhr online 
Nicolas Garrel 
15.04.2021 (Do) 13:30 Uhr online 
Tim Netzer Universität Innsbruck Quantum Magic Squares link The notion of a magic square is familiar to many people, the similar notion of a doubly stochastic matrix at least to many mathematicians. A doubly stochastic matrix can be defined as a square matrix that contains a probability measure in each row and column. The famous Theorem of Birkhoffvon Neumann states that these matrices are all convex combinations of permutation matrices. 
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Winter term 2020/21  
4.3.2021 (Do) 13:30 Uhr online 
Colin Jahel U Lyon Some progress on the unique ergodicity problem link In 2005, Kechris, Pestov and Todorcevic exhibited a correspondence between combinatorial properties of structures and dynamical properties of their automorphism groups. In 2012, Angel, Kechris and Lyons used this correspondence to show the unique ergodicity of all the actions of some subgroups of $S_\infty$. In this talk, I will give an overview of the aforementioned results and discuss recent work generalizing results of Angel, Kechris and Lyons. 
4.2.2021 (Do) 13:30 Uhr online 
Jitendra Bajpai Istitute of Geometry Arithmeticity and Thinness of hypergeometric groups link Password (usually not needed): *U#C2L The monodromy groups of hypergeometric differential equations of type nFn1 are often called hypergeometric groups. These are subgroups of GL_n . Recently, Arithmeticity and Thinness of these groups have caught a lot of attention. In the talk, a gentle introduction and recent progress to the theory of hypergeometric groups will be presented. 
28.1.2021 (Do) 13:30 Uhr online 
Julian Kaspczyk Institute of Algebra A characterization of the groups PSL(n,q) and PSU(n,q) by their 2fusion systems, q odd link Password (usually not needed): *U#C2L The classification of finite simple groups (CFSG) is one of the greatest achievements of modern mathematics. Its proof required thousands of pages in various journals and was developed by more than hundred mathematicians from all over the world. A shorter and more accessible proof of the CFSG would be very valuable. A programme working towards this goal was set up by Aschbacher. The goal of Aschbacher's programme is to obtain a new proof of the CFSG by using fusion systems. Roughly, Aschbacher's programme consists of two steps. The first step is the classification of simple fusion systems over finite $2$groups. In the second step, the first step is used in order to obtain a new proof of the CFSG. A crucial part of Step 2 is to identify finite simple groups from their $2$fusion systems. In this talk, I am going to present some recent progress on Step 2. In particular, I will present the main result of my PhD thesis, which characterizes the finite groups $PSL(n,q)$ and $PSU(n,q)$ by their $2$fusion systems, where $q$ is an odd prime power and $n \ge 2$. 
21.1.2021 (Do) 13:30 Uhr online 
Martin Schneider TU Freiberg Skewamenability of topological groups link with ZIHlogin link without ZIHlogin The talk will revolve around an amenabilitylike property of topological groups, its connections with representation theory and its manifestations in the realm of topological permutation groups. After briefly reviewing some aspects of (classical) amenability for topological groups, I will introduce the concept of skewamenability, which originated in a recent work by Pestov about topological groups of finiteenergy paths and loops. I will give an overview of closure properties of the class of skewamenable topological groups, explain representationtheoretic and dynamical consequences of skewamenability, and discuss some examples. The latter will include topological permutation groups built from Thompson's group F or Monod's group of piecewise projective homeomorphisms of the real line. 
14.1.2021 (Do) 13:30 Uhr online 
Philip Dittmann Institut für Algebra Axiomatisability and definability in finitely generated structures link Password (usually not needed): *U#C2L Given a finitely generated group or ring or field, can it be pinned down (i.e. characterised up to isomorphism) by adding a single axiom (i.e. firstorder sentence) to the group/ring/field axioms? This is a property known as quasifinite axiomatisability. Although it appears unexpected from the perspective of model theory for reasons to be discussed, it has recently been shown to be very common (work of Nies, AschenbrennerKhélifNaziazenoScanlon, D.Pop). Secondly, which sets in a given finitely generated group/ring/field can "explicitly described", i.e. are definable (by a firstorder formula)? This problem turns out to be closely related to the first one, and indeed one can frequently show that "every conceivable" subset is definable in a sense to be made precise. We will have a look at the underpinnings of these results both from mathematical logic (going back to Gödel) and arithmetic (connected to results on Hilbert's 10th Problem). 
7.1.2021 (Do) 13:30 Uhr online 
Arno Fehm Institute of Algebra What is ... a diophantine set? link Password (usually not needed): *U#C2L I will motivate the study of diophantine sets in fields and will discuss various ways to look at them. Then I will survey some results and will try to give an idea of different proof techniques. 
17.12.2020 (Do) 13:30 Uhr online 
Vadim Alekseev Institute of Geometry What is ... an arithmetic group? link Password (usually not needed): *U#C2L Arithmetic groups are fascinating objects which connect the worlds of countable groups, number theory, Lie groups, geometry and even ergodic theory. In this talk I will give a survey of some classical results about arithmetic groups, illustrating some of these connections, and  if time permits  explain how a question from a seemingly faraway field of operator algebras can get one to study arithmetic groups more profoundly. 
10.12.2020 (Do) 13:30 Uhr online 
Manuel Bodirsky Institute of Algebra Ramsey Expansions and Extreme Amenability link This talk is about classes of finite structures that are closed under substructures, have the joint embedding property, and have the socalled Ramsey property, which is a strong combinatorial property generalizing Ramsey's theorem. I will present the connection between Ramsey classes and extreme amenability of the automorphism group of the respective Fraisselimits. An important open problem in the field is the *Ramsey expansion conjecture*: does every homogeneous structure with a finite relational signature have a homogeneous finitesignature expansion whose age is Ramsey? I will also present a recent transfer result for the existence of Ramsey expansions by Mottet and Pinsker. 
3.12.2020 (Do) 13:30 Uhr online 
Andreas Thom Institute of Geometry Questions about word maps on groups link 
19.11.2020 (Do) 13:30 Uhr online 
Ellen Henke Institute of Algebra Topics and Methods in Finite Group Theory link Password (usually not needed): M@?22m In the talk I will introduce some important methods from finite group theory, which are used in the proof of the classification of finite simple groups but play also a role in other contexts. I will moreover briefly summarize how some aspects of finite group theory generalize to the theory of certain other algebraic structures called fusion systems and how one can hope to achieve a simplified proof of the classification of finite simple groups through this theory. 
