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Institut für Mathematik
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Oberseminar Diskrete Mathematik, Geometrie und Optimierung

Termin und Ort:

Dienstags, 16 c.t., Raum 711 gr., Robert-Mayer-Str. 10

Im Falle virtueller Vorträge wird der jeweilige Link über die Mailingliste bekanntgegeben. Bei Interesse Email an die Organisatoren.


Veranstalter: 

Raman Sanyal und Thorsten Theobald

Diskrete Mathematik, Geometrie und Optimierung

Jan 16 2026
14:15

Freitag, 14 c.t., Raum 711 gr., Robert-Mayer-Str. 10

Bernd Sturmfels: Maxout Polytopes- SONDERTERMIN

MPI Leipzig

Abstract: Maxout polytopes are defined by feedforward neural networks with maxout activation function and non-negative weights after the first layer. We characterize the parameter spaces and extremal f-vectors of maxout polytopes for shallow networks, and we study the separating hypersurfaces which arise when a layer is added to the network. We also show that maxout polytopes are cubical for generic networks without bottlenecks. Joint work with Andrei Balakin, Shelby Cox, Georg Loho.

Diskrete Mathematik, Geometrie und Optimierung

Dez 10 2025
14:15

Raum 711 gr., Robert-Mayer-Str. 10

Arne Riester: Summen nichtnegativer Kreispolynome und der algebraische Rand

Master-Abschlussvortrag

Diskrete Mathematik, Geometrie und Optimierung

Dez 9 2025
16:15

Raum 711 gr., Robert-Mayer-Str. 10

Prof. Elias Tsigaridas: Positivity certificates for multivariate polynomials

Sorbonne Université 

Abstract: We present mathematical, algorithmic, and complexity results on defining and computing SOS certificates of positivity for (multivariate) polynomials (in n >= 1 variables) with  rational coefficients, that are positive over R^n. 

Joint work(s) with Matias Bender, Chaoping Zhu, and Khazhgali Kozhasov.


Diskrete Mathematik, Geometrie und Optimierung

Okt 14 2025
16:15

Raum 711 gr., Robert-Mayer-Str. 10

Sandra Pejic: Varianten zur Reduktion von linearer Optimierung auf Nullsummenspiele

Master-Abschlussvortrag

Diskrete Mathematik, Geometrie und Optimierung

Sep 29 2025
14:15

Raum 711 gr., Robert-Mayer-Str. 10

Elvira Bunjaku: Maximale Paare stabiler Mengen in Graphen

Master-Abschlussvortrag

Diskrete Mathematik, Geometrie und Optimierung

Jul 1 2025
16:15

Raum 711 gr., Robert-Mayer-Str. 10

Martin Winter: Adjoint degrees and scissors congruence for polytopes -  joined work with Tom Baumbach, Ansgar Freyer and Julian Weigert

TU Berlin

Abstract: Hilbert's Third Problem asks whether for any two (3-dimensional) polytopes there is a way to cut the first one into finitely many pieces and rearrange them to obtain the second one (that is, we ask whether the polytopes are "scissors congruent"). Its resolution by Max Dehn (with a negative answer) marks the beginning of valuation theory, which to this day provides often one of the most elegant approaches to problems in the geometric theory of polytopes. In this talk we take a look at a particular valuation of recent interest - the canonical form - and we shall explore what it can teach us about scissors congruence for polytopes. It will turn out that the degree of the the so-called adjoint polynomial is a fundamental parameter in this context. We investigate the polytope classes defined by their adjoint degrees.

Diskrete Mathematik, Geometrie und Optimierung

Jun 3 2025
16:15

Raum 711 gr., Robert-Mayer-Str. 10

Prof. Sudhir Ghorpade: Counting zeros of multivariate polynomials over finite fields, Extremal Combinatorics, and Coding Theory

Indian Institute of Technology, Bombay


Abstract: It is elementary and well known that a nonzero polynomial in one variable of degree d with
coefficients in a field F has at most d zeros in F. It is meaningful to ask similar questions for
systems of several polynomials in several variables of a fixed degree, provided the base field
F is finite. These questions become particularly interesting and challenging when one restricts
to polynomials that are homogeneous, and considers zeros (other than the origin) that are
non-proportional to each other. More precisely, we consider the following question:


Given a system of a fixed number of linearly independent homogeneous polynomial equations of
a fixed degree with coefficients in a fixed finite field F, what is the maximum number ofcommon zeros they can have in the corresponding protective space over F?


The case of a single homogeneous polynomial (or in geometric terms, a projective hypersurface)
corresponds to a classical inequality proved by Serre in 1989. For the general case, an elaborate
conjecture was made by Tsfasman and Boguslavsky, which was open for almost two decades.
Recently significant progress in this direction has been made, and it is shown that while the
Tsfasman-Boguslavsky Conjecture is true in certain cases, it can be false in general. Some new
conjectures have been proposed, and these have been proved in several cases. Results from extremal combinatorics, such as Kruskal-Katona theorem and Clements-Lindstrǒm theorem play a useful role here.


We will give a motivated outline of these developments.Connections to coding  theory or to the 
problem of counting points of sections of Veronese varieties by linear  subvarieties of a fixed dimension 
will also be outlined.  This talk is mainly based on joint works with Mrinmoy Datta and with Peter
Beelen and Mrinmoy Datta.      




Diskrete Mathematik, Geometrie und Optimierung

Mai 27 2025
16:15

Raum 711 gr., Robert-Mayer-Str. 10

​Basile Orth: Die Polyedergeometrie von 4x4-Bimatrixspielen   

Bachelor-Abschlussvortrag

Diskrete Mathematik, Geometrie und Optimierung

Mai 13 2025
16:15

Raum 711 gr., Robert-Mayer-Str. 10

Prof. Dr. Andreas Löhne: Computing all Nash equilibria of low-rank bi-matrix games

Friedrich-Schiller-Universität-Jena

Abstract: Low-rank bi-matrix games are transformed into typically smaller bi-matrix games, where the constraints for both players are arbitrary polytopes rather than simplices. These constrained bi-matrix games, also called polytope games, are studied, in particular, all Nash equilibria are computed using bensolve, a solver for multi-objective linear programs. The connection between the Nash equilibria of the original game and the smaller
polytope game is investigated.

Co-Authors: Zachary Feinstein, Birgit Rudloff

Diskrete Mathematik, Geometrie und Optimierung

Feb 11 2025
16:15

Dr. Sebastian Debus: Symmetric function inequalities and superdominance

TU Chemnitz

Abstract: In this talk we consider inequalities of homogeneous symmetric functions, i.e., inequalities that hold in any number of variables. Therefore, we study the cones of symmetric sums of squares and nonnegative functions for fixed degrees. In polynomial optimization one is interested in the set-theoretic differences between the cones of sums of squares and nonnegative polynomials. A theorem of V. Kostov allows us to understand the extremal
rays of the cones for symmetric quartics. We find a symmetric quartic that is nonnegative but not a sum of squares in any non-trivial number of variables. To analyze higher degrees we investigate the tropicalization of the cones and discover a hidden combinatorial structure that can also be naturally expressed in terms of the superdominance order. This order turns out to completely characterize the valid inequalities of products of power sums on the nonnegative orthant.
This is joint work with J. Acevedo, G. Blekherman and C. Riener.