International Seminar
In diesem Arbeitsseminar werden aktelle Forschungsresultate von Institutsmitgliedern und Gästen diskutiert und weiterentwickelt.
Friday, 31.1.2020 13:30, WIL/C129 |
Proper Jordan schemes exist Sven Reichard (TU Dresden) Association schemes were introduced in the 1930's by Bose et al in the context of the design of statistical experiments. They relate systems of binary relations to algebras of matrices. There have been several generalizations, such as coherent configurations (Higman, Weisfeiler-Leman, 1968-70). If we want to generalize the concept of association schemes while considering only symmetric relations we can replace the matrix product by the Jordan product $A*B=\frac 12 (AB + BA)$, which is symmetric but not associative. This leads to the concept of Jordan schemes, first considered by Shah (1959). Given an association scheme $W$ one can always obtain a Jordan scheme $W'$ by symmetrization. It has been an open question (Cameron 2002, Bailey 2004) whether all Jordan schemes arise in this way, or if there are "proper" Jordan schemes with their own independent theory. Equivalently we can ask if symmetric Weisfeiler-Leman stabilization gives the same as ordinary WL followed by symmetrization. We answer these questions by providing two constructions for infinite families of proper Jordan schemes. This is joint work with M. Klin and M. Muzychuk. |
Friday, 24.1.2020 13:30, WIL/C129 |
Solving equation systems in omega-categorical algebras Thomas Quinn-Gregson We study the computational complexity of deciding whether a given set of term equalities and inequalities has a solution in an omega-categorical algebra A. There are omega-categorical groups where this problem is undecidable. We show that if A is an omega-categorical semilattice or an abelian group, then the problem is in P or NP-hard. The hard cases are precisely those where Pol(A,\neq) has a uniformly continuous minor-preserving map to the clone of projections on a two-element set. The results provide information about algebras A such that Pol(A,\neq) does not satisfy this condition, and they are of independent interest in universal algebra. In our proofs we rely on the Barto-Pinsker theorem about the existence of pseudo-Siggers polymorphisms. To the best of our knowledge, this is the first time that the pseudo-Siggers identity has been used to prove a complexity dichotomy. |
Friday, 10.1.2020 13:30, WIL/C129 |
Poset-valued functions and residuated maps Eszter Horvath (U Szeged) We analyze cuts of poset-valued functions relating them to residuated mappings. Dealing with the lattice-valued case we prove that a function μ: X → L induces a residuated map f: L → P(X) whose values are the cuts of μ and we describe the corresponding residual. Conversely, it turns out that every residuated map f from L to the power set of X determines a lattice valued function μ : X → L whose cuts coincide with the values of f. For general poset-valued functions, we give conditions under which the map sending an element of a poset to the corresponding cut is quasi-residuated, and then conditions under which it is also residuated. We prove that without additional conditions, the map analogue to the residual is a partial function hence we get particular weakly residuated maps which, on the power set of the domain, generate centralized systems instead of closures. We show that the main properties of residuated maps are preserved in this generalized case. We apply these results to the canonical representation of poset-valued and lattice-valued functions, using the corresponding closures and centralized systems. |
Friday, 13.12.2019 13:30, WIL/C129 |
Lattices of idempotent theories Anvar Nurakunov (Akad. d. Wiss, Bishkek, Kirgisien) Abstract |
Friday, 6.12.2019 13:30, WIL/C129 |
Constraint Satisfaction Problems in Monadic Second-Order Logic Johannes Brauer (Kolloquium zur Masterarbeit, Betreuer: Prof. M. Bodirsky) |
Friday, 29.11.2019 13:15, WIL/C129 |
Counting points on algebraic varieties over the rational numbers Philip Dittmann (Inst. f. Algebra) For both conceptual and practical reasons it is useful to have estimates on the number of points of algebraic varieties over Q, usually phrased in terms of asymptotics as the height of points increases. I will present a new such estimate obtained in joint work with Wouter Castryck, Raf Cluckers and Kien Huu Nguyen, improving a host of previous results. I will also present some applications of this result. |
Friday, 22.11.2019 13:15, WIL/C129 |
Problems and some positive solutions about bounds of non-p-soluble length in finite groups |
Friday, 15.11.2019 13:15, WIL/C129 |
Parabolic Cataland -- Origins Henri Mühle (Inst. f. Algebra, TU Dresden) We tell the story of the discovery of Parabolic Cataland. The stepping stone in this process is the realization that several Catalan families, as well as the Catalan numbers themselves, are intrinsically related to the symmetric group. Analyzing this connection from the point of view of Coxeter groups made it clear that analogues of Catalan families and Catalan numbers can be defined for every finite Cartan type. Thus, Cataland was found. Most recently, an expansion of Cataland---corresponding to parabolic quotients of finite Coxeter groups---was theorized. We present these constructions, and support them by concrete combinatorial realizations in the symmetric group case. This talk is based on joint work with Cesar Ceballos, Wenjie Fang and Nathan Williams. |
Friday, 8.11.2019 13:15, WIL/C129 |
On the lattice of congruence lattices Danica Jakubikova-Studenovska (U Košice) For a given finite set A, let E be the system of all congruence lattices of all algebras with the base set A. Then E is a lattice with respect to inclusion. We describe atoms and coatoms in E. Also, meet- and join- irreducible elements of E are dealt with. |
Friday, 25.10.2019 13:15, WIL/C129 |
Comeager conjugacy classes in automorphism groups of linearly ordered structures Aleksandra Kwiatkowska (U Münster) |
Friday,20.9.2019 13:15, WIL/C129 |
Quasi Jonsson Operations in Highly Transitive Closed Clones Sergej Scheck (Kolloquium zur Masterarbeit, Betreuer: Prof. Manujel Bodirsky) Jonsson terms play an important role in the study of varieties and of constraint satisfaction problems on finite sets. For structures with infinite base sets the idempotency of polymorphisms is a very strong assumption. A generalization of the concept of Jonsson terms that might be useful in the study of infinite structures are quasi Jonsson terms where the idempotency assumption is relaxed. Kazda, Kozik, McKenzie, and Moore (2015) proved that a variety has Jonsson terms if and only if it has directed Jonsson terms. We will show that also locally closed clones on countable sets that contain all permutations have quasi Jonsson operations if and only if they have quasi directed Johnsson operations. It also turns out that if a structure with a finite signature is preserved by all permutations and has quasi Jonsson polymorphisms, it also has a QNU polymorphism. |
Friday,6.9.2019 13:15, WIL/C129 |
Constraint Satisfaction Probleme in der Steuererklärung Hanna Möller (Kolloquium zur Masterarbeit, Betreuer: Prof. Manujel Bodirsky) Am Anwendungsbeispiel des deutschen Steuerformulars wird die Komplexität von Constraint Satisfaction Problemen untersucht. Dabei wird insbesondere das von J.C. Lagarias analysierte "Two-Variables-per-Inequality"- Problem (TVPI) betrachtet, welches Integer-Programming auf zwei Variablen pro Constraint beschränkt. Es wird gezeigt, dass dieses Problem über der unendlichen Grundmenge der ganzen Zahlen NP-vollständig ist, selbst wenn Kreisfreiheit des Constraint-Graphen gefordert wird. Beschränkt man sich allerdings auf eine endliche Grundmenge, so lassen sich TVPIs in polynomieller Zeit lösen. Im Steuerformular kommen für die Eingabe nur endlich viele Werte in Frage. Allerdings sind dort auch Multiplikationen von Variablen erlaubt. In meiner Master-Arbeit beschäftige ich mich auch damit, wie man mit diesen Nicht-Linearitäten umgehen kann. |
Friday,12.7.2019 |
New Topological Variants of Birkhoff’s Theorem II Manuel Bodirsky |
Friday, 5.7.2019, 13:15, WIL/C129 | New Topological Variants of Birkhoff’s Theorem Manuel Bodirsky |
Friday, 28.6.2019, 13:15, WIL/C129 | Parabolic Cataland -- A Type-A Story Henri Mühle In this talk we embark on a journey through Parabolic Cataland. We first get to know the various families inhabiting the currently explored part of Parabolic Cataland and study their interactions. We then introduce certain natural orders for each of these families and describe how they are related. We then use the infrastructure of Parabolic Cataland to prove a connection between the graded dimensions of a certain Hopf algebra and the number of certain lattice walks in the quarter plane, as well as recover a famous bijection on Dyck paths that combinatorially explains the symmetry of the bigraded Hilbert series of a certain module of diagonal harmonics. In parts, this is joint work with Cesar Ceballos, Wenjie Fang and Nathan Williams |
Monday, 24.6.2019, 15:00, WIL/C129 | Convergence of dynamical systems and unique ergodicity Felix Pogorzelski (U Leipzig) |
Monday, 17.6.2019, 13:30, WIL/C129 |
Reading group on PCP theorem: Alphabet reduction |