12.11.2020 (Do) 13:30 Uhr online 
Mario Kummer Instiitute of Geometry Some results and problems in real algebraic geometry link A widespread principle in real algebraic geometry is to find and use algebraic certificates for geometric statements. This covers for example writing a globally nonnegative polynomial as a sum of squares or expressing a polynomial with only real zeros as the minimal polynomial of a symmetric matrix. In the first part of the talk I will survey some classical results and open problems in this direction. Then I will present a quite general result from a joint work with Christoph Hanselka that implies several of the aforementioned results. 
5.11.2020 (Do) 13:30 Uhr online 
Uli Krähmer Institute of Geometry What is an operad? link 
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Summer term 2020  
  
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Winter term 2019/20  
30.1.2020 (Do) 13:30 Uhr WIL/B321 
Dirk Kreimer HU Berlin Feynman Graphs: From Combinatorics to Algebra and Geometry Quantum field theory is studied with the help of Feynman graphs. We introduce the Hopf algebra structure underlying them and discuss how it raises interesting problems in combinatorics, algebra and geometry. 
9.1.2020 (Do) 13:30 Uhr WIL/B321 
Maja Pech U Novi Sad All that homogeneity One of the most fascinating phenomena in model theory is homogeneity. In this talk I will present and discuss different notions of homogeneity with special emphasis to the youngest one  polymorphism homogeneity. 
19.12.2019 (Do) 13:30 Uhr WIL/B321 
Maxim Gheysens Institut für Geometrie A Group from Beyond Infinity The order topology on the first uncountable ordinal yields a fascinating topological space, well known for featuring "pathological" phenomena, such as sequential compactness without compactness, or a StoneCech compactification reduced to Alexandrov's onepoint compactification. In this talk, we introduce its homeomorphism group, which also comes with its own niceties. For instance, it is an amenable topological group which is strongly allergic to any idea of distance: all its continuous isometric actions have bounded orbits and all its continuous morphisms to metrisable groups are trivial. 
5.12.2019 (Do) 13:30 Uhr WIL/B321 
Andrew Zucker U Paris Weak amalgamation versus amalgamation Fraïssé classes are those classes F of finite structures satisfying the Hereditary Property (HP), the Joint Embedding Property (JEP), and the Amalgamation Property (AP). The JEP allows one to build some countably infinite structure K whose age (the collection of finite structures which embed into K) is the class F that we started with. If AP also holds, then there is a canonical such K which we denote K_F, the Fraïssé limit of the class. One can interpret this fact dynamically by considering the action of the group S_\infty on the space X_F of countable structures whose age is contained in F. One can give X_F a natural Polish topology, and the theorem of Fraisse is precisely the fact that this action has a comeager orbit. However, Ivanov, and later KechrisRosendal, isolated a strictly weaker property, the Weak Amalgamation Property (WAP), which also guarantees that the space X_F has a comeager orbit. This gives rise to a natural question: can we detect the difference between AP and WAP from the dynamical point of view? This talk will discuss an affirmative answer, linking these amalgamation properties to the dynamical notion of a highly proximal extension. 
28.11.2019 (Do) 13:30 Uhr WIL/B321 
Pablo Cubides Kovacsics Inst. f. Algebra Berkovich analytification of algebraic curves and definability Let k be a complete rank 1 algebraically closed nontrivially valued field. After recalling the construction of the analytification X^an of an algebraic variety X over k in the sense of Berkovich, we will show how, in the case of curves, one can have a definable version of this construction. More precisely, when X is a curve, we will show how to functorially associate to X^an a definable set X^S in a certain fist order language. If time permits, we will show how this definable version allows us to recover a result of Temkin about the "radiality" of the set of points of a given fixed multiplicity with respect to the analytification of a morphism between curves. This is a joint work with Jérôme Poineau. 
21.11.2019 (Do) 13:30 Uhr WIL/B321 
Aleksandra Kwiatkowska U Wroclaw Simplicity of the automorphism groups of order and tournament expansions of structures We prove that the automorphism groups of order and tournament expansions of Fraïssé limits of free, transitive and nontrivial amalgamation classes, in particular, the automorphism group of the ordered random graph, are simple. We obtain similar results for the bounded countable Urysohn metric space. This is joint work with Filippo Calderoni and Katrin Tent. 
14.11.2019 (Do) 13:30 Uhr WIL/B321 
Oleg Bogopolski U Düsseldorf Equations in acylindrically hyperbolic groups. Algebraic, verbal and existential closedness of subgroups of groups. 
24.10.2019 (Do) 13:30 Uhr WIL/B321 
Ezra Waxman TU Dresden Hecke Characters and Angles of Gaussian Primes A Gaussian prime is a prime element in the ring of Gaussian integers Z[i]. As the Gaussian integers lie on the plane, interesting questions about their geometric properties can be asked which have no classical analogue among the ordinary primes. Hecke proved that the Gaussian primes are equidistributed across sectors of the complex plane by making use of Hecke characters and their associated Lfunctions. In this talk I will present a refined conjecture for the variance of Gaussian primes across sectors, and introduce a function field analogue to the question of angular distribution across sectors. 
17.10.2019 (Do) 13:30 Uhr WIL/B321 
Arkady Leiderman Ben Gurion University of the Negev Embeddings of free (abelian) topological groups 
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Summer term 2019  
11.7.2019 (Do) 13:30 Uhr WIL/B321 
Gregor Schaumann U Würzburg Module categories and oriented 3d TFTs Tensor categories have a farreaching interpretation as quantum symmetries of 3dimensional topological field theory (3d TFT). This leads to a correspondence between algebraic structures related to tensor categories and TFT. In this talk I will discuss instances of this correspondence for pivotal structures on tensor categories, module categories, and defects in oriented TFTs. 
27.6.2019 (Do) 13:30 Uhr WIL/B321 
Lars Louder London Coherence for one relator groups with torsion 
20.6.2019 (Do) 13:30 Uhr WIL/B321 
Istvan Heckenberger Uni Marburg From PBW deformations to matrix algebras 
23.05.2019 (Do) 13:30 Uhr WIL/B321 
Michal Marcinkowski Universität Wroclaw Bounded cohomology of transformation groups Let M be a finitevolume Riemannian manifold and let \mu be the measure induced by the volume form. Denote by G_M the group of all \mupreserving homeomorphisms of M isotopic to the identity. We show how to construct classes in the bounded cohomology of G_M. As an application we show that, under certain conditions on \pi_1(M), the third bounded cohomology of G_M (and some of its subgroups) is highly nontrivial. This is a joint work with Michael Brandenbursky. 
9.5.2018 (Do) 13:30 Uhr WIL/B321 
Ulrich Krähmer Institut für Geometrie What is ... noncommutative geometry? 
