
Seminar Schedule
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please email: timhaga "at" math.unibremen.de
Note: times are meant sharp ('s.t.')
Talks
 Computation of the Alexander Polynomial of Projective Plane Curves
 Alexandru Dimca (Université Nice Sophia Antipolis)
March 29, 2017, 10:30 am, MZH 7200
Click for the abstract
For a reduced plane curve C in the complex projective space, its Alexander polynomial is the characteristic polynomial of the monodromy operator acting on the first cohomology of the corresponding Milnor fiber. In this talk I will report on joint results with Gabriel Sticlaru about the computation of this polynomial. When all the singularities of C are weighted homogeneous, e.g. for line arrangements, the algorithm is much faster due to a recent result by Morihiko Saito.
 Toric Degenerations of Flag Varieties via NewtonOkounkov Bodies
 Linear Degenerate Flag Varieties
 Ghislain Fourier (Universität Hannover)
March 15, 2017, 12:30 pm, MZH 7200
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The flag variety is probably one of the bestunderstood objects in geometric representation theory. There are several descriptions, for example using Plücker relations or linear algebra or highest weight orbits in representation theory or Schubert varieties to name just a few. In 2011, Evgeny Feigin introduced the degenerate flag variety as the highest weight orbit of a PBW degenerate highest weight module. This is a quite natural construction from the view point of representation theory. How can one see this construction using the other approaches to the flag variety? I'll explain the latest results on this. Further, I'll characterize and analyze all degenerations of the flag variety that can be obtained using the linear algebra approach and where to find in here the representation theory approach and the Schubert variety approach. This is joint work with G. CerulliIrelli, X.Fang, E.Feigin, M.Reineke.
 The Universal Family of Marked Poset Polytopes
 Christoph Pegel (Universität Bremen)
February 9, 2017, 1:00 pm, MZH 7200
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After motivating the study of marked poset polytopes as a generalization of poset polytopes as well as Gelfand–Tsetlin and Feigin–Fourier–Littelmann–Vinberg polytopes from representation theory, we introduce a continuous family of marked poset polytopes, parametrized by a unit hypercube, whose extremal cases include all marked chainorder polytopes, in particular the marked order and the marked chain polytope. The universal family continuously interpolates between all of these and combinatorial types stay constant along relative interiors of faces of the cube. We present a common polyhedral subdivision for all polytopes in the family. The vertices of the subdivision coincide with the vertices of the polytope in the generic case, i.e. for interior points of the parametrizing cube. We hope to gain better knowledge on the face structure of all marked poset polytopes by studying the generic case and how it degenerates. This is joint work with Xin Fang, Ghislain Fourier and JanPhilipp Litza.
 Problems around hyperplane arrangements (Part 2)
 Masahiko Yoshinaga (Universität Bremen)
January 5, 2017, 10:15 am, MZH 7200
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Coamoeba, phase matroid, and hyperfield. First I recall coamoeba of a hyperplane arrangement, and prove that the complement of an arrangement is homotopy equivalent to its coamoeba. Then we discuss the above "combinatorial decision problem" from the viewpoint of recently emerging "matroids over hyperfields".
 Abelian Tropical Geometry II
 Problems around hyperplane arrangements (Part 1)
 Masahiko Yoshinaga (Universität Bremen)
December 22, 2016, 10:15 am, MZH 7200
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Combinatorial decision problems in arrangements. I first recall the classical problem "what kind of topological invariants are combinatorially determined?", and then discuss briefly the comparison between the Aomoto complex (which is combinatorially detemined) and local system cohomology (unknown whether combinatorial or not). I also formulate a purelycombinatorial problem on words which indicates word solvability of arrangements fundamental groups.
 Das Ehrhartpolynom von Gitterpolytopen
 Christopher de Vries (Universität Bremen)
December 13, 2016, 9:00 am, MZH 7260
 Hyperplane arrangements and Hessenberg varieties
 Takuro Abe (Kyushu University, Japan)
December 8, 2016, 12:30 pm, MZH 7200
 Abelian Tropical Geometry
 The Degree of SO(n)
 Madeline Brandt (UC Berkeley/ MPI Leipzig)
November 22, 2016, 9:00 am, MZH 7200
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In this talk, I will give a closed formula for the degree of the projective closure of SO(n) over an algebraically closed field of characteristic zero, and outline the proof of this result. I will also describe some symbolic and numerical techniques used for computing this degree for small values of n.