Friday, 7.6.2019, 13:15, WIL/C129 | A Fraïssé theorem for IB-homogeneous structures Andres Aranda An L-structure M is IB-homogeneous if every isomorphism between finite substructures of M extends to a bimorphism (a bijective endomorphism) of M. I will present a version of Fraïssé's theorem relating the finite L-structures that embed into M, a family of monomorphisms between finite substructures, and the existence of an IB-homogeneous limit. |
Friday, 24.5.2019, 13:15, WIL/C129 |
Spectral Methods on Group Rings in a Non-Commutative Situation |
17.05.2019 (Fr), 13:15, WIL C 129 | A sampling algorithm for valued constraint satisfaction problems Caterina Viola |
Friday, 3.5.2019, 13:15, WIL/C129 | Zählspektren von Strukturen mit polynomiell vielen Orbits von n-elementigen Teilmengen Julia Grabinsky (diploma defence, supervisor: Prof. Manuel Bodirsky) |
Friday, 12.4.2019, 13:15, WIL/C129 |
Isogeny-based Post-Quantum Cryptography |
Friday, 5.4.2019, 13:15, WIL/C129 |
Varieties of PBZ*-lattices |
Wednesday, 13.3.2019, 13:15, WIL C 115 | mu-types and their stabilizers in algebraically closed valued fields Jinhe Ye (University of Notre Dame) In [2], it was proven that to any unbounded curve C ⊆ G in an o-minimal theory, where G is a definable group, one can associate a definable, one-dimensional subgroup of G. In the language of [1], it is proven that the above group is the μ-stabilizer of the branch of the curve at infinity. Furthermore, the notion of μ-stabilizers can be stated in a general context of topological groups. In this talk, we will investigate this problem in the context of linear algebraic groups and give some structral descrptions of the μ-stabilizers. References: [1] Ya’acov Peterzil and Sergei Starchenko. Topological groups, μ-types and their stabilizers. Journal of the European Mathematical Society, 19(10):2965–2995, 2017. [2] Ya’acov Peterzil and Charles Steinhorn. Definable compactness and definable subgroups of o-minimal groups. Journal of the London Mathematical Society, 59(3):769–786, 1999. |
Friday, 15.2.2019, 10:30, WIL/C133 |
CSP dichotomy for finite coverings of unary structures |
Friday, 1.2.2019, 13:15, WIL/C133 |
Stable Fields |
Friday, 25.1.2019, 13:15, WIL/C133 | Cover Problems, Dimensions and the Tensor Product of Complete Lattices Christian Jäkel This talk will treat different dimensional concepts of complete (ortho)lattices and their tensor products. The determination of these dimensions can be translated to certain set cover problems. This yields a sufficient condition for the multiplicativity of various lattice dimensions with respect to the tensor product of complete (ortho)lattices. |
Friday, 18.1.2019, 13:15, WIL/C133 |
Lattices with many sublattices |
Friday, 11.1.2019, 13:15, WIL/C133 | On an infinite family of highly regular graphs Maja Pech (U Novi Sad) Highly regular graphs for which not all regularities are explainable by symmetries are fascinating creatures. Some of them like, e.g., the line graph of W. Kantor's non-classical GQ(25,5), are stumbling stones for existing implementations of graph isomorphism tests.They appear to be extremely rare and even once constructed it is difficult to prove their high regularity.Yet some of them, like the McLaughlin graph on 275 vertices and Ivanov's graph on 256 vertices are of profound beauty. This alone makes it an attractive goal to strive for their complete classification or, failing this, at least to get a deep understanding of them.Recently, Ch. Pech discovered new methods for proving high regularity of graphs. Using these techniques, in this talk we report on a family of strongly regular graphs, originally discovered by A.V. Ivanov in 1990. We show that they are (3,5)-regular. |
Friday, 14.12.2018, 13:15, WIL/C133 |
Nazarov-Wenzl algebras, coideal subalgebras and categorified skew Howe duality |
Wednesday, 28.11.2018, 13:15, WIL/C115 |
Large rigid sets of algebras |
Friday, 16.11.2018, 13:15, WIL/C133 |
HH-homogeneous graphs with infinite independence number. |
Friday, 9.11.2018, 13:15, WIL/C133 | Some very weak height 1 identities Jakub Opršal A strong Maltsev condition is a finite set of identities in a finite algebraic language. Such condition is said to be satisfied in a set of operations (the set of all term operations of an algebra, a clone, a minion) if there is assignment of concrete operations to the symbols of matching arity which universally satisfies all the identities. These conditions are naturally (lattice) ordered by syntactic consequence. The resulting lattice has been studied since 70's. One of the results of Taylor from that time is that there is no such weakest non-trivial condition. Recently, the focus has been shifted to identities of height 1, i.e., identities that have exactly one function symbol on either side. This has been motivated by the study of complexity of CSP. In the talk, we will look into the ordered set of such height 1 conditions and its 'small' elements. |
Friday, 2.11.2018, 13:15, WIL/C115 |
The homogeneity of semigroups |
Friday, 26.10.2018, 13:15, WIL/C115 | Dissecting Shitpel'man's theorem Nikolaas Verhulst In this talk, we will dissect a classical proof from non-commutative valuation theory. We will introduce the necessary terminology, discuss the proof, and distil its vital parts. We will show how they can be used independently to generalise the original statement. |
Friday, 19.10.2018, 13:15, WIL/C115 | Graph algebras and graph varieties Erkko Lehtonen Graph algebras were introduced by Shallon in 1979. To each directed graph G = (V,E), we associate an algebra A(G) of type (2,0), whose universe is the set V∪{∞}, where ∞ is a new element not in V, considered as a nullary operation, and where the binary operation ("product") is defined as xy = x if (x,y)∈E and xy = ∞ otherwise. Encoding graphs as algebras in this way, we can view any algebraic properties of the graph algebra A(G) as properties of the graph G. Although the class of graph algebras does not constitute a variety (as it is not closed under direct products), it makes perfect sense to consider the satisfaction relation between graphs (that is, graph algebras) and identities of type (2,0). With respect to the Galois connection induced by this relation, the closed sets of graphs are called graph varieties and the closed sets of identites are called equational theories of graphs. In this talk, we give a brief overview on different approaches to studying graph varieties. We also report the speaker's recent work with Chaowat Manyuen (Khon Kaen University) on descriptions of graph varieties that are axiomatized by certain groupoid identities that are of general interest in algebra, such as the (left or right) semimedial and medial identities. |
Friday, 12.10.2018, 13:15, WIL/C115 |
Multiplicative and implicative derivations on residuated multilattices |
Friday 21.9.2018, 13:15, WIL/C115 | Temporal constraint satisfaction problems in least fixed point logic Jakub Rydval The constraint satisfaction problem (CSP) for a fixed structure L with finite relational signature is the computational problem of deciding whether a given finite structure of the same signature homomorphically maps to L. A temporal constraint language is a structure over the rational numbers Q whose relations are first-order definable in (Q;<). In 2009, Bodirsky and Kara presented a complete classification of the computational complexity of CSPs for temporal constraint languages. In contrast to finite domain structures, there are temporal constraint languages whose CSP cannot be solved by any Datalog program but can be expressed in least fixed point logic (LFP). An example is CSP(Q; {(x,y,z) | x>y or x>z}), known as the and/or scheduling problem. I will give a proof of a trichotomy for LFP expressibility of CSPs of temporal constraint languages. For a temporal constraint language L, at least one of the following is true: CSP(L) is expressible in LFP, the relation {(x,y,z) | x>y=z or y>z=x or z>x=y} has a primitive positive definition in L, or the two-element group has a primitive positive interpretation with parameters in L. In the latter case it is known that CSP(L) cannot be expressed in LFP. We conjecture that the same holds for the second case. |
Friday 14.9.2018, 13:15, WIL/C115 | Constraint Satisfaction over the Random Tournament Simon Knäuer The Random Tournament T is the Fraïssé limit of the class of all finite tournament graphs. The talk will introduce this structure and define the Constraint Satisfaction Problem of its first-order reducts. It will give a proof of the complexity dichotomy for CSPs of first-order expansions of T by injective relations. |
Friday 20.7.2018, 13:15, WIL/C115 | Highly regular graphs Maja Pech (University of Novi Sad) Highly regular graphs appear as a class of graphs with nontrivial degree of regularity that is not induced by symmetries. They are stumble stones for the existing implementations of graph isomorphism tests. So far, there is found just a modest number of examples of such graphs. In this talk, we analyze an infinite family of strongly regular graphs introduced by Brouwer, Ivanov and Klin and uncover certain regularities that are not explainable by their symmetries. This is joint work with Christian Pech. |