02.05.2019 (Do) 13:30 Uhr WIL/B321 
Jakub Gismatullin Uni Wroclaw Simplicity and amenability of metric ultraproducts of groups 
25.4.2019 (Do) 13:30 Uhr WIL/B321 
Manuel Bodirsky Institut für Algebra What is ... an oligomorphic permutation group? 
04.04.2019 (Do) 13:30 Uhr WIL/B321 
Adam Skalski Uni Warschau On C*completions of discrete (quantum) group rings To any discrete group one can associate its complex group ring, which is a unital *algebra. We will investigate when this algebra admits a unique C*completion (in other words, all its embeddings into a *algebra of bounded operators on a Hilbert space yield the same norm). Grigorchuk, Musat and Rordam observed this happens when the group in question is locally finite and asked if this is the only case. We will discuss what is known about their question and show that in the quantum world, i.e. when we look at C*completions of Hopf*algebras associated to compact quantum groups, the answer is negative. Based on the joint work with Martijn Caspers. 
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Winter term 2018/19  
24.01.2019 (Do) 13:30 Uhr WIL/B321 
Andreas Thom TU Dresden, Institut für Geometrie What is ... representation theory? 
29.11.2018 (Do) 13:30 Uhr WIL/B321 
Martin Schneider TU Dresden, Institut für Algebra Concentration and dissipation in topological groups 
22.11.2028 (Do) 13:30 Uhr WIL/B321 
Christoph Schweigert Uni Hamburg Hochschild cohomology and the modular group 
8.11.2018 (Do) 13:15 Uhr WIL/B321 
Franziska Jahnke WWU Münster Henselian fields in Shelah's classification theory In contemporary model theory, firstorder theories are classified by the infinite combinatorial patterns they encode. A fundamental theme is whether these purely combinatorial `dividing lines' correspond to natural algebraic properties when applied to fields. One particularly interesting combinatorial pattern is when a theory encodes a bipartite random graph; if not, the theory is called NIP. A conjecture by Shelah states that every infinite NIP field is either algebraically closed, real closed, or `like the padic numbers'. We will discuss this conjecture and its consequences, and present some evidence for it. The talk contains joint work with Sylvy Anscombe, Yatir Halevi and Assaf Hasson. 
25.10.2018 (Do) 13:15 Uhr WIL/B321 
Pablo Cubides Kovacsics Universite de Caen Polynomially bounded valued fields A theorem of Chris Miller states that given an ominimal expansion R of the real field R, either R is polynomially bounded or the exponential function is definable in R. The aim in this talk is to show that over nonarchimedean fields we have a very different behavior: all definable functions in "tame" expansions of Qp and Cp are polynomially bounded. A brief introduction to both ominimality and their nonarchimedean analogues will be given. No prior knowledge of model theory will be needed. This is a joint work with Francoise Delon. 
18.10.2018 (Do) 13:15 Uhr WIL/B321 
Bruno Duchesne Université de Lorraine Groups acting on dendrites Roughly speaking, a dendrite is a compact topological tree. More precisely, a dendrite is a connected compact metrizable space that is locally connected and such that any two points are joined by a unique arc. We will be interested in groups acting on dendrites by homeomorphisms. We will see obstructions to have interesting such actions. On the other side, we will see dendrites with a very interesting homeomorphism group. These groups also appear to be the automorphism groups of some countable structures. 
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Summer term 2018  
19.7.2018 (Do) 13:15 Uhr WIL/B321 
Philip Dittmann U Oxford Diophantine Predicates over the Rational Numbers A set of tuples of rational numbers is called diophantine if it is the projection of the zero set of a polynomial in some number of variables. Such sets are of interest in algebraic geometry and logic, where they are exactly the sets definable by existential firstorder formulae. In this talk I will present some recent diophantine definitions; notably, I will sketch a proof that irreducibility of a polynomial over the rationals is a diophantine condition on its coefficients, and give a geometric application. It follows for instance that the set of nonsquares is unexpectedly diophantine. The proof uses class field theory and central simple algebras, with some grouptheoretic input. 
12.7.2018 (Do) 13:15 Uhr WIL/B321 
Ehud Meir Hamburg symmetric monoidal categories, invariant theory and Hopf algrebas. In this talk I will explain a general approach for the study of algebraic structures using symmetric monoidal categories and geometric invariant theory. I will explain a construction of a symmetric monoidal category which is related to generic central simple algebras on the one hand, and to results of Deligne on the other hand. I will then concentrate especially on algebraic structures such as Hopf algebras and HopfGalois objects, and explain what new results can be proven for these structures using the symmetric monoidal categories approach. 
28.6.2018 (Do) 13:15 Uhr WIL/B321 
Clara Löh U Regensburg Simplicial volume of onerelator groups The size of singular homology classes can be measured in terms of the $\ell^1$seminorm. Onerelator groups have a canonical homology class in degree 2; in analogy with the case of manifolds, we define the simplicial volume of onerelator groups as the $\ell^1$seminorm of this class. In this talk, we will discuss the relation between simplicial volume of onerelator groups and stable commutator length of the relator. Moreover, we will give an application of these calculations to simplicial volume of manifolds. This is joint work with Nicolaus Heuer (Oxford). 
21.6.2018 (Do) 13:15 Uhr WIL/B321 
Sylvy Anscombe U of Central Lancashire (Preston) Generalised measurable homogeneous structures The notion of a `measurable structure' was introduced by Macpherson and Steinhorn, motivated by the work on pseudofinite fields by Chatzidakis, van den Dries, and Macintyre. In joint work between the speaker, Macpherson, Steinhorn, and Wolf we propose the broader framework of `generalised measurable structures'. Both the new definition and the original definition abstract the idea of assigning a `measure' and a `dimension' to sets definable in a given structure. Originally, measures were positive real numbers and dimensions were natural numbers; but in the newer framework we combine measure and dimension into one element of a more general algebraic object: a measuring semiring. Consequently, there is a much richer zoo of examples and we have more exotic model theory. In this talk I will give a fresh introduction to these notions and discuss a range of key motivating examples, including pseudofinite fields, the random graph, and vector spaces with bilinear forms. I will also discuss more recent (and ongoing) work with the generic trianglefree graph and Urysohn space, which gets into more interesting combinatorial territory. 