 Marked Order Polyhedra III: Facets, Minkowski Sums and a Subdivision
 Christoph Pegel (Universität Bremen)
October 13, 2016, 10:00 am, MZH 7200
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After a recap on the combinatorial description of the face structure of marked order polyhedra, we discuss a regularity condition that guarantees a correspondence between facets of the polyhedra and covering relations of the underlying poset. We further describe a Minkowski sum decomposition with summands being 01 marked order polytopes and a subdivision into products of simplices introduced by Jochemko and Sanyal.
 Marked Order Polyhedra II: Face Structure and Geometry of Marked Order Polyhedra
 Marked Order Polyhedra I: Polytopes in Order Theory, Representation Theory and Finite Frame Theory
 Christoph Pegel (Universität Bremen)
September 23, 2016, 10:30 am, MZH 7200
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We give an overview of related polytopes appearing in order theory, representation theory of Lie algebras and finite frame theory. The polytopes we discuss all share a common description, where an underlying (marked) poset dictates the defining equations and inequalities. They are instances of marked order polytopes introduced by Ardila, Bliem and Salazar in 2011.
 Higher Topological Complexity
 Kai Renken (Universität Bremen)
September 22, 2016, 10:00 am, MZH 7200
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Master Thesis Colloquium
 Broken Circuit Complexes and Hyperplane Arrangements
 Alexander Nover (Universität Bremen)
August 30, 2016, 2:00 pm, MZH 7200
 Model reduction of biological and chemical networks using methods from tropical geometry
 Andreas Weber (Universität Bonn)
August 30, 2016, 10:15 am, MZH 7200
 Freeness of (Multi)Arrangements and Characteristic Polynomials (Part 2)
 Erik Hanke (Universität Bremen)
August 18, 2016, 10:15 am, MZH 7200
 Freeness of (Multi)Arrangements and Characteristic Polynomials
 Erik Hanke (Universität Bremen)
August 4, 2016, 10:15 am, MZH 7200
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We investigate the notion of free hyperplane arrangements and study properties of their derivation modules, including Saito’s criterion for freeness. Also, we generalize the concept to multiarrangements and indicate its importance. SolomonTerao’s formula for the characteristic polynomial of an arbitrary arrangement is used to prove the factorization theorem for the characteristic polynomial of a free arrangement. If time allows, we indicate how to prove SolomonTerao’s formula. Prerequisites are basic notions such as “intersection lattice“ or “deletionandrestriction.“ The talk might be divided into two parts, in which case the second talk will be announced later.
 Der Satz von EagonReiner
 Serre's property FA
 Luisa Peter (Universität Bremen)
July 7, 2016, 10:15 am, MZH 7200
 A nullstellensatz for rings of global real analytic functions
 Francesca Acquistapace, Fabrizio Broglia (University of Pisa)
June 30, 2016, 10:15 am, MZH 7200
 The real Grassmanian as a CW Complex
 Tim Lindemann (Universität Bremen)
June 27, 2016, 10:15 am, MZH 7200
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The Grassmannian G(k,n) is the space of all kdimensional subspaces of R^n. It plays an important role in the study of real vector bundles and in some real world applications such as image processing. It is a wellbehaved space in the sense that it can be given a topological structure as a compact smooth manifold. In fact the space G(1,n+1) coincides with thereal, ndimensional projective space. We introduce a CWstructure on G(k,n) as given in "Hatcher, A.: 'Vector Bundles and Ktheory'", which was first investigated by Charles Ehresmann in the 1930's.
