|
|
Seminar Schedule
To suggest a talk or to subscribe to the mailing list
please email: timhaga "at" math.uni-bremen.de
Note: times are meant sharp ('s.t.')
Talks
- Ehrhart quasi-polynomials of almost integral polytopes
- Christopher de Vries (Universität Bremen / Hokkaido University, Japan)
October 7, 2021, 10:00 am, online via Zoom
Click for the abstract
A lattice polytope translated by a rational vector is called an almost integral polytope. The Ehrhart quasi-polynomial of every almost integral polytope derived from a symmetric polytope satisfies the algebraic property of symmetry. On the contrary, if the Ehrhart quasi-polynomials of every almost integral polytope derived from the same integral polytope is symmetric, the polytope is symmetric. A similar characterization exists for zonotopes and an algebraic property of quasi-polynomials called GCD-property. The proofs use a function that describes the constituents of Ehrhart quasi-polynomials of almost integral polytopes. This function turns out to be a polynomial.
- The classification problem of operations on convex bodies
- Fritz Grimpen (Universität Bremen)
July 12, 2021, 2:15 pm, online via Zoom
Click for the abstract
The various theories of compact convex sets depend fundamentally on the choice of an associative operation. It is well-known, that instances of such operations are the classical Minkowski addition and the L_p additions. This leads to the question whether there are other associative operations with good properties, which could lead to similar theories. First results in this direction were established by Gardner, Hug, and Weil in 2013. The authors proved that the only continuous in the Hausdorff metric, GL(n) covariant, and associative operations on n dimensional o-symmetric convex bodies are, apart from the trivial choices, L_p additions for some p ∈ [1, ∞], if n ≥ 2. Their methodology depends heavily on the projection covariance of the considered operations and leads to similar results for general operations on convex bodies and o-symmetrizations. In this presentation, we will discuss the classification result and demonstrate the underlying proof technique of utilizing projection covariance.
- Valuations on Convex Bodies
- Nico Lombardi (TU Wien)
July 7, 2021, 12:15 pm, online via Zoom
Click for the abstract
We will introduce the notion of valuation defined on the set of convex bodies, i.e. compact and convex subsets of R^n, denoted by K^n: a functional m:K^n->R is said to be a valuation if m(H)+m(K)=m(K\cap H)+m(K\cup H), for every K,H in K^n, whenever the union of K and H is in K^n. We can think as a first example of valuation the n dimensional Lebesgue measure restricted to K^n. After some more examples and properties, we will focus on the following problem: Is it possible under suitable hypothesis, as continuity (with respect to some notion of convergence) and invariance (with respect to the action of some groups over K^n), to classify completely the valuations on K^n and to characterize them? We will present some fundamental results related to this question. At the end we will introduce the notion of valuation on function spaces, a generalization that has been recently developed.
- On refinements of the Brunn-Minkowski inequality
- Jesús Yepes Nicolás (University of Murcia)
June 23, 2021, 12:15 pm, online via Zoom
Click for the abstract
The well known Brunn-Minkowski inequality asserts that, given convex bodies (non-empty compact convex sets) R^n, vol(1−λ)K+λL is a (1/n)-concave function in λ∈ [0,1]. This (1/n)-concavity is moreover the best one to be expected for such an inequality. Nevertheless, from a classical result by Bonnesen, we may state that vol(1−λ)K+λL≥(1−λ)vol(K)+λvol(L), provided that K and L have a common projection onto a hyperplane. Furthermore, the same can be obtained under the weaker assumption of a projection with the same measure. In this talk we will first overview such a classical refinement of the Brunn-Minkowski inequality, whose proof involves powerful geometrical tools such as both the Steiner and Schwarz symmetrizations. Next, we will show that the natural hypothesis of a common (n − k)-plane projection of the sets, for 2≤k≤n−1, does not imply however that the (1/k)-th powered volume function is concave. We will then conclude by showing which is the, somehow, best projection type assumption that is needed to get concavity for the k-th root of vol(1−λ)K+λL. This is about joint work with Marı́a A. Hernández Cifre (Universidad de Murcia).