Friday 13.7.2018, 13:15, WIL/C115 | On the characterization of particular orthogroups by disjunctions of identities Alexander Jende (University of Potsdam) Based on a general result by Clifford, it is a well-known fact that a semigroup is an orthogroup if and only if it is a semilattice of rectangular groups. In particular, every band is a semilattice of rectangular bands. Classes of semilattices of various particular rectangular groups can be characterized using the concept of disjunctions of identities. This concept, a generalization of the well-known identities, was introduced by Ljapin in the 1970s. Using disjunctions of identities, we characterize orthogroups which are semilattices of rectangular groups of various exponents. Furthermore, we consider chains of rectangular groups. Finally, we present some applications. For example, we describe several classes of strong semilattices of semigroups. |
Friday 29.6.2018, 13:15, WIL/C115 | Complexity of combinations of qualitative constraint satisfaction problems Johannes Greiner In 1979 Nelson and Oppen first presented a result for convex theories T and S, stating that the constraint satisfaction problem (CSP) of the union of T and S can be solved by combining the algorithms for T and S in a black-box way. We prove for a certain class of structures that convexity is also necessary for polynomial-time tractability of the union of their first-order theories. In particular, we will look at the generic combination of two relational structures A and B on infinite domains, which is a key idea in the proof. The generic combination of A and B, if it exists, is a structure that has the same CSP as the union of the first-order theories of A and B, where the signatures of A and B are assumed to be disjoint. Furthermore, its orbits of n-tuples are precisely the intersections of the orbits of n-tuples of A and of B. We characterize the existence of generic combinations and describe when the generic combination has a binary injective polymorphism, in which case the CSP is polynomial-time tractable. |
Friday 22.6.2018, 13:15, WIL/C115 | Twists of hyperelliptic curves without rational points François Legrand In this talk, I shall present several conditional and unconditional results on the lack of rational points on twisted hyperelliptic curves over the rational numbers. Time permitting, I shall also give a conjectural example of a 1-parameter family of affine curves over some number field, all with a rational point, but with no generic point, thus relating to an old problem of Schinzel. The talk requires no prior knowledge about rational points on curves. |
Friday 15.6.2018, 13:15, WIL/C115 | Stabilization of configurations Sven Reichard One origin of the notion of coherent configurations is the study of the complexity of the graph isomorphism problem. Given an edge-coloring of a complete graph the algorithm by Weisfeiler and Leman constructs a refinement of the coloring using invariants on the edges; the resulting refined coloring has the same automorphisms as the original coloring. The invariant that is used counts colored triangles involving a given edge. Coherent configurations may be defined as colorings that are stable under this procedure. The concepts above can be generalized in several directions. Other invariants can be used by considering subgraphs with more than three vertices (cf. Hestenes-Higman's t-vertex condition}). Instead of graphs we can consider (uniform) hypergraphs; this leads to k-ary coherent configurations (Babai, Immerman-Lander), which play a prominent role in recent advances in the study of the graph isomorphism problem. It is known that the algorithm of Weisfeiler-Leman is polynomial in complexity. Twenty years ago two implementations were described which both had their advantages and disadvantages. We will present a new framework that takes into account the generalizations described above as well as advances of modern computer architecture. The programs will be available as open source. |
Friday 8.6.2018, 13:15, WIL/C115 | Essential arguments and minors of partial functions Nareupanat Lekkoksung (Khon Kaen University) It is well known that the number of essential arguments of total functions does not increase upon formation of minors. This is no longer true for partial functions. Moreover, in contrast to total functions, it is possible that a nonconstant partial function has no essential argument. From this standpoint, essential arity seems slightly unsatisfactory as a quantity of structural complexity for partial functions. Our goal is to formulate alternative notions that would more accurately describe the dependence of partial functions on some arguments. We consider the question whether the corresponding quantities decrease upon formation of minors. We also investigate the structure of the minor poset of partial functions. M. Couceiro and M. Pouzet showed that the minor poset of Boolean functions is past-finite-universal. This property carries over to minor posets of partial functions on finite sets. We improve this result by showing that certain small fragments of this poset (e.g., partial projections, constant functions) are past-finite-universal. |
Friday, 25.5.2018, 13:15, WIL/C115 | A proof of CSP Dichotomy conjecture Dmitriy Zhuk (Lomonosov Moscow State University) Many natural combinatorial problems can be expressed as constraint satisfaction problems. This class of problems is known to be NP-complete in general, but certain restrictions on the form of the constraints can ensure tractability. The standard way to parameterize interesting subclasses of the constraint satisfaction problem is via finite constraint languages. The main problem is to classify those subclasses that are solvable in polynomial time and those that are NP-complete. It was conjectured that if a constraint language has a weak near unanimity polymorphism then the corresponding constraint satisfaction problem is tractable, otherwise it is NP-complete. The hardness result is known since 2001. We present an algorithm that solves Constraint Satisfaction Problem in polynomial time for constraint languages having a weak near unanimity polymorphism, which proves the remaining part of the conjecture. |
Friday, 18.5.2018, 13:15, WIL/C115 | Structures with small orbit growth Bertalan Bodor Let C be the class of those countable structures A for which there exist constants c_1 and c<1 so that the number of orbits of A acting on n-tuples with pairwise distinct entries is at most c_1n^{cn}. We showed that this class is also equal to the class of finite coverings of first-order reducts of unary omega-categorical structures. In this talk I will attempt to illustrate the basic ideas of the proof of this theorem, and I will present some interesting consequences. Joint work with Manuel Bodirsky. |
Friday, 11.5.2018, 13:15, WIL/C115 | Constraint Satisfaction over the Random Tournament Simon Knäuer The Random Tournament is the Fraïssé limit of the class of all finite tournament graphs. The talk will introduce this structure and define the Constraint Satisfaction Problems of its first-order reducts. It will also give an idea for the complexity classification of these CSPs. Temporal constraint satisfaction problems in least fixed point logic Jakub Rydval The constraint satisfaction problem (CSP) for a fixed structure L with finite relational signature is the computational problem of deciding whether a given finite structure of the same signature homomorphically maps to L. A temporal constraint language is a structure over the rational numbers Q, where all its relations are first order definable using the usual strict linear order <. In 2009, Bodirsky and Kara presented a complete classification of the computational complexity of CSPs for temporal constraint languages. In contrast to finite domain structures, there are temporal constraint languages whose CSP cannot be solved by Datalog but can be expressed in least fixed point logic (LFP). An example is CSP(Q; {(x,y,z) | x>y or x>z}), known as the and/or scheduling problem. The goal of my master thesis is to classify all CSPs for temporal constraint languages that can be expressed in LFP. In this talk, I present an LFP formula for every temporal constraint language that is preserved by the minimum operation. |
Wednesday, 9.5.2018, 13:15, WIL/C115 |
On a Generalization of von Staudt's theorem of cross-ratios |
Friday, 4.5.2018, 13:15, WIL/C115 | The complexity of solving equations and checking identities Michael Kompatscher (Charles University Prague) The equation solvability problem of an algebra A is the computational problem that asks, whether an equation of polynomials f(x_1,…,x_n) = g(x_1,…,x_n) has a solution in A or not. Besides their relevance in algebra, for finite algebras these problems encode many problems in NP, including all CSPs. The identity checking problem of A is the closely related problem that asks, whether an input equation holds for all substitutions of variables or not. In my talk I am first going to discuss some obstacles in classifying the complexity of both problems for all finite algebras. Then I will discuss how commutator theory and tame congruence theory bring us close to a P/NP-c (respectively P/coNP-c) dichotomy in congruence modular varieties. This is based on joint work with Idziak and Krzaczkowski. |