 Das Wortproblem in BaumslagSolitarGruppen
 Non realizability of uniform phased matroids
 Elia Saini (Université de Fribourg)
April 4, 2016, 10:15 am, MZH 7200
 Modeling Adversaries as Iterated Tasks
 Thibault Rieutord (Paris)
March 31, 2016, 1:00 pm, MZH 7200
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In a shared memory system, processes communicate using persistent shared objects such as registers. Characterizing what can be solved in a shared memory system is a very complex question. This is why the iterated immediate snaphot, IIS, model has been proposed. Instead of dealing with unbounded interleavings of process steps the IIS model divides the computation into simple iterated units of computation. The IIS model can be represented as iterated subdivisions of the standard chromatic subdivided simplex, taking advantage of combinatorial topology techniques. It has been shown that the waitfree shared memory model, prone to any number of crash failures, is equivalent to the IIS model in terms of its power to solve distributed tasks. An adversarial model determines sets of processes that are allowed to fail in a system run, which abstracts out systems with correlated and nonuniform faults. In this talk we will show that similarly, a large class of adversarial models can be characterized, redarding task solvability, by a reduction to simpler ones defined as subsets of simplices in the second degree of the standard chromatic subdivision, which correspond to a set of 2round runs of the iterated immediate snapshot model. Our results boil down to a characterization of combinatorial structures corresponding to a generic simulation protocol that represents a run in an adversarial model as waitfree run on a smaller number if processes.
 An introduction to topological complexity
 Kai Renken (Universität Bremen)
March 31, 2016, 10:15 am, MZH 7200
 On tropical Igusa invariants
 Paul Helminck (Rijksuniversiteit Groningen)
February 10, 2016, 12:30 pm, MZH 1110
 Sample Theory: Lineare Algebra als Lückenfüller
 Tim Lindemann (Universität Bremen)
January 21, 2016, 12:30 pm, MZH 7200
Click for the abstract
In vielen Anwendungen zum Thema Datenübertragung ist es wichtig Rekonstruktionsmethoden für fehlerhafte Übertragungen zu gewinnen. Mithilfe von linearer Algebra werden wir untersuchen, wie man Vektoren (von denen einige Koordinaten unbekannt sind) wieder vervollständigt, falls diese in günstigen Untervektorräumen liegen. Dazu leiten wir die Fouriersche Unschärferelation her und verwenden das Ergebnis um elementare Bildkompression und das Approximieren verlorengegangener Pixel in Bilddateien zu diskutieren. Inhaltlich orientieren wir uns an dem Buch 'Frames for Undergraduates' aus der Reihe 'AMS student mathematical library'.
 Milnor fibers and monodromy
 Pauline Bailet (Universität Bremen)
January 14, 2016, 12:30 pm, MZH 7200
Click for the abstract
The second talk is devoted to Milnor fibers of hyperplane arrangements. After recalling the definition and some properties of Milnor fibers, we will speak about the action of the monodromy on their cohomology groups and their decomposition into eigenspaces. The computation of these eigenspaces and their determination from the intersection lattice is indeed a famous open question which has been recently intensively studied. I will also give two recent results which carry further developments and conjectures.
 Introduction to hyperplane arrangements
 Pauline Bailet (Universität Bremen)
January 13, 2016, 12:30 pm, MZH 7200
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In this first talk we introduce the main objects of hyperplane arrangements theory, such as intersection lattice, OrlikSolomon algebra, Aomoto complex and arrangements complements. We will also give an overview ofsome related results and open questions. The end of this talk is also a preparatory work for the studying of Milnor fibers (second talk).
 A probabilistic algorithm for computing datadiscriminant of likelihood equations
 Xiaoxian Tang (Universität Bremen)
December 17, 2015, 12:15 pm, MZH 7200
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An algebraic approach to the maximum likelihood estimation problem is to solve a very structured parameterized polynomial system called likelihood equations that have finitely many complex (real or nonreal) solutions. The only solutions that are statistically meaningful are the real solutions with positive coordinates. In order to classify the parameters (data) according to the number of real/positive solutions, we study how to efficiently compute the discriminants, say datadiscriminants (DD), of the likelihood equations. We develop a probabilistic algorithm with three different strategies for computing DDs. Our implemented probabilistic algorithm based on Maple and FGb is more efficient than our previous version presented in ISSAC2015, and is also more efficient than the standard elimination for larger benchmarks. By applying RAGlib to a DD we compute, we give the real root classification of 3 by 3 symmetric matrix model.
