Goethe-Universität

Aktuelle Vorträge: Oberseminar Diskrete Mathematik, Geometrie und Optimierung

Archiv: Oberseminar-DIGO - Diskrete-Mathematik -Geometrie und Optimierung (2021 - 2024)

Datum	Sprecher / Thema


03.12.2024	Prof. Dr. Anand Srivastav (Universität Kiel und Goethe-Universität Frankfurt) The k-Hamilton-Cycle Maker - Breaker Game Abstract: We study the Maker-Breaker k-Hamilton cycle game, k an integer constant, on the complete graph on n nodes, where the aim of Maker is to build k Hamilton cycles, while Breaker wishes to prevent it. This is a two person perfect information game on a finite board, namely the edges of the complete graph. The game is played under the following rules. Maker and Breaker alternately choose edges of the complete graph not taken by any of the players so far. Maker starts, and chooses one edge of the complete graph. Thereafter, Breaker may choose upto b free edges. The game ends without a draw latest after all edges have been choosen by the two players. In such games, the challenging problem is to find the threshold bias b, an integer, so that for b < b there is a winning strategy for Maker, but for b > b* Breaker has a winning strategy, and to present such strategies. Krivelevich (J. AMS 2010) determined in a breakthrough paper, extending foundational work of Chvatal and Erdös (1978), the asymptotially exact threshold bias to be (1 - o(1))n/ln(n) for k = 1. Brüstle, Clusiau, Narayan, Ndiaye, Reed & Seamone (2023) showed that for k = 1 the game can be won by Maker in at most n + Cn/sqrt(ln(n)) many rounds, C a constant,if b < n/ln(n) - cn/ln(n)^{3/2}. This is an asymptotically optimal round complexity. The game for k > 1 is much more complicated because we must ensure edge-disjointness of the k Hamilton cycles, while these cycles are competing for favorable edges. We show that Maker wins the k-Hamilton cycle game, if b < n/ln(n) - cn/ln(n)^{3/2}, in at most kn + c'n/sqrt(ln(n)) rounds, c, c' being constants depending on k only. This round complexity is asymptotically optimal as well. (joint work with Jan Geest, Department of Mathematics, Kiel University )
12.11.2024	Nate Bottmann (MPI Bonn) The role of compactified configuration spaces in categorical symplectic geometry Abstract: Categorical symplectic geometry studies a suite of algebraic structures, including the Fukaya category and symplectic cohomology. These structures are defined by counts of J-holomorphic maps from decorated Riemann surfaces into symplectic manifolds. I will begin by explaining how the operadic structure of the configuration spaces of domains inform the nature of the resulting algebraic invariants. I will then explain the central object in my research program: the Symplectic (A-infinity,2)-Category, which unites symplectic manifolds and their Fukaya categories into a single structure. The relevant configuration spaces here are called "2-associahedra". In recent work with Backman and Poliakova, we produced fan realizations of the 2-associahedra (moreover, the n-associahedra). I hope to convince you that configuration spaces of domains are an important and underappreciated link between symplectic geometry and combinatorics, which can produce new math in both directions.
05.11.2024	Christopher Voll (Universität Bielefeld) Hall-Littlewood polynomials, affine Schubert series, and lattice enumeration Abstract: In this talk, I would like you to meet Hall-Littlewood-Schubert series, a new class of multivariate generating functions. Their definition features semisimple Young tableaux and polynomials resembling the classical Hall-Littlewood polynomials. Their intrinsic beauty notwithstanding, I will give you three reasons why you might care about these fascinating functions: first, an affine version of classical Schubert calculus; second, a new formula for Macdonald's formula for the Hecke series for symplectic groups; third, combinatorially defined integral quiver representations. This is joint work with Joshua Maglione. I will explain things from scratch, assuming no familiarity with the advanced technical vocabulary used in this abstract.
16.07.2024	Marc Nuber Perfekte Graphen und Summen von Quadraten (Bachelor-Abschlussvortrag)
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) Acyclonestohedra 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 (Master-Abschlussvortrag)
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 (Bachelor-Abschlussvortrag)
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 (Bachelor-Abschlussvortrag)
16.05.2023	Lorenzo Vecchi ( Universität Bologna ) Categorical valuative invariants of matroids
09.05.2023	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)
07.02.2023	Benjamin Schröter Valuative invariants for large classes of matroids
13.12.2022	Doppelvortrag Jan Stricker Über die Geometrie und Kombinatorik von 2-level Polytopen (Bachelor-Abschlussvortrag) Jakob Dany Verallgemeinerte Bipermutaeder (Bachelor-Abschlussvortrag)
25.10.2022	Irem Portakal (TU München): Nonlinear algebra in game theory
04.10.2022	Marlene Meißner: Beziehungen zwischen stabilen Polynomen und Matroidtheorie (Bachelor-Abschlussvortrag)
12.09.2022	Marcel Wack Restringierte signomiale Optimierung mittels eines SAGE-Positivstellensatzes (Master-Abschlussvortrag)
30.08.2022	David Zimmermann Optimale Punkte konditionaler SAGE-Zertifikate in der signomialen Optimierung (Master-Abschlussvortrag)
19.07.2022	Federico Castillo (Universidad Católica de Chile) Polyhedral bases for deformation cones
12.07.2022	Constantin Ickstadt Eine semidefinite Verallgemeinerung von Bimatrixspielen (Master-Abschlussvortrag)
24.06.2022,	"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 (Master-Abschlussvortrag)
05.04.2022	Jonas Ellwanger Nichtnegative Signome mit wenigen negativen Termen (Bachelor-Abschlussvortrag)
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)
26.10.2021	Alexander Black (University of California, Davis) Polyhedral Geometry of Pivot Rules (Abstract)
26.10.2021	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 (Bachelor-Abschlussvortrag)
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) https://tu-dresden.de/mn/math/algebra/das-institut/beschaeftigte/henri-muehle/ressourcen/dateien/talks/guf_refined.pdf
11.05.2021	Dominik Sorg Konvexe Ecken, Spiegelungsgruppen und das Mahler-Volumen (Master-Abschlussvortrag)
04.05.2021	Adriana Knop Summen nichtnegativer Kreispolynome und reguläre Unterteilungen (Master-Abschlussvortrag)
13.04.2021	Mahsa Sayyary (Goethe-Universität) Real algebraic geometry of plane curves

Darmstadt-Frankfurt Afternoon on Optimization (2019)

Archiv: Vorträge Diskrete Mathematik, Geometrie und Optimierung (2019-2024)