Friday, 20.4.2018, 13:15, WIL/C115 | Surjective-morphism extension classes of graphs, part 2 Andrés Aranda Two new morphism-extension classes were introduced recently for infinite relational structures: HE, the class of all L-structures such that any homomorphism between finite induced substructures extends to a surjective endomorphism, and MB, the class of all L-structures such that any monomorphism between finite induced substructures extends to a bijective endomorphism. In this talk, I will show that all MB-homogeneous graphs are HE-homogeneous and all "interesting" (i.e., not a union of finite cliques) HE-homogeneous graphs are MB-homogeneous. In the second talk, I will prove that every MB-homogeneous graph is HE-homogeneous. |
Friday, 13.4.2018, 13:15, WIL/C115 | Surjective-morphism extension classes of graphs Andrés Aranda Two new morphism-extension classes were introduced recently for infinite relational structures: HE, the class of all L-structures such that any homomorphism between finite induced substructures extends to a surjective endomorphism, and MB, the class of all L-structures such that any monomorphism between finite induced substructures extends to a bijective endomorphism. In this talk, I will show that all MB-homogeneous graphs are HE-homogeneous and all "interesting" (i.e., not a union of finite cliques) HE-homogeneous graphs are MB-homogeneous. |
Friday, 6.4.2018, 13:15, WIL/C115 | Splitting fields of central simple algebras of exponent 2 Karim Becher (University of Antwerp) Central simple algebras over fields have been studied for over a century, starting with the work of Cayley, Hamilton, Dickson and Wedderburn. As a crucial result of class field theory, these algebras are completely classified over number fields. Over an arbitrary base field, even though these algebras are abstractly classified by the Brauer group, their structure, or more particularly the structure of finite-dimensional division algebras is still a mystery. By Merkurjev’s Theorem every central simple algebra of exponent two is Brauer equivalent to a tensor product of quaternion algebras. In particular, if every quaternion algebra over a given field is split, then there exists no central simple algebra of exponent two over this field. I give an independent elementary proof of the latter fact. While this proof is based on Zorn's Lemma, the statement should also have a constructive proof, leading to an explicit bound of the degree of a splitting 2-extension in terms of the degree of the algebra. |
Friday, 23.2.2018, 13:15, WIL/C115 | Counting relational structures Leopold Schlicht (Hans-Erlwein-Gymnasium Dresden) Let K be a class of finite, relational structures. This talk is about the following combinatorial function: the *profile* of K takes a natural number n as an argument and yields the number of structures in K of size n (up to isomorphism). Pouzet conjectured for hereditary K satisfying the joint embedding property that if the profile of K is bounded by a polynomial, then the profile is eventually a quasi-polynomial. I will give an overview of the current state of research regarding this conjecture. After that I will use the method of generating functions to prove the conjecture for classes of all graphs that embed into the disjoint union of infinitely many copies of a (directed or undirected) path. Finally, a list of open special cases of the conjecture is given. |
Friday, 2.2.2018, 13:15, WIL/C115 | The Alternate Order of Congruence-Uniform Lattices Henri Mühle A (finite) lattice L is congruence-uniform if and only if it can be obtained from the singleton lattice by a sequence of interval doublings. If we indicate which edge of the poset diagram of L is created at which step in the sequence, we obtain a natural edge-labeling of L. This set of edge labels can be used to define an alternate partial order on the elements of L. The main source of examples for this constructions comes from posets of regions of a real hyperplane arrangement. When such a poset of regions is a congruence-uniform lattice, then the alternate order is a lattice, too. In general, however, it is an open problem to characterize the congruence-uniform lattices whose alternate orders are lattices again. We provide a necessary condition for the lattice property of the alternate order and we discuss constructions that either preserve or destroy the lattice property. |
Friday, 26.1.2018, 13:15, WIL/C115 | Linkage of quaternion algebras Parul Gupta A quaternion algebra over a field is given by a pair of nonzero parameters from the field, which we call its slots. We discuss the property for a field F, called strong linkage, that any finite number of quaternion algebras over F have a common slot. The study of this field property is motivated by its relation to quadratic forms and further by the examples of global fields, where it can be shown using Class Field Theory. We study the strong linkage property for the rational function field over quasi-finite fields, that is perfect fields having a unique extension of each degree. An interesting example other than finite fields is the field of Laurent series over an algebraically closed field of characteristic 0. In this talk I will discuss relation of the linkage problem to quadratic form theory and different tools which are useful to show strong linkage. |
Friday, 19.1.2018, 13:15, WIL/C115 | Morphism extension classes of infinite L-colored graphs Andrés Aranda An L-structure M is in HH_L (homomorphism-homogeneous) if every homomorphism between finite induced substructures of M can be extended to an endomorphism of M; similarly, M is in MH_L if every local monomorphism can be extended to an endomorphism of M. It is known that for some languages L (for example, graphs), MH_L and HH_L coincide, while for others HH_L is a proper subclass of MH_L. If L is a finite partial order, an L-colored graph is a graph in which elements of L are assigned to the edges. Hartman, Hubička and Mašulović proved that in the case of finite graphs colored by linear orders, MH=HH even when colorings of the vertices were allowed, and that MH=HH for vertex-uniform (all vertices of the same color) finite graphs colored by a diamond (an antichain enriched by a bottom element and a top element), but differ when vertex colorings are allowed. In this talk, I will show that MH=HH for countable L-colored graphs when L is a linear order, give an example of an infinite MH L-colored graph that is not HH when L is a diamond, and prove that if MH=HH for infinite vertex-uniform L-colored graphs, then L is a join-semilattice. This is joint work with David Hartman. |
Wednesday 17.1.2018, 13:15, WIL/C115 | CD-independent subsets Eszter Horváth (University of Szeged) A subset X of a finite lattice L is called CD-independent if the meet of any two incomparable elements of X equals 0. Czédli, Hartmann and Schmidt has an important result about CD-bases (maximal CD-independent subsets) of distributive lattices. In the talk, we define CD-independent subsets in an arbitrary poset in a natural way. Actually, CD-independence is in close relationship with trees. More precisely, if we have a CD-independent subset in a poset and we remove its possible 0, then we obtain a forest. We show that the CD-bases of any poset can be characterized as maximal chains in a related poset. We use this result to investigate CD-bases in semilattices and in more general lattice classes. Finally, I give some overview about other results, in particular about some combinatorial aspects of CD-independence. |
Friday 12.1.2018, 13:15, WIL/C115 |
Solution sets of systems of equations |
Friday 5.1.2018, 13:15, WIL/C115 | The undecidability of joint embedding for hereditary graph classes, and related problems Sam Braunfeld (Rutgers University) A class of structures has the joint embedding property if for any two structures in the class, there is a third structure in the class embedding both. We will sketch a proof of the undecidability of joint embedding for finitely-constrained hereditary graph classes. Time permitting, we will discuss the analogous question in other classes of structures. |
Friday 15.12.2017, 13:30, WIL/C204 | ε-homomorphisms and complexity reduction Alexandr Kazda (Charles University) |
Friday 8.12.2017, 13:15, WIL/C115 | The promise(d) land of constraint satisfaction Jakub Opršal The promise constraint satisfaction problem can be viewed as a generalization of CSP. The domain of a PCSP is not one, but two relational structures A and B in the same language. PCSP(A, B) refer to the decision problem which on input gets a pp-sentence φ in the common language of A and B, and decides between two cases: * (Completeness) A satisfies φ, or * (Soundness) B does not satisfy φ. An important instance of this problem is approximate graph coloring (the corresponding structures are a d-clique and a e-clique for fixed e>d): the goal is to decide whether a given graph is d-colorable or not even e-colorable. The complexity of this graph coloring is mostly open, but believed to be NP-hard for all constants e>d. Recently, Brakensiek and Guruswami rediscovered a Galois correspondence between pairs of relational structures and minor closed sets of functions which is a key ingredient of the algebraic approach. We will discuss the natural follow-up, the full algebraic approach to PCSP and how it relates to the fact that the complexity of CSP depends only on the height 1 (linear) identities satisfied by the corresponding polymorphism clone. This opens a new possibility of applying algebra in several approximation problems. |
