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

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Organisatoren: Raman Sanyal und Thorsten Theobald

Datum Sprecher / Thema

16.07.2024 Marc Nuber
Perfekte Graphen und Summen von Quadraten

09.07.2024 Boulos El Hilany (TU Braunschweig)
Non-properness set of a tropical polynomial map

Abstract: A tropical polynomial map is a piecewise-linear map between real Euclidean spaces. These maps are increasingly studied for their applications in ReLU neural networks. They represent a degeneration of classical polynomial maps between over valued fields. Accordingly, some of the pertinent classical topological invariants can be translated to polyhedral ones.
In this talk, I will define the tropical analogue of the non-properness set of polynomial maps. This is the set of points at which the preimage has an extra solution "at infinity". Studying the non-properness set is beneficial to applications such as enhancing cylindrical algebraic decomposition algorithms from semi-algebraic geometry. The tropical non-properness set, on the other hand, is useful in describing the polyhedral geometry of piecewise-linear maps. I will present a correspondence theorem that relates the classical non-properness set to its tropical analogue, and illustrate a purely combinatorial procedure to compute it.

18.06.2024 Arnau Padrol (Universitat de Barcelona)

Abstract: Motivated by Galashin's poset associahedra, we introduce oriented building sets defined on the ground set of an oriented matroid, and their associated acyclic nested complexes, which are nested complexes fulfilling an additional acyclicity condition. Feichtner and Kozlov defined building sets and nested complexes for arbitrary meet semi-lattices, and acyclic nested complexes are those associated to the Las Vergnas face lattices of acyclic oriented matroids. They can be realized via stellar subdivisions, which provides a polytopal realization whenever the original oriented matroid is realizable.  When
the original oriented matroid is the graphical matroid of a Hasse diagram, we recover this way Galashin's realization of poset associahedra as an iterated stellar subdivision of an order polytope. Since the las Vergnas lattices are atomic, acyclic nested complexes can be embedded into (boolean) nested complexes. For realizable oriented matroids, we provide a novel polytopal construction that realizes this embedding geometrically by exhibiting acyclonestohedra as sections of
certain (boolean) nestohedra.

This is joint work with Chiara Mantovani and Vincent Pilaud.

11.06.2024 Merima Mustafic
Nash-Gleichgewichte in Bimatrixspielen und die Kombinatorik von Polytopen

07.05.2024 Aryaman Jal ( KTH Royal Institute of Technology Stockholm )
Polyhedral combinatorics of bisectors and bisection fans

Abstract: Every symmetric convex body induces a norm on its affine hull. The object of our study is the bisector of two points with respect to this norm.
A topological description of bisectors is known in the 2 and 3-dimensional cases and recent work of Criado, Joswig and Santos (2022) expanded this to a fuller characterisation of the geometric, combinatorial and topological properties of the bisector.  A key object introduced was the bisection fan of a polytope which they were able to explicitly describe in the case of the tropical norm. We will discuss the bisector as a polyhedral complex, introduce the notion of bisection cones and give combinatorial descriptions of the bisection fan corresponding to other polyhedral norms. This is joint work with Katharina Jochemko.

06.02.2024 Moritz Grillo ( TU Berlin )
Topological Expressivity of ReLU Neural Networks

07.11.2023 Christoph Hertrich ( Goethe Universität )
How to Use Polyhedral Theory to Understand Neural Networks

26.09.2023 Laura Kossytorz
Multi-Splits of Point Configurations in the Plane

06.06.2023 Kristina Wicke ( New Jersey Institute of Technology )
Mathematical approaches to biodiversity conservation: some recent developments and challenges in phylogenetic diversity research

23.05.2023 Eugen Cernomazov
Basis-Austauschgraphen von induzierten Fahnenmatroiden

16.05.2023 Lorenzo Vecchi ( Universität Bologna )
Categorical valuative invariants of matroids

Jacob Matherne ( MPI und Universität Bonn )
Polynomials in combinatorics and representation theory

02.05.2023 Katherina von Dichter (TU München und BTU Cottbus)
The diameter-width-ratio for complete and pseudo-complete sets

25.04.2023 Linus Eschmann
Der Potenzkegel in der konvexen Optimierung (Bachelor-Abschlussvortrag)

18.04.2023 Christopher Lorenz:
Insider trading in discrete time Kyle games

28.02.2023 Nadine Defoßa
Sublineare Kreise in der restringierten Optimierung von Signomen (Master-Abschlussvortrag)


Benjamin Schröter 
Valuative invariants for large classes of matroids



Jan Stricker
Über die Geometrie und Kombinatorik von 2-level Polytopen
Jakob Dany
Verallgemeinerte Bipermutaeder
Irem Portakal (TU München):
Nonlinear algebra in game theory