- On Grünbaum type inequalities
- Francisco Marín Sola (University of Murcia)
June 9, 2021, 12:15 pm, online via Zoom
Click for the abstract
Given a compact set K of positive volume in an euclidean space, if K is convex with centroid at the origin, then, a classical and powerful result by Grünbaum, says that one can find a lower bound for the ratio vol(K-)/vol(K) depending only on the dimension of K, where K- denotes the intersection of K with a halfspace bounded by a hyperplane passing through its centroid. In this talk we will give an extensive introduction to Grünbaum's inequality, showing also how the Brunn-Minkowski inequality plays a crucial role in its proof. Finally, if time allows, we will present an overview on our recent results about some generalizations of Grünbaum's inequality, which are part of a joint work with Jesús Yepes Nicolás.
- Einführung in die Geometrie der Zahlen, der Satz von Minkowski und der Satz von Blichfeldt
- Safwan Alrahmoun (Universität Bremen)
January 15, 2021, 1:00 pm, online via Zoom
- Brunn-Minkowski and isoperimetric type inequalities for the lattice point enumerator
- Eduardo Lucas Marín (University of Murcia)
December 16, 2020, 10:00 am, online via Zoom
Click for the abstract
The classical Brunn-Minkowski inequality in the n-dimensional Euclidean space asserts that the volume (Lebesgue measure) to the power 1/n is a concave functional when dealing with convex bodies (non-empty compact convex sets). It quickly yields, among other results, the classical isoperimetric inequality, which can be summarized by saying that the Euclidean balls minimize the surface area measure (Minkowski content) among those convex bodies with prescribed positive volume. There exist various facets of the previous results, due to their different versions, generalizations and extensions. In this talk we will discuss and show certain discrete analogues of the above inequalities for the lattice point enumerator, which yields the number of integer points of a given set, when dealing with arbitrary bounded subsets of the n-dimensional Euclidean space. Moreover, we will show that these new discrete inequalities imply the corresponding classical results for non-empty compact sets.
- Discrete Morse Theory in Topological Data Analysis
- Gideon Klaila (Universität Bremen)
December 2, 2020, 12:15 pm, online via Zoom
Click for the abstract
The Topological Data Analysis assumes, that the given data is part of an underlying, higher-dimensional space. One tool to identify the different shapes that can occur is the persistent homology. For an increasing distance value, filtrations are created by adding cells each time two data-points have a smaller distance than this value. For these filtrations, the homology classes are calculated. The result can be displayed in a barcode, where one can identify the birth and death of new features for different distance values. One challenge of this method is the arbitrary amount of cells for each filtration, which are used for the calculation of the persistent homology. To improve the calculation, the Discrete Morse Theory by Robin Forman can be applied. This theory could solve the problem, if an efficient algorithm for the construction can be found. The algorithm of Konstantin Mischaikow and Vidit Nanda seems to be a good approach, even if it is not optimal. This gives reason to make further study of the efficiency of the algorithm and possibly improvements.
- Cosystoles and Cheeger Constants of the Simplex
- Kai Renken (Universität Bremen)
November 4, 2020, 10:00 am, online via Zoom
Click for the abstract
The classical Cheeger constant of a graph is an intensively studied concept, which roughly speaking measures the stability of connectedness of a connected simple graph. In this talk I give an introduction to a higher dimensional generalization of that concept to simplicial complexes. We will mainly study those constants for the standard simplex and discuss the latest results of research. Furthermore, I give an overview of some tools to investigate the cosystolic norm of a cochain, a value that is necessary to understand when we want to determine higher dimensional Cheeger constants. A basic understanding of simplicial homology / cohomology is helpful to follow this talk.