14.6.2018 (Do) 13:15 Uhr WIL/B321 
Jakob Schneider TU Dresden, Institut für Geometrie Word images are dense 
7.6.2018 (Do) 13:15 Uhr WIL/B321 
Rémi Coulon CNRS  Université de Rennes 1 Growth gap in hyperbolic groups and amenability (joint work with Françoise Dal'Bo and Andrea Sambusetti) Given a finitely generated group G acting properly on a metric space X, the exponential growth rate of G with respect to X measures "how big" the orbits of G are. If H is a subgroup of G, its exponential growth rate is bounded above by the one of G. In this work we are interested in the following question: what can we say if H and G have the same exponential growth rate? This problem has both a combinatorial and a geometric origin. For the combinatorial part, Grigorchuck and Cohen proved in the 80's that a group Q = F/N (written as a quotient of the free group) is amenable if and only if N and F have the same exponential growth rate (with respect to the word length). About the same time, Brooks gave a geometric interpretation of Kesten's amenability criterion in terms of the bottom of the spectrum of the Laplace operator. He obtained in this way a statement analogue to the one of Grigorchuck and Cohen for the deck automorphism group of the cover of certain compact hyperbolic manifolds. These works initiated many fruitful developments in geometry, dynamics and group theory. We focus here one the class of Gromov hyperbolic groups and propose a framework that encompasses both the combinatorial and the geometric point of view. More precisely we prove that if G is a hyperbolic group acting properly cocompactly on a metric space X which is either a Cayley graph of G or a CAT(1) space, then the growth rate of H and G coincide if and only if H is coamenable in G. In addition if G has Kazhdan property (T) we prove that there is a gap between the growth rate of G and the one of its infinite index subgroups. 
31.5.2018 (Do) 13:15 Uhr WIL/B321 
Martin Widmer Royal Holloway, University of London Heights  a survey: from dynamics to (un)decidability A height is a realvalued function that measures the arithmetic complexity of an algebraically defined object such as an algebraic number. The concept was introduced and developed by Weil, Siegel and Northcott in the first half of the last century, and since then it has played a major role in number theory. In this talk I will explain Northcott's original motivation, describe the construction and basic properties of the socalled Weil height, and discuss more recent applications of heights, including to (un)decidability questions about certain subfields of the algebraic numbers. This talk is aimed at a general audience of mathematicians. 
17.5.2018 (Do) 13:15 Uhr WIL/B321 
Uli Krähmer TU Dresden Clones form comonoids The endomorphism operad of a cocommutative comonoid in an arbitrary monoidal category is shown to be a clone. An example associated to coquasitriangular Hopf algebras is discussed. 
3.5.2018 (Do) 13:15 Uhr WIL/C133 
Lucia Rotheray TU Dresden Trees, quivers, bigraphs: combinatorial bialgebras from monoidal Möbius categories 
26.4.2018 (Do) 13:15 Uhr WIL/B321 
Peter P. Palfy Renyi Institute, Budapest Groups of finite abelian width There are various ways to measure how abelian a group is. A few examples: the class of a nilpotent group; the probability that two random elements commute; the order of the commutator subgroup; etc. Our new concept is the abelian width, that is the smallest number of factors in a decomposition of the group into a product of abelian subgroups. If no such decomposition exists, then we say that the group has infinite abelian width. For example, the group of finitary permutations of an infinite set has infinite abelian width. However, quite surprisingly, the full symmetric group on an infinite set has finite abelian width. With the exception of the alternating groups, all finite simple groups have bounded abelian width. This is a joint project with M. Abért, A. Maróti, L. Pyber, and B. Szegedy. 
19.4.2018 (Do) 13:15 Uhr WIL/B321 
Manuel Bodirsky TU Dresden Semilinear relations preserved by the median operation 
12.4.2018 (Do) 13:15 Uhr WIL/B321 
Andreas Thom TU Dresden Stability and Invariant Random Subgroups 
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Winter term 2017/18  
1.2.2018 (Do) 13:15 Uhr WIL/C133 
François Legrand TU Dresden, Inst. f. Algebra On a Weak version of the Inverse Galois Problem The Inverse Galois Problem over a field k asks whether every finite group occurs as the Galois group of a finite Galois extension of k. The original problem of Hilbert and Noether is the case k=Q and, despite many efforts in the last decades, remains widely open. In 1980, Fried proved by elementary techniques that every finite group occurs as the automorphism group of a finite extension of Q (not necessarily Galois). This motivates the study of a Weak version of the Inverse Galois Problem where the notion of "Galois group" is replaced by that of "automorphism group". In this talk, we will discuss this variant over more general fields and, using (inverse) Galois theoretic and group theoretic tools, reveal the gap between it and the usual Inverse Galois Problem. This is based on a joint work with Elad Paran and a work in progress with Bruno Deschamps. 
18.01.2018 (Do) 13:15 Uhr WIL/C 133 
FranzViktor Kuhlmann University of Szczecin Ball spaces  generic fixed point theorems for contracting functions In Fixed Point Theory there are many well known theorems that work with functions that are (explicitly or implicitly) contracting. Just to mention a few areas of mathematics where fixed point theorems play a role: metric spaces (Banach Fixed Point Theorem), ultrametric spaces, topological spaces, partially ordered sets, lattices (KnasterTarski Fixed Point Theorem), logic programming. The question arises: what is the common denominator of the proofs of such theorems, and of the conditions that have to be met by the functions and the spaces on which they live? I will report on an approach that reduces the structure on the spaces to the bare minimum that is necessary to formulate the conditions on the spaces. In analogy to the ultrametric world, we call this condition "spherical completeness": every chain of distinguished subsets, called "balls", must have a nonempty intersection. I will show how this translates into, e.g., completeness for metric and compactness for topological spaces. This approach allows us to prove generic fixed point theorems (with proofs based on Zorn's Lemma) which then can be specialized to the various areas of application. Moreover, it allows us to transfer ideas and notions from one area to another. For instance, the KnasterTarski Theorem can be transferred to topological and ultrametric spaces, and there is also a generic form of the Tychonoff Theorem, which in turn can be specialized e.g. to ultrametric spaces. The metric spaces used to be the misfits in the big picture, because in contrast to ultrametric balls the metric balls do not behave well and one is still better off working with Cauchy sequences instead. However, recently we found that new insight into the famous CaristiKirk Theorem changes the picture completely. There are alternatives to the metric balls which fit perfectly into the framework of our ball spaces. This is joint work with Katarzyna Kuhlmann. 