Friday, 1.12.2017, 13:15, WIL/C115 | Counting rational points on definable sets Margaret Thomas (Universität Konstanz) The results outlined in this talk are part of a wider, flourishing interaction between diophantine geometry and model theory. The central aim is to bound the density of rational and algebraic points lying on certain `transcendental' subsets of the reals. Following influential work by Pila and Wilkie in this area, our focus is on sets which are first-order definable in various o-minimal expansions of the real field. We shall survey background and some results in this area, in particular concerning possible improvements to the Pila–Wilkie bound. These include instances of a conjecture of Wilkie, which proposes an improvement for the real exponential field, and some recent progress made towards finding an effective version of the Pila–Wilkie Theorem. |
Friday, 24.11.2017, 13:15, WIL/C115 |
The homomorphism order: monounary algebras |
Friday, 17.11.2017, 13:15, WIL/C115 |
Time Complexity of NP-Hard CSPs |
Friday, 10.11.2017, 13:15, WIL/C115 |
Profiniteness in finitely generated varieties is undecidable |
Friday, 3.11.2017, 13:15, WIL/C115 |
Homogeneous structures and a new poset |
Friday, 27.10.2017, 13:15, WIL/C115 |
Twisting the zero-divisors away |
Tuesday, 24.10.2017, 11:00, WIL/C115 |
A Dichotomy Theorem for the Inverse Satisfiability Problem |
Friday, 20.10.2017, 13:15, WIL/C115 |
Ultraproducts preserve finite subdirect reducibility |
Friday, 13.10.17, 13:15, WIL/C115 |
open problems session |
Friday, 8.9.2017, 13:15, |
Free combinations of omega-categorical structures |
Friday, 1.9.2017, 13:45, WIL/C115 |
Monotone Monadic SNP 2: proof of the universal-algebraic dichotomy conjecture Antoine Mottet (joint work with Manuel Bodirsky) The forbidden patterns problem of the set of vertex-coloured graphs {H1,…,Hk} is the decision problem of the form: given a finite graph G as input, is it possible to colour the vertices of G in a way that none of H1, …, Hk homomorphically maps to the resulting coloured graph. The logic MMSNP can be seen as a complexity class whose problems are forbidden patterns problems of finite sets of coloured relational structures. It was conjectured by Feder and Vardi that this complexity class exhibits a complexity dichotomy (i.e., that every forbidden patterns problem is in P or NP-complete). Feder and Vardi showed that every problem in MMSNP reduces in probabilistic polynomial-time to the CSP of a structure with finite domain, and Kun later derandomized this reduction. Thus, MMSNP and finite-domain CSPs are computationally equivalent. Following up on Manuel's talk, I will present a completely new reduction from MMSNP to finite-domain CSPs that uses recent techniques and results from universal algebra, model theory, and Ramsey theory. This proves a stronger form of the Feder-Vardi-Kun result, and shows in particular that the Bodirsky-Pinsker tractability conjecture holds for all CSPs in MMSNP. |
Friday, 1.9.2017, 13:15, WIL/C115 |
Monotone Monadic SNP 1: classical results and applications |
Friday, 14 July .2017, 13:15, WIL/C115 |
Submodular Semilinear Valued Constraint Languages Caterina Viola I will present some new results on the characterisation of submodular semilinear functions and an algorithm solving the VCSP for an interesting subclass of them. I will also show a generalisation of the NP-hardness condition for semilinear VCSPs. This is joint work with M. Bodirsky and M. Mamino. |
Friday, 30 June 2017, 9:30, WIL/C207 |
Polynomial growth of concept lattices, canonical bases and generators: extremal set theory in Formal Concept Analysis |
Friday, 23 June 2017, 13:15, WIL/C115 |
Practically efficient algorithms for coherent configurations Sven Reichard In complexity theory we study the /theoretical/ complexity of algorithms, that is, the asymptotic behaviour of the amount of required resources (time, space, energy) as a function of the input size. For the practitioner who uses the algorithms it may be more interesting to know the /practical/ complexity, the resources required for specific instances of the problem on given hardware. Here, the size of the constants does matter. It turns out that in this case the simple model of computation with one processing unit and uniform memory access is not adequate. We look at two algorithmic problems related to coherent configurations, which are relational systems with a strong algebraic flavour. Weisfeiler-Leman (WL) stabilization computes the coarsest coherent refinement of a given configuration. It features in the recent improvements to the solution of the graph isomorphism problem. Its two-dimensional variant is of interest in algebraic graph theory. Two implementations were developed in the 1990's, with diverse theoretical and practical characteristics. We describe a few ways to outperform both classical implementations. S-rings are two-dimensional coherent configurations which admit a regular group of automorphisms. They play a role in the theory of Cayley graphs. The set of S-rings over a given group G is related to the set of two-closed overgroups of the regular action of G. Knowledge of their structure helps us solve the isomorphism problem for Cayley graphs over G. Enumeration of S-rings is hard, but it provides plenty of opportunity for efficient implementation. |
Friday, 9 June .2017, 13:15, WIL/C115 |
Reflection-closed varieties of multisorted algebras and minor identities Erkko Lehtonen, Reinhard Pöschel Reflections (as introduced by L. Barto, J. Opršal, M. Pinsker) generalize the classical operators of taking subalgebras and homomorphic images. We generalize this notion to multisorted algebras. We ask for a characterization of reflection-closed varieties (RP-varieties) and consider the Galois connection Mod-mId between multisorted algebras and minor identities. Analogously to the classical Birkhoff theorem, it turns out that the Galois closed sets of algebras are just the reflection-closed varieties of multisorted algebras, i.e., Mod mId K = RP K. Similarly, we characterize the minor-equational theories of multisorted algebras, i.e., the closed sets of minor identities. We also discuss how RP-varieties and usual varieties of multisorted algebras are related to each other. This is joint work with Tamás Waldhauser. |
Friday, 2 June .2017, 13:15, WIL/C115 |
Parking Functions and Noncrossing Partitions |
Friday, 26 May .2017, 13:15, WIL/C115 |
Towards a non-commutative Chevalley-style algebraic geometry |
Friday 12 May 2017, 13:15, WIL/C115 |
Complexity of term representations of functions |
Friday, |
Residuated multilattices: the first glimpse into their structure |
Friday, 21 April 2017, 13:15, WIL/C115 |
Primitive positive definability over complex numbers Sebastian Meyer (Martin-Andersen-Nexö-Gymnasium Dresden) |
Friday, |
Complexity of NP-Complete Constraint Satisfaction Problems |
Friday, 3 Feb 2017, 13:15, WIL/C115 |
Extremal lattices: where we go from here Bogdan Chornomaz (V.N. Karazin Kharkiv National University) In 2015 Alexandre Albano and I managed to prove an exact upper bound on the number of elements in a lattice with bounded VC-dimension. In this talk I'll try to show that, instead of closing the topic, this result may be considered as a starting point for deeper, more challenging, but in the same time natural studies. |
Friday, 27 Jan 2017, 13:15, WIL/C115 |
Majors of functions Erkko Lehtonen We consider the minor ordering of functions of several arguments. A function is said to be a minor of another function, if the former can be obtained from the latter by permutation of arguments, identification of arguments, and introduction of inessential arguments. The very definition of minor provides a natural way of going downwards in the minor order. In this talk, we are interested in going upwards in the minor order, i.e., in majors of functions, and, in particular, in upper covers of functions. This talk is based on joint work with Miguel Couceiro. |
Friday, 20 Jan 2017, 13:15, WIL/C115 |
Supersingular Isogeny Diffie-Hellman Key Exchange Juliane Prochaska (TU Dresden) The Diffie-Hellman key exchange is a well-known and important protocol in modern cryptographic applications. It is, however, vulnerable to quantum algorithms. A promising candidate for post-quantum cryptography is the supersingular isogeny Diffie-Hellman key exchange, which has been introduced by de Feo, Jao and Plût in 2011. This talk presents the protocol and its underlying mathematical concepts, including an introduction to elliptic curves and their use in cryptography. |
Friday, |
Upper bounds for the number of Galois-closed sets arising from finite binary relations Alexandre Albano We will do a gentle and short introduction to Formal Concept Analysis and give a mini-survey of results associated to the FCA-motivated question: how many closed sets does a Galois connection induced by a binary relation have? The general perspective here is that of complete lattices, but the focus will be combinatorial. |
Friday, |
Introduction to mean-payoff games |
Wednesday 30 Nov 2016, 13:15, WIL/C115 |