- Algebraic integral geometry (CANCELLED)
- Andreas Bernig (Goethe Universität Frankfurt am Main)
March 12, 2020, 10:00 am, MZH 7200
Click for the abstract
I give an overview of recent developments on kinematic formulas on flat and curved spaces. The classical kinematic formula due to Chern-Blaschke-Santalo is related to flat euclidean space. It may be generalized to hermitian and quaternionic vector spaces, and more generally to isotropic Riemannian manifolds. To determine these formulas in an explicit way is a difficult task which was solved in many but not all cases. In the particular case of complex space forms, Alesker's theory of valuations on manifolds and algebraic structures such as product and Poincaré duality of valuations play a central role.
- Introduction to (higher) inductive types
- Carl Hammann (Universität Bremen)
March 10, 2020, 11:00 am, MZH 7200
Click for the abstract
After an introduction to the necessary rudiments of (Homotopy) Type Theory, we will have a look at the solved problem of defining what an inductive type is and the partially solved problem of doing the same for higher inductive types. The two guiding slogans are that "higher inductive types are the type-theoretic counterpart of cell complexes" and that, if ordinary inductive types are modelled by free monads, "higher inductive types correspond to presentations of monads". This talk is meant as a high-level overview.
- The theory of valuations on the space of quasi-concave functions
- Nico Lombardi (Università degli Studi di Firenze, Italy)
March 5, 2020, 10:00 am, MZH 7200
- Introduction to valuation on function spaces
- Nico Lombardi (Università degli Studi di Firenze, Italy)
February 27, 2020, 10:00 am, MZH 7200
- Valuation theory on convex bodies
- Nico Lombardi (Università degli Studi di Firenze, Italy)
February 20, 2020, 10:00 am, MZH 7200
- Theory of convex bodies
- Nico Lombardi (Università degli Studi di Firenze, Italy)
February 13, 2020, 10:00 am, MZH 7200
- Approximative Persistent Homology with Discrete Morse Theory
- Arkadi Schelling (Universität Bremen)
February 21, 2019, 8:30 am, MZH 7200
Click for the abstract
Persistent homology is a tool for topological data analysis, that can help to analyse deformed geometric shapes like connected components, circles, voids and higher dimensional homology. The computation of persistent homology is based on the construction of a filtered cell complex and scales roughly cubic in the number of cells. Discrete Morse theory reduces the number of cells in a complex without changing its homology. In 2013 Vidit Nanda and Konstantin Mischaikow used filtration-wise Morse reductions to proof a speed up for certain persistent homology computations and implemented the software /Perseus/. In practice, many filtered cell complexes grow by one simplex per filtration value and cannot be reduced by Nanda and Mischaikow's approach, e.g. Cech complexes. This talk will show some ideas how to trade off an approximated result for a faster computation. The new construction of an /induced/ filtered acyclic matchings helps for an informed choice of the approximation parameter. Also, the theoretical construct of pairings on a graded multiset of real numbers unifies persistent homology and filtered acyclic matchings. As an aside this allows the purely combinatorial proof of a filtered Euler formula for all such pairings.
- On Rogers-Shephard type inequalities for general measures
- Jesús Yepes Nicolás (Universidad de Murcia, Spain)
December 6, 2018, 10:00 am, MZH 7260
- An introduction to combinatorial rigidity
- Fusion Grammars
- Aaron Lye (Universität Bremen)
February 26, 2018, 12:30 pm, MZH 7200
Click for the abstract
In this talk, I will give an introduction into fusion grammars which are a novel device for the generation of (hyper)graph languages. Fusion grammars are motivated by the observation that many large and complex structures can be seen as compositions of a large number of small basic pieces. A fusion grammar is a hypergraph grammar that provides the small pieces as connected components of the start hypergraph. To get arbitrary large numbers of them, they can be copied multiple times. To get large connected hypergraphs, they can be fused by the application of fusion rules.