14.12.2017 (Do) 13:15 Uhr WIL/C 133 
Andreas Thom TU Dresden, Institut für Geometrie Stability of asymptotic representations, cohomology vanishing, and nonapproximable group 
07.12.2017 (Do) 13:15 Uhr WIL/C133 
Tobias Fritz MPIMIS, Leipzig On the decidability of noncommutative sums of squares, with applications to Connes' embedding problem and quantum logic Due to Positivstellensätze, sums of squares play a fundamental role in real algebraic geometry. While this remains true in the noncommutative case, the noncommutativity makes the problem generally undecidable: there is no algorithm to decide whether a given noncommutative polynomial can be approximated by sums of squares. I will explain why this is the case, how it implies the undecidability of quantum logic, and how it relates to Connes' embedding problem. Based on arXiv:1207.0975 and arXiv:1607.05870. 
30.11.2017 (Do) 13:15 Uhr WIL/C133 
Gabriella Böhm Wigner Research Centre for Physics of the Hungarian Academy of Sciences, Budapest A unified treatment of quantum symmetries Symmetries in various situations are described classically by groups. In the last decades, however, many indications lead to the appearance of more general symmetry structures, and many (interrelated) competing notions have been proposed. In the talk we will survey some of these socalled `quantum’ symmetries. As a highlight, we will illustrate how these apparently different algebraic structures can be seen as instances of the unifying notion of Hopf monad in a monoidal bicategory. 
23.11.2017 (Do) 13:15 Uhr WIL/C133 
Lukas Pottmeyer U DuisburgEssen Small points and free abelian groups The height of an algebraic number can be seen as a measure for the arithmetic complexity of the algebraic number. For any algebraic extension $F$ of the rationals, the height induces a norm on the group $F^*/Tors(F^*)$  the torsion points in $F^*$ are precisely the roots of unity in $F$. Using some group theory it follows that $F^*/Tors(F^*)$ is free abelian if there are no points in $F$ of arbitrarily small positive height. In this talk we prove that the converse is not true; i.e. there are fields $F$ such that $F^*/Tors(F^*)$ is free abelian, but there are points of arbitrarily small positive height in $F$. We conclude by giving some (weak) group theoretical support for a widely open arithmetical conjecture due to G. Rémond. Most of this is joint work with R. Grizzard and P. Habegger. 
16.11.2017 (Do) 13:15 Uhr WIL/C133 
Andrei Krokhin U Durham The complexity of valued constraint satisfaction problems The Valued Constraint Satisfaction Problem (VCSP) is a wellknown combinatorial problem. An instance of VCSP is given by a finite set of variables, a finite domain of labels for the variables, and a sum of functions, each function depending on a subset of the variables. Each function can take finite rational values specifying costs of assignments of labels to its variables or the infinite value, which indicates an infeasible assignment. The goal is to find an assignment of labels to the variables that minimizes the sum. The case when all functions takeonly values 0 and infinity corresponds to the standard CSP. We study (assuming that P\neq NP) how the computational complexity of VCSP depends on the set of functions allowed in the instances, the socalled constraint language. Helped greatly by algebra, massive progress has been made in the last three years on this complexity classification question, and our work gives, in a way, the final answer to it, modulo the complexity of CSPs. This is joint work with Vladimir Kolmogorov and Michal Rolinek (both from IST Austria). 
2.11.2017 (Do) 13:15 Uhr WIL/C133 
Martin Hils U Münster Imaginärenklassifikation in separabel abgeschlossenen bewerteten Körpern 
26.10.2017 (Do) 13:15 Uhr WIL/C133 
Jan Hladky TU Dresden Relating the cutdistance and weak* convergence for graphons Around 2004, Borgs, Chayes, Lovasz, Sos, Szegedy, Vesztergombi came up with limit objects, socalled graphons, that can be associated to sequences of graphs. This has subsequently led to a number of breakthrough applications in extremal graph theory and random graph theory. All these results rely on the key fact that the space of graphons equipped with the socalled cutdistance is compact. In the talk I will present a new view on the cutdistance, which in particular gives an alternative proof of compactness. The talk will be selfcontained. This is based on joint work with Dolezal [arXiv:1705.09160] and further extensions with Dolezal, Grebik, Noel, Piguet, Rocha, Rozhon, Saumell. 
19.10.2017 (Do) 13:15 Uhr WIL/C133 
Jakub Oprsal TU Dresden Infinite algebras with few subalgebras of powers For a finite algebra, there can be up to doubly exponentially many in $n$ subalgebras of the $n$th power. It is known that if this is not the case, the algebra has few subpowers, i.e., there is a polynomial $p$ such that there are at most $2^{p(n)}$ subalgebras of the $n$power. All finite algebras having this property have been characterized in 2009 by Berman, Idziak, Markovic, McKenzie, Valeriote, and Willard. In the talk, we will focus on infinite algebras with few subpowers; in particular we require that we have a finite number of subalgebras of powers. These algebras seems to be much rarer than their finite counterparts. We will give a few examples, and describe how the clasification of the finite algebras generalize to the infinite, and in particular to algebras that are obtained by taking polymorphisms of countable structures. 
12.10.2017 (Do) 13:15 Uhr WIL/C133 
Arno Fehm TU Dresden Elementary equivalence of profinite groups I will discuss some results and questions concerning elementary equivalence and isomorphisms of profinite groups. 
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Summer term 2017  
29.6.2017 (Do) 13:15 Uhr WIL/C133 
Sylvy Anscombe U of Central Lancashire, Preston, UK Multidimensional asymptotic classes and generalised measurable structures Macpherson and Steinhorn introduced `1dimensional asymptotic classes' of finite structures, which are those classes that satisfy an asymptotic counting condition on definable sets, which is modelled on Chatzidakis, vandenDries, and Macintyre's work on finite fields. This notion gives insights into the model theory of such classes: for example their infinite ultraproducts are supersimple of finite rank. In this talk I will introduce `multidimensional asymptotic classes', which broadens the original notion to allow more exotic examples, such as finitedimensional vectors spaces over finite fields, equipped with a bilinear form. I will also define the notion of `generalised measurable structures', which are infinite structures satisfying an analogous condition on definable sets. I will show that free homogeneous structures are generalised measurable; and that certain homogeneous structures are not elementarily equivalent to ultraproducts of classes satisfying an *exact* version of the asymptotic condition. This is joint work with Dugald Macpherson, Charles Steinhorn, and Daniel Wolf. 