 Landau Singularities of Feynman Diagrams
 Isabella Bierenbaum (HU Berlin)
September 30, 2015, 2:45 pm, MZH 7200
 Wonderful compactifications in Quantum Field Theory
 Marko Berghoff (HU Berlin)
September 30, 2015, 1:30 pm, MZH 7200
 Linkages and polygon spaces
 Kai Renken (Universität Bremen)
September 17, 2015, 12:15 pm, MZH 7200
 Nestohedra associated with root systems
 Eleonora Galassi (Università di Pisa)
September 9, 2015, 10:15 am, MZH 7200
 A computational method for topological classification of global dynamics
 Paweł Pilarczyk (IST Austria)
August 13, 2015, 1:00 pm, MZH 7260
Click for the abstract
A computational framework will be introduced for automatic classification of global dynamics in a dynamical system depending on a few parameters. This framework is based on a setoriented topological approach, using Conley's idea of a Morse decomposition, combined with rigorous numerics, graph algorithms, and computational algebraic topology. This method allows one to effectively compute outer estimates of all the recurrent dynamical structures encountered in the system (such as equilibria or periodic solutions), as perceived at a prescribed resolution. It thus provides a concise and comprehensive classification of all the dynamical phenomena found across the given parameter ranges. The method is mathematically rigorous, and has a potential for wide applicability thanks to mild assumptions on the system. A few specific applications in population biology, theoretical physics, and epidemiology will be highlighted.
 Expander graphs
 Roy Meshulam (Technion, Haifa, Israel)
August 4, 2015, 2:00 pm, MZH 7200
 SATbased verification of graph transformation units
 Marcus Ermler (Universität Bremen)
July 2, 2015, 10:15 am, MZH 7200
 Distributed computing II: models and calculability
 Damien Imbs (Universität Bremen)
March 26, 2015, 10:30 am, MZH 7200
 Milnor fibers of real line arrangements
 Big polygon spaces
 Matthias Franz
January 8, 2015, 12:10 pm, MZH 7200
Click for the abstract
Polygon spaces are configuration spaces of polygons with prescribed edge lengths. I will present a related family of spaces, called big polygon spaces. They come with a canonical action of a "2torus" G = (Z/2Z)^n and exhibit new features in equivariant cohomology. I will will say a little bit about equivariant cohomology and then discuss the construction and properties of big polygon spaces as well as those of another family of Gmanifolds related to normed division algebras.
 What is... Distributed Computing?
 Damien Imbs (Universität Bremen)
December 18, 2014, 12:10 pm, MZH 7200
 What is... Tropical Geometry? (Part 2)
 Kirsten Schmitz (Universität Bremen)
December 11, 2014, 12:20 pm, MZH 7200
 What is... Tropical Geometry?
 Kirsten Schmitz (Universität Bremen)
December 4, 2014, 12:10 pm, MZH 7200
 What is... A Spectral Sequence?
 Viktoriya Ozornova (Universität Bremen)
November 20, 2014, 12:10 pm, MZH 7200
 What is... Matroid Theory? (extended)
 Martin Burger (Universität Bremen)
November 13, 2014, 12:00 pm, MZH 7200
 What is... Matroid Theory?
 Christoph Pegel (Universität Bremen)
October 30, 2014, 12:00 pm, MZH 7200
 Homotopy Theory of Categories
 Viktoriya Ozornova (Universität Bremen)
October 8, 2014, 10:15 am, MZH 7200
 Combinatorial Invariants of Toric Arrangements
 Sonja Riedel (Universität Bremen)
July 29, 2014, 10:20 am, MZH 7200
 Phasing classes of matroids
 Elia Saini (Universität Bremen)
July 29, 2014, 9:00 am, MZH 7200
 An Equivariant Patchwork Theorem
 Ralf Donau
July 24, 2014, 10:30 am, MZH 7200.
 ALTA Bachelor Seminar
 ALTA Bachelor Students
July 23, 2014, 9:30 am, MZH 7200.
 Stable Homotopy Theory: An Introduction
 Lennart Meier (University of Virginia, USA)
June 26, 2014, 10:15 am, MZH 7200.
 Matching trees on simplicial complexes and some splitting results
 Demet Taylan (Universität Bremen)
June 19, 2014, 10:15 am, MZH 7200.
 A cofibrantly generated model structure on the category of small acyclic categories
 Roman Bruckner (Universität Bremen)
June 5, 2014, 11:00 am, MZH 7200.