Marlene Meißner:
Beziehungen zwischen stabilen Polynomen und Matroidtheorie

Marcel Wack
Restringierte signomiale Optimierung mittels eines SAGE-Positivstellensatzes

30.08.2022 David Zimmermann
Optimale Punkte konditionaler SAGE-Zertifikate in der signomialen Optimierung

19.07.2022 Federico Castillo (Universidad Católica de Chile)
Polyhedral bases for deformation cones

12.07.2022 Constantin Ickstadt
Eine semidefinite Verallgemeinerung von Bimatrixspielen


"Frankfurt-Darmstadt Afternoon on Optimization"
Venkat Chandrasekaran (California Institute of Technology)
Fitting Tractable Convex Sets to Support Function Data

Max Klimm (TU Berlin):
Optimal Information Design for Congested Networks

21.06.2022 Doppelvortrag:

Katharina Jochemko (KTH Stockholm @ Frankfurt)
The Eulerian transformation

Darij Grinberg (Drexel University @ Bochum)
The one-sided cycle shuffles in the symmetric group algebra

14.06.2022 Bastian von Harrach (Goethe-Universität)
Von inversen Problemen in partiellen Differentialgleichungen zu semidefiniter Optimierung

07.06.2022 Germain Poullot (Sorbonne Université)
Deformation cones of hypergraphic polytopes

24.05.2022 Doppelvortrag:

Luis Ferroni (KTH Stochholm @ Bochum)
Valuative invariants for large classes of matroids

Lorenzo Venturello (KTH Stockholm @ Frankfurt)
Gorenstein algebras from simplicial complexes

17.05.2022 Andrés Vindas Meléndez (MSRI/Berkeley)
Ehrhart Theory of Paving and Panhandle Matroids (Abstract)

19.04.2022 Niklas Lütjeharms
Geometrie und Kombinatorik von Max-Slope-Pivotpolytopen

05.04.2022 Jonas Ellwanger
Nichtnegative Signome mit wenigen negativen Termen

15.02.2022 Frederic Matter (TU Darmstadt)

Sparse Recovery Under Side Constraints Using Null Space Properties (Abstract)

08.02.2022 Gaku Liu (Uni Washington) 
Unimodular triangulations of sufficiently large dilations (Abstract)

01.02.2022 Lukas Kühne (Uni Bielefeld)

Geometry of Flag Hilbert-Poincaré series (Abstract)

25.01.2022 Philip Dörr (Magdeburg)

Extreme Values of Permutation Statistics in Suitable Triangular Arrays (Abstract)

07.12.2021 Mariel Supina (KTH)
The Universal Valuation for Coxeter Matroids (Abstract)

30.11.2021 Georg Loho (Twente)

Generalized permutahedra and complete classes of valuated matroids (Abstract)

23.11.2021 Laura Escobar (WUSL)

Determining the complexity of Kazhdan-Lusztig varieties (Abstract)

16.11.2021 Jesus de Loera (University of California)

Stochastic Tverberg-type theorems and their relevance in Machine Learning and Statistical Inference (Abstract)


Alexander Black (University of California, Davis)
Polyhedral Geometry of Pivot Rules (Abstract)


Christian Krattenthaler (Universität Wien)
Reciprocity between Dyck paths and alternating sequences - heaps, orthogonal polynomials, … (Abstract)

06.07.2021 Sebastian Debus (UiT - The Arctic University of Norway)

Higher Specht polynomials and sums of squares (Abstract)

29.06.2021 Ralph Morrison (Williams College)

Tropically planar graphs: counting and constraints (Abstract)

22.06.2021 Eva Philippe (École Normale Supérieure de Paris)

Sweep polytopes, lineup polytopes, and generalized exclusion principle in quantum physics (Abstract)

15.06.2021 Sven Geserick
Multivariate Matching-Polynome

08.06.2021 Sophie Rehberg (FU Berlin)

Combinatorial reciprocity theorems for generalized permutahedra, hypergraphs, and pruned inside-out polytopes (Abstract)

25.05.2021 Henri Mühle (TU Dresden)

Posets from Polytopes and Refined Face Enumeration (Abstract)


11.05.2021 Dominik Sorg
Konvexe Ecken, Spiegelungsgruppen und das Mahler-Volumen

04.05.2021 Adriana Knop
Summen nichtnegativer Kreispolynome und reguläre Unterteilungen



Mahsa Sayyary (Goethe-Universität)

Real algebraic geometry of plane curves