22.6.2017 (Do) 13:15 Uhr WIL/C133 
Oleg Verbitsky HU Berlin The many facets of logic with two variables Firstorder logic with two variables has surprising connections to seemingly distant concepts of discrete mathematics. For example, two graphs are indistinguishable by sentences with two firstorder variables and counting quantifiers if and only if they are fractionally isomorphic and if and only if their universal covers are isomorphic. Due to these connections, 2variable logic provides a convenient framework for analysis of various problems in theory of computing. We will survey these applications with a focus on the graph isomorphism problem. In particular, we will discuss the following result and its algorithmic consequences: If a graph is definable in 2variable logic with counting quantifiers, then the polytope of the fractional automorphisms of this graph is integral, i.e., all extreme points of this polytope have integer coordinates (or, in other terms, every definable graph is compact in the sense of Tinhofer). The talk is based on joint work with A.Krebs, V.Arvind, J.Köbler, and G.Rattan. 
15.6.2017 (Do) 13:15 Uhr WIL/C133 
Alejandra Garrido Uni Düsseldorf Primitive groups of intermediate word growth 
1.6.2017 (Do) 13:15 Uhr WIL/C133 
Ulrich Krähmer TU Dresden Cyclic homology arising from adjunctions This will be a talk on joint work with Niels Kowalzig and Paul Slevin in which I'll explain how distributive laws between (co)monads lead to cyclic homology theories. 
18.5.2017 (Do) 13:15 Uhr WIL/C133 
Martin Schneider TU Dresden Topological groups of measurable maps 
11.5.2017 (Do) 13:15 Uhr WIL/C133 
Andres Aranda U Calgary Ramsey properties of metrically homogeneous graphs Homogeneous structures are countably infinite structures that satisfy the strong symmetry condition of having every isomorphism between finite substructures induced by an automorphism. Gregory Cherlin has produced a classification of metrically homogeneous graphs, conjectured to be complete. It is known that the class of finite structures embeddable in a homogeneous structure can often be extended to a class with the Ramsey property; we present a recent approach to proving the Ramsey and other related properties (EPPA, existence of a stationary independence relation) that can be applied to Cherlin's catalogue and has some potential for more general application. 
4.5.2017 (Do) 13:15 Uhr WIL/C133 
Itay Kaplan Hebräische Universität Jerusalem On dense subgroups of permutation groups I will present a criterion that ensures that Aut(M) has a 2generated dense subgroup when M is a countable structure (which holds in many natural examples), and then show how expanding an omega categorical structure might help in getting a finitely generated dense subgroup. This is joint work with Pierre Simon. 
27.4.2017 (Do) 13:15 Uhr WIL/C133 
Jakob Schneider TU Dresden Metric approximation of groups by finite groups Sofic groups are precisely the groups which can be approximated by finite symmetric groups with normalized Hamming metric. It is an open question whether nonsofic groups exist. In the first part of this talk we define the concepts of Capproximable abstract and topological groups for a class C of finite groups, as a generalization of sofic and weakly sofic groups, and present examples of such groups. In the second part we give examples of groups which cannot be approximated by certain classes of finite groups, varying the above question. At first we discuss the question raised by Glebsky whether all abstract groups are approximable by finite solvable groups. Finally, referring to questions of Doucha and Zilber, we turn to the approximability of Lie groups by finite groups, considering two different kinds of approximation. All results we present will be consequences of theorems on commutators and generators in finite groups by Nikolov and Segal. This is joint work with A. Thom and N. Nikolov. 
20.4.2017 (Do) 13:15 Uhr WIL/C133 
Tim Netzer U Innsbruck Operator Systems and Spectrahedra Spectrahedra are the feasible sets of semidefinite programming, and important objects in convex algebraic geometry. Many of its properties can only be fully understood by considering their free versions, i.e. adding matrix levels to the usual setup. In this way one obtains a special class of operator systems, namely those that admit a finitedimensional realization. We thus examine abstract operator systems, and their concrete realizations. We give a characterization of finitedimensional realizability, and apply it to systems constructed from convex cones at scalar level. In this way we obtain interesting results about classical spectrahedra. For example, we can completely classify the cases where an approach of BenTal and Nemirovski for detecting inclusion is exact. We can also deduce results about the number of different matrix inequalities defining the same spectrahedron. The talk is based on joint results with T. Fritz and A. Thom. 
06.04.2017 (Do) 13:15 Uhr WIL C133 
Barnaby Martin Durham University Generating sets for powers of finite algebras and the complexity of Quantified Constraints. Let A be a finitedomain algebra. We can associate a function f_A:N>N, giving the cardinality of the minimal generating sets of the sequence A, A^2, A^3, ... as f(1), f(2), f(3), ..., respectively. We may say A has the gGP if f(m) < g(m) for all m. The question then arises as to the growth rate of f and specifically regarding the behaviours constant, logarithmic, linear, polynomial and exponential. Wiegold proved that if A is a finite semigroup then f_A is either linear or exponential, with the former prevailing precisely when A is a monoid. This dichotomy classification may be seen as a gap theorem because no growth rates intermediate between linear and exponential may occur. We say A enjoys the polynomially generated powers property (PGP) if there exists a polynomial p so that f_A=O(p) and the exponentially generated powers property (EGP) if there exists a constant b so that f_A=Omega(g) where g(i)=b^i. A new result by Dmitriy Zhuk states that this gap between PGP and EGP holds for all finitedomain algebras. Furthermore, the PGP cases obey a certain property called switchability. This "switchability" was introduced in the context of the Quantified Constraint Satisfaction Problem (QCSP) as something more general than "collapsibility", also introduced in the context of the QCSP. We study the relationship between switchability and collapsibility and use the PGPEGP Gap Theorem of Zhuk to give a full dichotomy classification for the computational complexity of QCSPs, where the PGP cases correspond to QCSPs in NP while the EGP cases correspond to QCSPs that are coNPhard. 
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Wintersemester 2016/17  
15.12.2016 (Do) 13:15 Uhr WIL C133 
Dr. Vadim Alekseev TU Dresden Operator algebras, discrete groups and finite approximations 
17.11.2016 (Do) 13:15 Uhr WIL C133 
Prof. Dr. Eamonn O'Brien University of Auckland, New Zealand Effective algorithms for matrix groups 
10.11.2016 (Do) 13:15 Uhr WIL C 133 
Dr. Wied Pakusa RWTH Aachen The search for a logic capturing polynomial time (Abstract) 
03.11.2016 (Do) 13:15 Uhr WIL C 133 
Gabor Kun MTA Alfred Renyi Institute of Mathematics, Budapest, Ungarn Sofic groups A group is called sofic if any of its labeled Cayley graphs admits a local approximation by finite labeled graphs. Sofic groups were introduced by Gromov (the word sofic was coined by Weiss). Many classical conjectures are proved for sofic groups: Gottschalk’s conjecture, Kaplansky’s direct finiteness conjecture and Connes’ embedding conjecture. It is not known if every group is sofic. Sofic groups and related notions have attracted a great attention in many fields from algebra to logic and graph theory. I will explain the basics. 
