Clemens Brüser

Conferences

Mathematics

SIAM Conference on Applied Algebraic Geometry (AG25), Madison, Wisconsin, 07.-11.07.2025.

LAW '25, 9th Linear Algebra Workshop, Portorož, 02.-06.06.2025.

Combinatorial Synergies East, Max-Planck-Institute for Mathematics in the Sciences, 19.-21.03.2025.

Moments, Non-Negative Polynomials, and Algebraic Statistics, Winter School, University of Konstanz, 17.-21.02.2025.

Real Algebraic Geometry and Hodge Theory, Summer School, TU Dresden, 09.-13.09.2024.

• Editor of lecture notes of the summer school (in preparation; joint with Lorenzo Baldi, Dmitrii Pavlov, David Sawall)

MEGA - Effective Methods in Algebraic Geometry, Max-Planck-Institute for Mathematics in the Sciences, Leipzig, 29.07.-02.08.2024.

MoPAT - Moments and Polynomials: Applications and Theory, University of Konstanz, 11.-14.03.2024.

Let's get Real, Max-Planck-Institute for Mathematics in the Sciences, Leipzig, 07.-08.06.2023.

New Directions in Real Algebraic Geometry, Mathematisches Forschungsinstitut Oberwolfach, 19.-24.03.2023.

• Reporter of the Oberwolfach Report 15/2023.

Macaulay2 Bootcamp, Max-Planck-Institute for Mathematics in the Sciences, Leipzig, 13.-14.12.2022.

Latin

Sapiens Ubique Civis VIII, Szeged, 01.-03.09.2021.

Talks

Mathematics

(Positive) Real Determinantal Representations of Quartic Curves, Oberseminar der Reelle Algebra und Geometrie, Universität Konstanz, 28.11.2025.

Smoothness and Determinantal Representations of Adjoint Hypersurfaces, Math Seminar at CSBD, CSBD Dresden, 20.11.2025.

Quadratic Determinantal Representations of Positive Polynomials. SIAM Conference on Applied Algebraic Geometry (AG25), Madison, Wisconsin, 07.-11.07.2025.

Determinantal Representations of Real Positive Polynomials. LAW '25, 9th Linear Algebra Workshop, Portorož, 02.-06.06.2025.

Quadratic Determinantal Representations of Positive Polynomials. Institute of Algebra at University of Innsbruck, research stay 07.-08.11.2024.

Quadratic Determinantal Representations of Positive Polynomials. MoPAT - Moments and Polynomials: Applications and Theory, University of Konstanz, 11.-14.03.2024.

What is ... a semi-algebraic set? Planck Institute of Molecular Cell Biology and Genetics, 08.03.2024.

Real root counting algorithms. Let's get Real, Max-Planck-Institute for Mathematics in the Sciences, Leipzig, 07.-08.06.2023.

Positive Semidefinite Quadratic Determinantal Representations. Geometry Seminar/Graduate Lectures TU Dresden, 16.05.2023.

Positive Semidefinite Determinantal Representations. Dresden-Leipzig-Seminar Algebra und Geometrie, Leipzig, 28.04.2023.

Latin

The choir in Agamemnon suimet victor by Joseph Resch. Sapiens Ubique Civis VIII, Szeged, 01.-03.09.2021.

Posters Presentations

Mathematics

Adjoints of Polytopes: Determinantal Representations and Smoothness. Computations in Algebraic Geometry: Complex, Real, and Tropical, ETH Zürich, 25.-29.08.2025.

Mathematics

Papers

B. C., Weigert Julian: Geometry of Adjoint Hypersurfaces for Polytopes [arXiv preprint: 2511.13537].

B. C., Kummer Mario, Pavlov Dmitrii: Adjoints of Polytopes: Determinantal Representations and Smoothness, International Mathematics Research Notices 2026/2. [arXiv preprint: 2507.01672].

B. C., Kummer Mario: (Positive) Quadratic Determinantal Representations of Quartic Curves and the Robinson Polynomial, Linear Algebra and its Applications 728, 2026, 232-262. [arXiv preprint: 2412.02319].

Theses

Quadratic Determinantal Representations of Nonnegative Ternary Polynomials. Dissertation, Technical University Dresden, 2026.

Quantifier Elimination in Matrix Algebras. Master thesis, University of Innsbruck, 2022.

Reviews

Review: Blekherman Grigoriy, Dunbar Alex: A topological approach to simple descriptions of convex hulls of sets defined by three quadrics, SIAM Journal on Applied Algebra and Geometry 9/2, 2025, 310-342.

Review: Han Kangjin, Moon Hyunsuk: A Family of Explicit Waring Decompositions of a Polynomial, Journal of the Korean Society for Industrial and Applied Mathematics 27/1, 2023, 1-22.

Latin

Papers

Zum Chor in Joseph Reschs Agamemnon suimet victor, Humanistica Lovaniensia 73, 2024, 611-631.

Mathematics and Panegyric. The Problema Austriacum by Albert Curtz, LIAS 2021/1, 35-61.

Theses

Albert Curtz: „Problema Austriacum”. Text mit Einleitung, Übersetzung, Anmerkungen und didaktischen Überlegungen, Diploma thesis, University of Innsbruck, 2019.

In the past, I supervised exercise classes in the following subjects at the University of Innsbruck and the University of Freiburg:

•  Linear Algebra 1-2
• Analysis 1
• Algebra und Number Theory
• Commutative Algebra
• Elementary Geometry

For me, the connection between Latin studies and Mathematics is primarily of historic interest, which is rooted in the following reasons.

• For the most part of modern time (~ 1450-1750), Latin was the language of science. Many groundbreaking results were first published in Latin. Jakob Bernoulli published his ideas on probability theory in 1713 in the treatise Ars Coniectandi. Other famous examples for the significance of the Latin language are Gauß' Disquisitiones Arithmeticae (1801) or the diverse works of Leonhard Euler. In 1889 still, Giuseppe Peano published his Arithmetices Principia in Latin. These works and ideas cannot be read in their original form without knowledge of the Latin language.
• More general one should ask about the history of mathematics. Mathematics thrives on its inherent logic and few results appear out of the blue, but rather are natural in its modern phrasing after being inaccessible for a long time. Therefore their genesis is of great interest. From this perspective, many recent and elaborate results can be motivated. As an example, axiomatic geometry can be developed purely from incidence realtions and related concepts. But its origins lie in Euclid's Elements - along with the extensive discussion (often in Latin) of the famous parallel postulate in the subsequent centuries. Based on this approach, today's axioms are just a natural abstraction of the intuition in ancient times. This natural process is traced very well in the book Geometry: Euclid and Beyond (Robin Hartshorne, 2000).
• Beyond scientific results studying the history of mathematics also offers a glimpse into the thoughts and minds of the people establishing them. 
• Neo-Latin mathemtaical treatises are interesting in and of themselves, precisely because they do not conform to today's norms on mathematical literature. They often convey a completely different intent, but do so in the language of Mathematics. As an example, in a New Year's letter to a friend, Johannes Kepler writes about sexangular snowflakes (De nive sexangula, 1611), but also states Kepler's Conjecture, which has been proven only recently.

Nihil equidem magis opto, quam ut iis, quibus scientiarum incrementa cori sunt, placeant, quae vel hactenus desiderate explent, val aditum ad nove aperiunt. (C.F. Gauß, Disquisitiones Arithmeticae, p. XII)
And I desire nothing more than that all those, to whom the promotion of scientific knowledge is important, will find joy in these ideas, which either solve problems that had been unsolved so far, or which show the way to new insight.