- G-Tutte polynomials and abelian Lie group arrangement
- Masahiko Yoshinaga (Universität Bremen)
July 19, 2017, 10:15 am, MZH 7200
Click for the abstract
The Tutte polynomials are classical and important invariants for matroids, since it has several remarkable specializations e.g., chromatic polynomials (of graphs), characteristic polynomials (of arrangements), Jones polynomials (of certain links), partition functions (of certain statistical mechanics models), etc. Recently, further "Tutte-like" (quasi)polynomial invariants, have been defined and studied, e.g., arithmetic Tutte polynomial (for toric arrangements) and characteristic quasi-polynomial (related to Ehrhart theory). Based on the observation that the above "Tutte-like" polynomials are all defined by means of counting certain homomorphisms between abelian groups, we propose to introduce the notion "G-Tutte polynomial" for a list A and an abelian group G. I will discuss how the notion of G-Tutte polynomials unify these invariants and recover classical results. (Joint work with Ye Liu and Tan Nhat Tran)
- Answers to some questions for high order freeness of hyperplane arrangements
- Norihiro Nakashima (Tokyo Denki University)
June 12, 2017, 1:00 pm, MZH 7200
Click for the abstract
An m-free hyperplane arrangement is a generalization of a free arrangement. Some results are known about m-freeness. However, the behavior of m-freeness has not been well analyzed yet when m is greater than or equal to 2. Some basic questions remain open. In particular, Holm asked the following two questions: (1) Does m-free imply (m+1)-free for any arrangement? (2) Are all arrangements m-free for m large enough? In this talk, I present a characterization of m-freeness for product arrangements and a proposition for localizations of an m-free arrangement. From these results, I give answers to Holm's questions.
- 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 Newton-Okounkov Bodies
- Linear Degenerate Flag Varieties
- Ghislain Fourier (Universität Hannover)
March 15, 2017, 12:30 pm, MZH 7200
Click for the abstract
The flag variety is probably one of the best-understood 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. Cerulli-Irelli, 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
Click for the abstract
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 chain-order 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 Jan-Philipp Litza.
- Problems around hyperplane arrangements (Part 2)
- Masahiko Yoshinaga (Universität Bremen)
January 5, 2017, 10:15 am, MZH 7200
Click for the abstract
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
Click for the abstract
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 purely-combinatorial 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
Click for the abstract
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
Click for the abstract
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 0-1 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
Click for the abstract
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
Click for the abstract
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
Click for the abstract
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. Solomon-Terao’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 Solomon-Terao’s formula. Prerequisites are basic notions such as “intersection lattice“ or “deletion-and-restriction.“ The talk might be divided into two parts, in which case the second talk will be announced later.
- Der Satz von Eagon-Reiner
- 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
Click for the abstract
The Grassmannian G(k,n) is the space of all k-dimensional 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 well-behaved 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, n-dimensional projective space. We introduce a CW-structure on G(k,n) as given in "Hatcher, A.: 'Vector Bundles and K-theory'", which was first investigated by Charles Ehresmann in the 1930's.
- Das Wortproblem in Baumslag-Solitar-Gruppen
- 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
Click for the abstract
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 wait-free 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 non-uniform 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 2-round 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 wait-free 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
Click for the abstract
In this first talk we introduce the main objects of hyperplane arrangements theory, such as intersection lattice, Orlik-Solomon 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 data-discriminant of likelihood equations
- Xiaoxian Tang (Universität Bremen)
December 17, 2015, 12:15 pm, MZH 7200
Click for the abstract
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 non-real) 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 data-discriminants (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 set-oriented 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
- SAT-based 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 "2-torus" 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 G-manifolds 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
- Jan-Philipp Litza
April 15, 2014, 1:00 pm, MZH 7200.
- Weak symmetry breaking and abstract simplicial paths
- Dmitry Feichtner-Kozlov (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 Hermitian-Yang-Mills 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, Bures-sur-Yvette)
November 13, 2013, 11:00 am, MZH 6340
Click for the abstract
The classical Upper Bound Theorem of McMullen-Stanley 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 f-vector can be bounded by estimating the Hilbert series of the Stanley--Reisner 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
Bachelorarbeit-Vorträge.
- Topology of random 2-dimensional complexes
- Jean-Marie 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
- Zero-one 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
- Zero-one 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
Click for the abstract
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
Click for the abstract
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 re-launched 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
Click for the abstract
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).
|