Representation problems for monoids of endomorphisms Danica Jakubíková-Studenovská (U Košice) The present talk deals with the following representation problems: (A) ABSTRACT: (i) Is every monoid isomorphic to the monoid of all endomorphisms of some algebraic structure? (ii) Is every group isomorphic to the group of all automorphisms of some algebraic structure? (B) CONCRETE: (i) Is every monoid of transformations of a non-empty set U equal to (not just isomorphic to) the monoid of all endomorphisms of some algebraic structure? (ii) Is every group of permutations of a non-empty set U equal to (not just isomorphic to) the group of all automorphisms of some algebraic structure? We will consider also different types of the algebraic structures. |
Friday, |
Submodular semilinear valued constraint satisfaction problems Caterina Viola Submodular functions are an important class of cost functions in optimisation theory. Given a totally ordered domain D, we say that a rational-valued function f on D^n is submodular if, for all x, y in D^n, it holds that f(x)+f(y) ≥ f(max(x,y))+f(min(x,y)), where max and min are applied componentwise. I focus on submodular cost functions f that are semilinear, that is, the underlying domain D is the set of rational numbers and f is first-order definable in (Q;<,+,1). Let us consider a (finite) set Gamma of submodular semilinear cost functions. An instance of the valued constraint satisfaction problem (VCSP) for Gamma is specified by a finite set of variables and by an objective function which is given as the sum of applications of the cost functions in Gamma to some of the variables. The goal is to find an assignment to the variables minimising the objective function. Our strategy to obtain a polynomial-time algorithm solving the VCSP for submodular semilinear cost functions is as follows. In a first step, we show that all submodular semilinear functions have an explicit syntactic characterisation. In a second step, we show how to reduce the problem to submodular VCSPs over finite domains, which are known to be polynomial-time solvable. |
Friday, 18 Nov 2016, 13:15, WIL/C115 |
open problems session |
Friday., 11 Nov 2016, 13:15, WIL/C115 |
Indecomposabilty of two equational theories We will discuss the indecomposability of two Mal'cev conditions—namely the conditions describing congruence modular varieties, and varieties that are congruence n-permutable for some n—in the following strong sense: Suppose that we have two sets of identities in disjoint languages such that their union implies the Mal'cev condition, then one of the sets implies the Mal'cev condition. |
Friday., |
On Noncrossing Partitions In this survey talk I will try to follow the timeline of this evolution, emphasize properties and connections to other objects, and outline potential generalizations. |
Friday., 28 Oct 2016, 13:15, WIL/C115 |
Local Movement and Jordan Groups Robert Barham I will explain what a Jordan Group is, what it means for it to be locally moving, and how this relates to Reconstruction from Automorphism Groups and the complexity of certain CSPs. This work builds on the results I presented last time I spoke at the International Seminar, but I will not assume any prior specialist knowledge. |
Friday., 21 Oct 2016, 13:15, WIL/C204 |
problems presented by participants |
Friday., 14 Oct 2016, 13:15, WIL/C207 |
Minors of functions and permutations, reconstruction problems, and the order of first occurrence Erkko Lehtonen |
Fr., 15.7.2016, 13:15 Uhr, WIL/C115 | Enumeration of S-rings over the elementary abelian group of order 64 Sven Reichard S-rings, as introduced by Schur and Wielandt, are certain subrings of the group ring C[G] for a finite group G. There is a one-to-one correspondence between S-rings over G and association schemes invariant under a regular action of G. Hence they provide a link between Group Theory and Combinatorics. They have been successfully utilized for example in the study of the complexity of the isomorphism problem for circulants. S-rings have been classified over all groups of order less than 64. The case of the elementary abelian group $Z_2^{^6}$ poses particular challenges. We report on progress toward the enumeration of S-rings over this group. |
Di., 12.7.2016, 10:00 Uhr, WIL/C115 | Generalized Concepts of Distance, Proximity and Betweenness in Comparison Mosadak Al Salamat (Vortrag zur Masterarbeit, Betreuer: Prof. Stefan Schmidt) |
Fr., 8.7.2016, 13:15 Uhr, WIL/C115 |
Decidable and undecidable properties of universal first-order theories André Schrottenloher (École polytechnique, TU Dresden) We study the decidability of various properties that one might ask for finite universal first-order theories T. On the one hand, for example, the equivalence of T to a universal Horn theory is decidable. On the other hand, it is an open problem whether one can effectively decide the Joint Embedding Property for the class of models of T. Finally, we show that the following problem is undecidable: are the universal-negative consequences of T finitely axiomatisable? All these questions have applications in the study of constraint satisfaction problems (CSPs) that are given by such finite universal first-order theories, since properties of the CSP can be reformulated as properties of its theory. |
Do., 7.7.2016, 13:15 Uhr, WIL/C115 | Subdirectly and almost subdirectly irreducible monounary algebras Danica Jakubíková-Studenovská (Pavol Jozef Šafárik University in Košice) |
Fr., 1.7.2016, 13:15 Uhr, WIL/C115 | Lower bounds and reconstruction algorithms for sums of affine powers Timothée Pécatte (École normale supérieure de Lyon) A sum of affine powers is an expression of the form f(x) = a_1 * (x - b_1)^e_1 + ... + a_s * (x - b_s)^e_s. Although quite simple, this model is a generalization of two well-studied models: Waring decomposition and sparsest shift. For these three models there are natural extensions to several variables, but this talk will be focused on univariate polynomials. We will present efficient algorithms for reconstructing the smallest expression for an input polynomial f. These algorithms build on techniques developed for proving lower bounds on the number of terms s needed to represent a polynomial. |
Fr., 24.06.2016, 13:15 Uhr, WIL/C115 |
Submaximal Strong Partial Clones Victor Lagerqvist |
Fr., 10.06.2016, 13:15 Uhr, WIL/C115 | On products of amalgams and amalgams of products Maja Pech We study amalgamated free sums in strict amalgamation classes of finite relational structures that are closed with respect to finite products. Examples of such classes are the class of finite partial orders, the class of non-empty finite metric spaces, the class of finite simple graphs, … In particular, we are interested in the interaction between amalgamated free sums and direct products. It turns out that there is a canonical homomorphism between the amalgamated free sum of products and the product of amalgamated free sums. When is this canonical homomorphism an embedding? In this talk we will present results toward the general answer to this question. |
Fr., 3.6.2016, 13:15 Uhr, WIL/C115 | Constraint Propagation and Pebble Games Christoph Berkholz (Humboldt-Universität zu Berlin) A generic method for solving the constraint satisfaction problem is "constraint propagation" where one iteratively derives new constraints in order to shrink the search space or to detect inconsistencies in the instance. A classical and very basic algorithm in this area is the so-called k-consistency test that iteratively derives local constraints involving only k variables. In this talk I will give an introduction to this method and show that the k-consistency test is tightly connected to a simple combinatorial pebble game originally introduced in the context of finite model theory. Afterwards I will present some results on the structure and complexity of the k-consistency test that have been obtained via this pebble game in the last years. |
Fr., 18.3.2016, 13:15 Uhr, WIL/C115 | Strong Partial Clones and the Complexity of Constraint Satisfaction Problems Victor Lagerqvist This seminar is concerned with properties of strong partial clones and their applicability to study the computational complexity of constraint satisfaction problems. Loosely, the approach boils down to the well-known fact that sets of relations invariant under partial functions can be characterized by primitive positive definitions without existential quantification. These quantifier-free primitive positive definitions provides a method to study the complexity of problems where the normal Galois connection between clones and relational clones does not result in reductions that are fine-grained enough. We are going to see applications of partial clone theory to study the worst-case time complexity of NP-complete Boolean constraint satisfaction problems, and also touch upon some unavoidable complications with this strategy, which somewhat limits its applicability in practice. |
Fr., 5.2.2016, 13:15 Uhr, WIL/C115 | Unifying Tone System Definitions: Ordering Chromas Tobias Schlemmer The talk describes the background of a musical tone system definition that has been proposed [1] in the proceedings of the MCM2015 in London.[2] This definition uses abstract ordered groups as interval groups. The common operation of octave identification is replaced by a folding operation for ordered sets that is based on the factorisation of groups by normal subgroups. The resulting structure is used to provide a chroma system definition that can preserve a certain amount of the order relation. Additionally, a path is shown that allows the integration of the David Lewin's theory of Generalized Interval Systems into the extensional language that has been proposed by Rudolf Wille and Wilfried Neumaier. |