 Combinatorial stratifications of complex arrangements
 JanPhilipp Litza
April 15, 2014, 1:00 pm, MZH 7200.
 Weak symmetry breaking and abstract simplicial paths
 Dmitry FeichtnerKozlov (Universität Bremen)
April 14, 2014, 10:15 am, MZH 7200.
 Cluster algebras, part II
 Tim Haga (Universität Bremen)
April 7, 2014, 10:15 am, MZH 7200
 A crash course on toric varieties, II
 Christoph Pegel
April 2, 2014, 1:00 pm, MZH 7200.
 Cluster algebras
 Tim Haga (Universität Bremen)
March 31, 2014, 10:15 am, MZH 7200.
 Cohomology of arrangements
 Lasse Paetz
March 25, 2014, 10:15 am, MZH 7200.
 Zonotopes and production theory
 Simona Settepanella (Hokkaido University, Japan/ Scuola Superiore Sant'Anna, Italy)
February 13, 2014, 10:00 am, MZH 6240
 (Hilbert Space) Frames meet Algebraic Geometry
 Emily King (Universität Bremen)
February 5, 2014, 10:15 am, MZH 6240
 Homotopy theory of posets
 George Raptis (Universität Osnabrueck)
February 4, 2014, 2:15 pm, MZH 2340
 A crash course on toric varieties, I
 Christoph Pegel
January 8, 2014, 10:15 am, MZH 6240
 Approximate HermitianYangMills structures on semistable Higgs bundles
 Elia Saini (SISSA Trieste)
November 19, 2013, 10:30 am, MZH 3150
 Combinatorics of Buchsbaum modules and applications to Upper bound theorems and isoperimetry.
 Karim Adiprasito (IHÉS, BuressurYvette)
November 13, 2013, 11:00 am, MZH 6340
Click for the abstract
The classical Upper Bound Theorem of McMullenStanley bounds the number of faces of a simplicial sphere on a given number of vertices. Stanley's method stems from commutative algebra: he uses the fact that the fvector can be bounded by estimating the Hilbert series of the StanleyReisner ring associated to the simplicial polytope. Since then, there have been several questions similar to the Upper Bound Problem, some of which notoriously resisted a treatment based on algebraic methods. Among them is the problem of providing a sharp upper bound for the number of faces of the Minkowski sum of simplicial polytopes. In my talk, I will sketch some new methods, and illustrate them by examples. In particular, I will present a complete resolution to the Upper Bound Problem for Minkowski sums. Joint work with Raman Sanyal
 Farkas'Lemma,Das Spiel ``Shapley''
 Angelina Degner, Wienke Menges
July 3, 2013, 10:45 am, MZH 6340
Click for the abstract
BachelorarbeitVorträge.
 Topology of random 2dimensional complexes
 JeanMarie Droz
February 28, 2013, 10:00 am, MZH 2490
 continuation: an inequality with applications to thresholds and percolation
 Christian Bey
February 21, 2013, 10:00 am, MZH 2490
 Zeroone laws for graph properties (Part II)
 Sonja Riedel
February 14, 2013, 10:00 am, MZH 2490
 continuation: An inequality with application to thresholds and precolation
 Christian Bey
January 31, 2013, 10:00 am, MZH 2490
 Zeroone laws for graph properties
 Sonja Riedel
January 24, 2013, 10:00 am, MZH 2490
 An inequality involving degrees of hypergraphs, with applications to expansion, thresholds and percolation (Part II)
 Christian Bey
January 17, 2013, 10:00 am, MZH 2490
 The classification of covering spaces
 Lasse Paetz
January 15, 2013, 10:15 am, MZH 7050
 An inequality involving degrees of hypergraphs, with applications to expansion, thresholds and percolation
 Christian Bey
January 10, 2013, 10:00 am, MZH 2490
 Introduction to random graphs, Part 3
 Martin Dlugosch
December 20, 2012, 10:00 am, MZH 2490
 Introduction to random graphs, thresholds for connectivity
 Michał Adamaszek
December 13, 2012, 10:00 am, MZH 2490
 Introduction to random graphs, part I.
 Expansion properties for simplicial complexes.