27.10.2016 (Do) 13:15 Uhr WIL C 133 
Szymon Torunczyk U Warschau Entropy bounds for conjunctive queries I will talk about a problem emerging from database theory, concerning bounding the worstcase size of a result of a conjunctive query. In the basic form, this problem has been solved by Atserias, Grohe, Marx in '13 using entropy. I will present yet another proof of their result using Shannon's information inequalities, and discuss the relationship with several inequalities in geometry, e.g., the LoomisWhitney inequality and BollobasThomason inequality and Friedgut's inequality. The result can be also stated in terms of bounds concerning finite groups, using a connection between entropy and groups first discovered by Zhang and Yeung in '98. I will also briefly discuss an open problem concerning a generalization obtained by allowing functional dependencies. 
20.10.2016 (Do) 13:15 Uhr WIL C 133 
Julius Jonusas U St. Andrews, UK Universal words and sequences Given a group, I am particularly interested in finding (preferably minimal) generating set of the group. However, every generating set of an uncountable group must be of the same cardinality as the group itself, in which case generating sets proved very little new information about the structure of the group. In this talk, I will introduce notions of universal words and universal sequences for groups and semigroups, and then show how universal sequences can be thought as an extension of the notion of generation. 
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Summer term 2016
16.6.2016 (Do) 13:15 Uhr WIL C 133 
Dr. Henry Bradford U Göttingen Expansion, Random Walks and Sieving in SL2(Fp [t]) 
09.6.2016 (Do) 13:15 Uhr WIL C 133 
Dr. Martin FinnSell U Wien Semigroups in coarse geometry and operator algebras 
02.6.2016 (Do) 13:15 Uhr WIL C 133 
Tamás Waldhauser Bolyai Institute, Szeged, Hungary Polycyclic monoids and Cuntz algebras via strange number systems 
12.5.2016 (Do) 13:15 Uhr WIL C 133 
Dr. Alessandro Carderi TU Dresden An exotic group as limit of finite special linear groups 
28.4.2016 (Do) 13:15 Uhr WIL C 133 
Dr. Benedikt Stufler Mathematisches Institut der LMU München Limits of random treelike combinatorial structures 
21.4.2016 (Do) 13:15 Uhr WIL C 133 
Dr. Johann Thapper Université ParisEst, France Fractional polymorphisms and LP relaxations of VCSPs 
14.4.2016 (Do) 13:15 Uhr WIL C 133 
Prof. Dr. Miklós Abért MTA Alfréd Rényi Institute of Mathematics, Budapest, Hungary Entropy and graph convergence 
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Winter term 2015/16
21.1.2016 (Do) 13:15 Uhr WIL C 133 
Manuel Bodirsky TU Dresden Treelike Homogeneous Structures, their reducts, automorphism groups, and polymorphism clones 
7.1.2016 (Do) 13:15 Uhr WIL C 133 
Marcello Mamino TU Dresden Maxclosed semilinear constraints 
17.12.2015 (Do) 13:15 Uhr WIL C 133 
Jérémie Brieussel Université de Montpellier Speed of random walks, isoperimetry and compression on finitely generated groups 
10.12.2015 (Do) 13:15 Uhr WIL C 133 
Michael Pinsker Czech Academy of Sciences, Prague Uniform Birkhoff 
3.12.2015 (Do) 13:15 Uhr WIL C 133 
Katrin Tent U Münster Kurze Beschreibungen endlicher Gruppen 
26.11.2015 (Do) 13:15 Uhr WIL C 133 
Sean Eberhard MMath (Cantab) Oxford University Invariable generation of the symmetric group 
19.11.2015 (Do) 13:15 Uhr WIL C 133 
Andreas Thom TU Dresden Quasiisometry and topological orbitequivalence 
5.11.2015 (Do) 13:15 Uhr WIL C 133 
Hanno Lefmann TU Chemnitz Infinite partition regular linear systems of equations 
29.10.2015 (Do) 13:15 Uhr WIL C 133 
Damain Osajda U Wroclawski and IMPAN Embedding expanders in groups and applications 
15.10.2015 (Do) 13:15 Uhr WIL C 133 
Agelos Georgakopoulos U Warwick Group Walk Random Graphs I will discuss a construction of finite 'geometric' random graphs motivated by the study of random walks on infinite groups. This construction has connections to other topics, including the Poisson boundary and Sznitman's random interlacements (which I will try to introduce in a gentle way). 
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Summer term 2015
16.7.2015 (Do) 13:15 Uhr WIL C 133 
Phillip Wesolek UC Louvain Elementary amenable groups and the space of marked groups The space of marked groups is a compact totally disconnected space that parameterizes all countable groups. This space allows for tools from descriptive set theory to be applied to study grouptheoretic questions. The class of elementary amenable groups is the smallest class that contains the abelian groups and the finite groups and that is closed under group extension, taking subgroups, taking quotients, and taking countable directed unions. In this talk, we first give a characterization of elementary amenable groups in terms of a chain condition. We then show the set of elementary amenable marked groups is not in the Borel sigma algebra of the space of marked groups. This gives a new proof of a theorem of Grigorchuk: There are finitely generated amenable nonelementary amenable groups. We conclude by discussing further questions and possible generalizations of the techniques. 
11.6.2015 (Do) 13:15 Uhr WIL C 133 
Anusch Taraz TU HamburgHarburg Embedding and packing large graphs into dense and sparse graphs Extremal combinatorics is often concerned with the forced appearance of highly organized structures. In this talk, we explain two major research avenues that deal with such situations. On the one hand, density results assert that these substructures must be present in any sufficiently dense host configuration. On the other hand, partition theorems guarantee that, no matter how we partition a sufficiently large object, at least one of the partition classes must contain the desired substructure. We first survey old and new results of both types, to give a flavour of the field and its methods, and then focus on a sequence of results that generalize the existence of paths and cycles to graphs of sublinear bandwidth. 