Mo., 1.2.2016, 16:40 Uhr, WIL/C207 | Mathematische Morphologie und ihre Fuzzyfizierung Lars Lumpe (Diplomverteidigung, Betreuer: Prof. S. Schmidt) |
Fr., 29.1.2016, 13:15 Uhr, WIL/C115 | Laws for finite groups Andreas Thom |
Fr., 22.1.2016, 13:15 Uhr, WIL/C115 | Lattice-valued functions Eszter Horvath (Universität Szeged) |
Fr., 15.1.2016, 13:15 Uhr, WIL/C115 | The complexity of CSPs for reducts of the random partial order Trung Van Pham The random partial order is defined as the Fraissé limit of the class of finite partial orders. In this talk, we will give a full complexity classification for the constraint satisfaction problems (CSPs) on the class of reducts of the random partial order. This result confirms a dichotomy conjecture on infinite CSPs. |
Fr., 18.12.2015, 13:15 Uhr, WIL/C/115 | On permutation groups and permutation pattern classes Erkko Lehtonen |
Fr., 4.12.2015, 13:15 Uhr, WIL/C/115 | Mashups algebras and constraint satisfaction problems Antoine Mottet Abstract: We study the class of locally closed function clones whose unary operations are all injections that fix a given finite set of elements. For such a clone C, we prove that either there exists a uniformly continuous map from C to the clone of projections that preserves equations of height one and left composition with unary operations, or there is a canonical operation in C which is a Siggers operation modulo left composition with unaries. In the context of constraint satisfaction problems, this implies that every CSP whose constraint language is definable with parameters and equality is in P or NP-complete if and only if the Feder-Vardi conjecture for finite-domain CSPs holds. |
Fr., 20.11.2015, 13:00 Uhr, WIL/C/207 | Topologische Charakterisierung und endliche Repräsentation nominaler Mengen Albrecht Schmidt (Kolloquium zur Diplomarbeit, Betreuer: Jun.-Prof. M. Schneider) |
Fr., 13.11.2015, 13:15 Uhr, WIL/C/115 | Ratio Quantiles Daniel Gburek (Fak. Informatik) In this talk we show that so-called ratio quantiles for finite Markov chains with rewards can be efficiently computed. That is, the exact computation of optimal thresholds, which are almost surely or with positive probability exceeded by the ratio between two reward functions, can be done in polynomial time. We also provide polynomial-time algorithms solving related decision problems on ratio objectives. This is joint work with Christel Baier, Clemens Dubslaff, and Jana Schubert. |
Fr., 6.11.2015, 13:15 Uhr, WIL/C/206 | CSPs or Orientations of Trees - Computational Experiments on their Tractability via Polymorphisms Jana Fischer (Verteidigung der Diplomarbeit; Betreuer: Prof. Manuel Bodirsky) In der Theorie der Constraint-Satisfaction-Probleme (CSP) dreht sich derzeit alles um die Tractability Conjecture. Diese von Bulatov/Jeavons/Krokhin im Jahr 2000 aufgestellte Vermutung beschreibt eine algebraische Eigenschaft, von der man glaubt, dass sie ein CSP im Fall Ihres Vorliegens tractable ("leicht lösbar") und im Fall ihres Nichtvorliegens NP-vollständig ("schwer lösbar") macht. Für einige Klassen von CSPs ist die Richtigkeit der Vermutung bereits bewiesen worden, doch zu einem allgemeinen Beweis ist es noch ein weiter Weg. In meiner Arbeit habe ich mich auf experimentelle Weise mit der Tractability Conjecture für eine weitere Klasse von CSPs, definiert durch Orientierungen von Bäumen, beschäftigt. In diesem Vortrag stelle ich die Ergebnisse meiner Diplomarbeit vor. |
Fr., 30.10.2015, 13:15 Uhr, WIL/C/115 | A homogenisable fragment of existential second-order logic Manuel Bodirsky |
Fr., 23.10.2015, 13:15 Uhr, WIL/C/115 | Locally Moving Clones Robert Barham A locally moving group is a group that acts on a complete atomless Boolean algebra in a special way. These were introduced by M. Rubin to study reconstruction from automorphism groups. A locally moving clone is a clone where: 1. the group of invertible elements is a locally moving group; and 2. there are enough `algebraically canonical' elements. After defining these things fully, I will prove that every locally moving polymorphism clone has automatic homeomorphicity with respect to all polymorphism clones, and that if (Q,L) is a reduct of the rationals such that: 1. Aut(Q,L) is not the symmetric group; and 2. End(Q,L)=Emb(Q,L), then Pol(Q,L) is locally moving. |
Fr., 16.10.2015, 13:15 Uhr, WIL/C/115 | Lattices generated by the chip-firing game model Trung Van Pham Chip-firing game (also known under the name Sandpile model) is a discrete dynamical model which is defined on graphs. In this talk we will discuss about the lattices generated by this model, and give a necessary and sufficient condition for that class of lattices. Based on that condition we give a polynomial time algorithm for determining whether a given lattice is generated by a chip-firing game. |
Mi., 14.10.2015, 15:00 Uhr, WIL/C/115 | Über sofische Monoide Johannes Hüsam (Kolloquiumsvortrag zur Masterarbeit, Betreuer: Jun.-Prof. M. Schneider) |
Fr., 9.10.2015, 13:15 Uhr, WIL/C/115 | The Model Companions of Permutation Pattern Avoidance Classes Lisa Hutschenreiter (Kolloquium zur Masterarbeit, Betreuer: Prof. M. Bodirsky) |
Fr., 9.10.2015, 10:00 Uhr, WIL/C/115 | Topologische Charakterisierung und endliche Repräsentation nominaler Mengen Albrecht Schmidt (Kolloquium zur Diplomarbeit, Betreuer: Jun.-Prof. M. Schneider) |
Do., 8.10.2015, 13:15 Uhr, WIL/C/115 | CSPs of Orientations of Trees: Computational Experiments on their Tractability via Polymorphisms Jana Fischer (Kolloquium zur Diplomarbeit, Betreuer: Prof. M. Bodirsky) This is the inofficial talk of my Diploma thesis. |
Fr., 25.09.2015, 13:15 Uhr, WIL/C/115 | Pattern structures and their morphisms Lars Lumpe & Stefan Schmidt In 2001, Bernhard Ganter and Sergei Kuznetsov published the paper Pattern Structures and Their Morphisms, which started a research domain on its own. Here, a pattern structure consists of a map from a set of objects into a partially ordered set of patterns such that every subset of objects possesses a greatest common sub-pattern. Their investigation was inspired by methods from formal concept analysis. |
Fr., 11.9.2015, 13:15 Uhr, WIL/C/115 | Every simple compact semiring is finite Martin Schneider A Hausdorff topological semiring is called simple if every non-zero continuous homomorphism into another Hausdorff topological semiring is injective. A classical result due to Anzai and Kaplansky states that every compact Hausdorff topological ring is profinite, i.e., representable as a projective limit of finite discrete rings. Hence, every simple compact Hausdorff topological ring is finite. Of course, the profiniteness theorem does not generalize to arbitrary compact semirings: in fact, there are numerous examples of connected compact semirings, which therefore cannot be profinite. However, we show that any simple compact Hausdorff topological semiring is finite. |
Fr., 4.9.2015, 13:15 Uhr, WIL/C/115 |
The Countably Infinite Boolean Vector Space and Constraint Satisfaction Problems Francois Bossiere Given a relational structure Gamma, the problem CSP(Gamma) takes as an argument a primitive positive sentence phi and asks whether Gamma satisfies phi. Let (V ; +) be the countably infinite vector space over the two-element field. A first-order definable structure over (V ; +) with domain V is called a reduct of (V ; +). This talk presents a method combining universal algebra, model theory and Ramsey theory in order to classify the complexity of CSPs over reducts of (V ; +). |
Fr., 21.8.2015, 16:15 Uhr, WIL/C/129 | Zu formalen Kontexten mit gegebener Ferrers-k-Kodimension Anna Thurm (Verteidigung der Diplomarbeit, Betreuer: Prof. B. Ganter) |
Fr., 14.8.2015, 16:15 Uhr, WIL/C/129 | Automatic Construction of Implicative Theories for Mathematical Domains Artem Revenko Implication is a logical connective corresponding to the rule of causality "if ... then ...". Implications allow one to organize knowledge of some field of application in an intuitive and convenient manner. This thesis explores possibilities of automatic construction of all valid implications (implicative theory) in a given field. As the main method for constructing implicative theories a robust active learning technique called Attribute Exploration was used. Attribute Exploration extracts knowledge from existing data and offers a possibility of refining this knowledge via providing counter-examples. In frames of the project implicative theories were constructed automatically for two mathematical domains: algebraic identities and parametrically expressible functions. This goal was achieved thanks both pragmatical approach of Attribute Exploration and discoveries in respective fields of application. The two diverse application fields favourably illustrate different possible usage patterns of Attribute Exploration for automatic construction of implicative theories. |
Fr., 24.7.2015, 13:15 Uhr, WIL/C/115 | On simple compact topological semirings Jens Zumbrägel |