 Anna Gundert (ETHZ)
December 4, 2012, 10:00 am, MZH 7050
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For graphs, combinatorial expansion properties are closely related to the eigenvalues of the adjacency matrix and the Laplacian. One result expressing this relationship is the Cheeger Inequality, which states in particular that spectral expansion (a large spectral gap) implies edge expansion. In my talk, we will consider generalizations of graph matrices to higher dimensional simplicial complexes as well as a higher dimensional analogue of edge expansion, recently introduced by Gromov, Linial and Meshulam and Newman and Rabinovich. We will see that in higher dimensions the most straightforward attempt at an analogue of Cheeger's Inequality fails: A large spectral gap for the generalized Laplacian doesn't imply combinatorial expansion. We will also look at concentration results for the spectra of random complexes which match the corresponding results on spectra of random graphs. Joint work with Uli Wagner.
 Äquivariante Kohomologie und Syzygien.
 Brylawski's conjecture and the arithmetic Tutte polynomial.
 Consistent scale selection for exploratory visualization and analysis of data sets.
 Daniel Müllner, Stanford U.
July 11, 2012, 1:00 pm, MZH 7050
Click for the abstract
Choosing an appropriate scale is a frequently encountered problem in data analysis, and paradigms in the field support both the choice of strategies to make smart, definite choices and the hierarchical or persistence approach of looking at all scales at once. In the first part, I will give a brief introduction to the ideas of topological data analysis, in particular persistent homology. I will then focus on the ''Mapper' algorithm for visualization and analysis of point cloud data. Here, a scale choice must be made multiple times for overlapping fragments of the data set. I will discuss two techniques which are independent but play nicely together to make scale choices locally consistent and deal with noise. By making consistent decisions at local scope while retaining global flexibility, we can make more plausible choices, overcome existing weaknesses, validate results more easily and simplify the data analysis process for the user. (Joint work with Gunnar Carlsson, Facundo Mémoli and Gurjeet Singh.) '
 Infinite graphs and matroids.
 Johannes Carmesin, Uni Hamburg.
June 20, 2012, 11:00 am, MZH 7050
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Infinite graph theory has been put on a new footing in recent years after it was realised that ends, and topology, are key ingredients that were previously overlooked. Likewise, infinite matroid theory was essentially relaunched two years ago after Bruhn et al showed that infinite matroids could, contrary to common belief, be axiomatised in a way that allowed for duality as known from finite matroid theory. I shall attempt to give a brief introduction to both these developments, and then speak about a problem in which they meet: if all the finite minors of a given infinite matroid M are graphic, must M be graphic too? (And what exactly does this mean?)
 Topological Representation of Tropical Oriented Matroids.
 Dr. Silke Horn, TU Darmstadt.
June 6, 2012, 11:00 am, MZH 7050
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Tropical oriented matroids were defined by Ardila and Develin in 2007. They are a tropical analogue of classical oriented matroids in the sense that they encode the properties of the types of points in an arrangement of tropical hyperplanes  in much the same way as the covectors of (classical) oriented matroids describe the types in arrangements of linear hyperplanes. Not every oriented matroid can be realised by an arrangement of linear hyperplanes though. The famous Topological Representation Theorem by Folkman and Lawrence, however, states that every oriented matroid can be represented as an arrangement of pseudohyperplanes. I present a tropical analogue for the Topological Representation Theorem. Moreover, I discuss relations of tropical oriented matroids to subdivisions of products of simplices.
 Critical points of master functions.
 Prof. Dr. Michael Falk, Northern Arizona University
May 22, 2012, 4:15 pm, MZH 1090
 Partition functions, toric arrangements, and arithmetic matroids.
 Dr. Luca Moci, Università di Roma 1 ``La Sapienza''
May 8, 2012, 4:15 pm, MZH 1090
 F1: a mathematical object in search of a definition.
 Prof. Dr. Yuri Manin, Direktor MPI Mathematik, Bonn
May 8, 2012, 12:15 pm,
 Mathematics as a Toolkit: From Models to Data Mining.
 Prof. Dr. Yuri Manin, Direktor des MPI Mathematik, Bonn
May 7, 2012, 7:30 pm, Olbers Saal, Haus der Wissenschaft
 Arithmetische Matroide: Grundlagen und Dualität.
 Constructing a tropical linear monoid (part 2).