21.5.2015 (Do) 13:15 Uhr WIL C 133 
Alessandro Carderi ENS Lyon Space of actions, ultraproducts and sofic entropy 
7.5.2015 (Do) 13:15 Uhr WIL C 133 
Viola Meszaros TU Berlin Voronoi game on graphs The discrete Voronoi game is played on a graph G by two players A and B for a fixed number t of rounds. Player A starts and they alternatingly claim vertices of G in each round. No vertex can be claimed more than once. At the end of the game also the remaining vertices are divided among the players. Each player receives the vertices that are closer to his/her claimed vertices. If a vertex is equidistant to both players then we split it among them. In general it is hard to determine who gets more and therefore wins the game. First Demaine, Teramoto and Uehara dealt with this question. They proved that it is NPcomplete to determime the winner of the Voronoi game on a general graph G. The game on trees was studied further by Kiyomi, Saitoh and Uehara. They showed that on a path it always ends in a draw unless the number of vertices is odd and t=1 when A wins by one. We were interested in knowing when either player could control a large portion of the graph by the end of the game. We proved that there are graphs for which player B gets almost all vertices. The proof is inspired by a geometric construction. On a tree, player A can get at least one quarter of the vertices. If the game lasts for two rounds on a tree, then A can even get one third of all vertices. But A cannot get much more. A construction shows that this result cannot be improved when t is least two. In one round A can always claim half of the vertices of a tree. Inspired by the outcome of the game on a star, we investigated how much B can ensure on graphs with bounded degree. We also made some observations relating the result with many rounds to the oneround game. It is a joint work with D. Gerbner, D. Palvolgyi, A. Pokrovskiy and G. Rote. 
30.4.2015 (Do) 13:15 Uhr WIL C 133 
Christian Pech TU Dresden Reconstructing the topology of polymorphism clones Every clone of functions comes naturally equipped with a topology  the topology of pointwise convergence. A clone C is said to have automatic homeomorphicity with respect to a class K of clones, if every cloneisomorphism of C to a member of K is already a homeomorphism (with respect to the topology of pointwise convergence). I am going to talk about automatic homeomorphicityproperties for polymorphism clones of countable homogeneous relational structures. The results base on (and extend) previous results by Bodirsky, Pinsker, and Pongrácz. 
23.4.2015 (Do) 13:15 Uhr WIL C 133 
Andreas Thom TU Dresden Group laws for finite simple groups 
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Winter term 2014/15
5.2.2015 (Do) 13:15 Uhr WIL C 133 
Friedrich Martin Schneider TU Dresden Invariants of group actions and their connection to amenability 
29.1.2015 (Do) 13:15 Uhr WIL C 133 
Anton Klyachko Moscow Surprising divisibilities in group theory I shall talk about a general theorem which implies some amusing facts. For instance, in any group, the number of elements whose 2015th powers belong to a given subgroup is always a multiple of the order of this subgroup. The talk is based on joint results with Anna Mkrtchyan. 
15.1.2015 (Do) 13:15 Uhr WIL C 133 
Marcello Mamino TU Dresden Groups definable in two orthogonal sorts We will investigate the following question. Let (Z,R) be a first order structure with two sorts Z and R, which is simply the disjoint union of a structure Z and a structure R  i.e. there is no function and no relation in the language connecting the two structures. Can groups definable in (Z,R) be analyzed in terms of groups definable in Z and groups definable in R separately? 
8.1.2015 (Do) 13:15 Uhr WIL C 133 
Jan Hladky Czech Academy of Sciences, Prague The LoeblKomlosSos conjecture Many problems in extremal graph theory fit in the following framework: Does a certain density condition imposed on a host graph guarantee the existence of a given subgraph? Perhaps the most famous example in this direction is Mantel's Theorem from 1907: If a graph on n vertices contains at more than n^2/4 edges, then it must contain a triangle. I will give further examples, explain the basic concepts of extremal graphs and stability, and show the role of the celebrated Szemeredi Regularity Lemma in proving similar results. I will then report on joint progress with Janos Komlos, Diana Piguet, Miklos Simonovits, Maya Stein, Endre Szemeredi on the LoeblKomlosSos conjecture, an extremal problem about containment of trees, which has been open for two decades. 
11.12.2014 (Do) 13:15 Uhr WIL C 133 
Isolde Adler U Frankfurt PAC learning of FO definable concepts & nowhere dense graph classes In machine learning, the problem of "concept learning" is to identify an unknown set from a given concept class (i.e. a collection of sets). In the model of "probably approximately correct" (PAC) learning, the learner receives a number of samples and must be able to identify the unknown set approximately, in a probabilistic sense. It is wellknown the the sample size for PAC learning is characterised by the VapnikCervonenkis (VC) dimension of the concept class. We are interested in the VC dimension of concept classes that are definable in some logic on graph classes. In 2004, Grohe and Turán showed that for any subgraph closed class C, monadic secondorder definable concept classes have bounded VC dimension on C if and only if C has bounded treewidth. We show that for any subgraph closed class C, firstorder definable concept classes have bounded VC dimension on C if and only if C is nowhere dense. 
20.11.2014 (Do) 13:15 Uhr WIL C 133 
JanChristoph SchlagePuchta U Rostock Der Product Replacement Algorithmus auf der symmetrischen Gruppe Der Product Replacement Algorithmus auf der symmetrischen Gruppe erzeugenden kTupel von G eine Irrfahrt gestartet, und am Ende ein Element dieses Tupels ausgegeben. In der Praxis hat sich dieser Algorithmus gut bewährt, eine theoretische Analyse ist in den meisten Fällen jedoch nicht möglich. In diesem Vortrag werde ich für die symmetrische Gruppe S_n zeigen, dass der Graph auf dem die Irrfahrt abläuft einerseits für kleinere k zusammenhängend ist, als man bisher wusste, andererseits der Zusammenhang numerisch schwerer nachweisbar ist, als man zunächst dachte. 
13.11.2014 (Do) 13:15 Uhr WIL C 133 
John Wilson U Oxford Metric ultraproducts of finite simple groups Metric ultraproducts of structures have arisen in a variety of contexts. The study of the case when the structures are finite groups is recent and motivated partly by the connection with sofic groups. We report on current joint work with Andreas Thom on the topological and algebraic properties of metric ultraproducts of finite simple groups. 
6.11.2014 (Do) 13:15 Uhr WIL C 133 
Tim Netzer Tu Dresden Convex sets with semidefinite representations 
30.10.2014 (Do) 13:15 Uhr WIL C 133 
Wieslav Kubis U Prag BanachMazur games on categories We shall discuss a natural game played on a category with amalgamations, in the spirit of the classical BanachMazur game. Among applications, we obtain new characterizations of various generic objects, including Fraisse limits, as well as a new tool for detecting generic structures in continuous model theory. 
23.10.2014 (Do) 13:15 Uhr WIL C 133 
Andreas Thom Tu Dresden Sofic groups and applications 
16.10.2014 (Do) 13:15 Uhr WIL C 133 
Manuel Bodirsky Tu Dresden Ramsey Theory and Topological Dynamics 