Fr., 17.7.2015, 13:15 Uhr, WIL/C/115 | Bipartite Kneser graphs are Hamiltonian, Dr. Torsten Muetze (ETH Zuerich) For integers k>=1 and n>=2k+1, the bipartite Kneser graph H(n,k) is defined as the graph that has as vertices all k-element and all (n-k)-element subsets of {1,2,...,n}, with an edge between any two vertices (=sets) where one is a subset of the other. It has long been conjectured that all bipartite Kneser graphs have a Hamilton cycle, i.e., a cycle that visits every vertex exactly once. The special case of this conjecture concerning the Hamiltonicity of the graph H(2k+1,k) became known as the 'middle levels conjecture' or 'revolving door conjecture', and has attracted particular attention over the last 30 years. One of the motivations for tackling these problems is an even more general conjecture due to Lovász, which asserts that in fact every connected vertex-transitive graph (as e.g. H(n,k)) has a Hamilton cycle (apart from five exceptional graphs). |
Fr., 3.7.2015, 13:15 Uhr, WIL/C/115 | Higher commutators: Results and open problems Dr. Nebojša Mudrinski (U Novi Sad) |
Fr., 19.6.2015, 13:15 Uhr, WIL/C/115 | Structures with a Maltsev Polymorphism Christoph Glinzer (Vorstellung der Bachelorarbeit; Betreuer: Manuel Bodirsky) Constraint Satisfaction Problems over the Integers with Successor Antoine Mottet Abstract: I will present a dichotomy result for the complexity of constraint satisfaction problems whose templates are first-order definable in (Z;succ), the integers with the successor function. This structure is neither finite nor omega-categorical, and therefore the classical universal algebraic approach cannot be used in this case. We will see how to adapt this approach in our setting, using the model-theoretic notion of saturation. This is joint work with Manuel Bodirsky and Barnaby Martin. |
Fr., 29.5.2015, 13:15 Uhr, WIL/C/115 | Profinite algebras and affine boundedness Martin Schneider Profinite algebras are topological algebras that are isomorphic to a projective limit of finite discrete algebras. In general this property concerns both the topological and algebraic characteristics of a topological algebra. However, for topological groups, rings, semigroups, and distributive lattices, profiniteness turns out to be a purely topological property as it is is equivalent to the underlying topological space being a Stone space, i.e. a totally disconnected compact Hausdorff space. |
Fr., 22.5.2015, 13:15 Uhr, WIL/C/115 | On the reconstructibility of functions from identification minors Erkko Lehtonen (University of Lisbon) We consider functions of several arguments from $A$ to $B$, i.e., mappings $f \colon A^n \to B$ for some $n \geq 1$. For any $I = \{i, j\} \subseteq \{1, \dots, n\}$ with $i < j$, let $f_I \colon A^{n-1} \to B$ be the function given by the rule $f_I(a_1, \dots, a_{n-1}) = f(a_1, \dots, a_{j-1}, a_i, a_j, \dots, a_{n-1})$ for all $a_1, \dots, a_{n-1} \in A$. (Note that $a_i$ occurs twice on the right side of the above equality: both at the $i$-th and the $j$-th position.) Such a function $f_I$ is called an \emph{identification minor} of $f$. We present some results -- both positive and negative -- and open problems concerning the following reconstruction problem: Is a function $f \colon A^n \to B$ uniquely determined, up to permutation of arguments, by the collection of its identification minors? A related open problem is to determine which functions have a unique identification minor. The speaker conjectures that for sufficiently large arity, the only functions with a unique identification minor are those which are 2-set-transitive or determined by the order of first occurrence, up to permutation of arguments. This talk is partly based on joint work with Miguel Couceiro and Karsten Schölzel. |
Fr., 8.5.2015, 13:15 Uhr, WIL/C/115 | Finding p-indecomposable Functions Artёm Revenko Parametric expressibility of functions is a generalization of expressibility via composition. All parametrically closed classes of functions form a lattice. For finite domains the lattice is shown to be finite, however straight-forward iteration over all functions is infeasible, and so far the indecomposable functions are only known for domains with two and three elements. In this work we show how p-indecomposable functions can be computed more efficiently by means of an extended version of attribute exploration - a robust active learning technique. Under certain assumptions it is possible to complete the lattice of parametrically closed classes of functions for a finite domain. |
Fr., 24.4.2015, 13:15 Uhr, WIL/C/115 | Complexity Bounds For Arithmetic Nets And Some Related Problems Thomas Olschewski (TU Dresden) Determining the number of rational operations it takes to evaluate polynomials is a classical problem of algebraic complexity theory. Many lower and (somewhat fewer) upper bounds have been derived since the early 1970s which differ in coefficient field K, set of operations (division free or not ...), cost measure (non-scalar, multiplicative, additive, time-space tradeoff ...). For several types of polynomials evaluation complexity has been determined up to some constant factor, for some even exactly. For algebraically closed fields K the known methods for deriving lower bounds are mostly of an algebraic nature. In case of the binary field, counting methods and advanced proof methods have been employed for deriving lower and upper bounds. Subject of this talk are methods for proving lower bounds for arithmetic nets and some more recent results. |
Fr., 17.4.2015, 13:15 Uhr, WIL/C/115 | Endomorphisms monoids of omega-categorical structures Michael Kompatscher (TU Wien) Two omega-categorical structures are bi-interpretable iff their automorphism groups are isomorphic as topological groups. For a lot of well-known omega-categorical structures this theorem still holds, if we ignore the topology. Is this true in general? The answer is no: In 1990 Evans and Hewitt constructed two omega-categorical structures with isomorphic, but not topologically isomorphic automorphism groups. In my talk I want to discuss their example and show that also the endomorphism monoids of the structures are isomorphic, but not topologically isomorphic. |
Mi., 1.4.2015, 14:00 Uhr, WIL/C/207 | Konstruktion und Validierung von Wissensstrukturen mit den Methoden der Formalen Begriffsanalyse Matthias Lange (Verteidigung der Diplomarbeit; Betreuer: Prof. B. Ganter) |
Fr., 27.3.2015, 13:15 Uhr, WIL/C/115 | Generated Groups, Shellability and Transitivity of the Hurwitz Action Henri Mühle (U Paris 7) Abstract: Let G be a group generated by a conjugation closed set A. There is a natural action of the braid group on k strands on the set of reduced A-decompositions of any group element of length k, the Hurwitz action. It can informally be described as ``shifting letters to the right, and conjugating as you go''. Whenever this action is transitive, we can deduce important geometric and representation-theoretic consequences. Moreover, in the given setting we can naturally define a subword order on G, and it is immediate the reduced A-decompositions of any group element are in bijection with the maximal chains in the principal order ideal generated by this element. Using this perspective, we present a new approach to proving the transitivity of the Hurwitz action, in that we establish a connection between the shellability of this subword order and the Hurwitz transitivity. This work, which is joint work with Vivien Ripoll from the University of Vienna, culminates in the observation that these two properties (whose proofs are in general far from being trivial) follow from a simple local criterion, namely the existence of a well-behaved total order of A. |
Mo., 23.3.2015, 13:00 Uhr, WIL/C/115 | translation invariant max-closed semilinear constraints over the reals, and connections to stochastic games Marcello Mamino |
Fr., 13.3.2015, 14:00 Uhr, WIL/C/129 | Forbidden Permutation Patterns and Constraint Satisfaction Problems Verteidigung der Diplomarbeit von Tom Hanika (Betreuer: Manuel Bodirsky) |
Fr., 20.2.2015, 13:15 Uhr, WIL/C/115 | Forbidden Permutation Patterns and Constraint Satisfaction Problems Tom Hanika |
Do., 12.2.2015, 13:15 Uhr, WIL/C/115 | GAP - Groups, Algorithms, Programming - a System for Computational Discrete Algebra Sven Reichard |
Fr., 6.2.2015, 13:15 Uhr, WIL/C/115 | Group extensions as binary relation orbifolds Tobias Schlemmer |
Fr., 30.1.2015, 13:15 Uhr, WIL/C/102 | Extremely amenable groups Martin Schneider |
Fr., 16.1.2015, 13:15 Uhr, WIL/C/102 | Some enumerative and lattice theoretic aspects of islands and related investigations Eszter K. Horvath (Szeged) |
Fr., 9.1.2015, 13:15 Uhr, WIL/C/102 | Centralizer clones Reinhard Pöschel |
Fr., 19.12.2014, 13:15 Uhr, WIL/C/207 | Homomorphic Signatures for Network Coding Johannes Greiner |
Fr., 12.12.2014, 13:15 Uhr, WIL/C/207 | The Discrete Logarithm Problem in finite fields of small characteristic Jens Zumbrägel |
Fr., 5.12.2014, 13:15 Uhr, WIL/C/102 | Homomorphic Signatures for Network Coding Johannes Greiner |
Fr., 21.11.2014, 13:15 Uhr, WIL/C/102 | On an algorithmic problem of weighted Markov chains Daniel Krähmann (Fak. Informatik) |
Fr., 14.11.2014, 13:15 Uhr, WIL/C/102 | Galois theory for semiclones Mike Behrisch (U Linz) |
Fr., 7.11.2014, 13:15 Uhr, WIL/C/102 | Reconstructing cycle-free partial orders from their abstract automorphism groups Robert Barham |
Fr., 17.10.2014, 13:15 Uhr, WIL/C/102 | Concepts of Connection in Directed Hypergraphs Paul Mittelstädt |