HD-Combinatorics

The High Dimensional Combinatorics seminars take pace on Mondays at the IIAS, Feldman Building, Givat Ram.
2018 Jan 15

Michael Farber: "Robot motion planning and equivariant Bredon cohomology"

9:00am to 11:00am

Location: 

IIAS, Feldman Building, Givat Ram

Abstract: The motion planning problem of robotics leads to an interesting invariant of topological spaces, TC(X), depending on the homotopy type of X = the configuration space of the system. TC(X) is an integer reflecting the complexity of motion planning algorithms for all systems (robots) having X as their configuration space. Methods of algebraic topology allow to compute or to estimate TC(X) in many examples of practical interest. In the case when the space X is aspherical the number TC(X) depends only on the fundamental group of X.

2018 Jan 29

HD-Combinatorics Special day: Pseudo-randomness (organised by Uli Wagner)

10:00am to 5:00pm

Location: 

IIAS, Feldman Building, Givat Ram
10:00-11:00     Anna Gundert Uli Wagner - Quasirandomness and expansion for graphs

11:30-12:30     Anna Gundert Uli Wagner - Quasirandomness for hypergraphs

13:45- 14:45    Uli Wagner - Szemeredi's regularity lemma for dense graphs

15:00-16:00     Tamar Ziegler - Gowers uniformity norms

16:30-17:30     Anna Gundert Uli Wagner - Hypergraph regularity 
2018 Jan 01

HD-Combinatorics: Alan Lew, "Spectral gaps of generalized flag complexes"

2:00pm to 4:00pm

Location: 

Eilat Hall, Feldman Building (IIAS), Givat Ram
Abstract: Let X be a simplicial complex on n vertices without missing faces of dimension larger than d. Let L_k denote the k-Laplacian acting on real k-cochains of X and let μ_k(X) denote its minimal eigenvalue. We study the connection between the spectral gaps μ_k(X) for k ≥ d and μ_{d-1}(X). Applications include: 1) A cohomology vanishing theorem for complexes without large missing faces. 2) A fractional Hall type theorem for general position sets in matroids.
2017 Sep 11

IIAS Seminar: Nikolay Nikolov, "Gradients in group theory"

11:00am to 12:00pm

Location: 

Feldman building, Room 128
Abstract: Let G be a finitely generated group and let G>G_1>G_2 ... be a sequence of finite index normal subgroups of G with trivial intersection. We expect that the asymptotic behaviour of various group theoretic invariants of the groups G_i should relate to algebraic, topological or measure theoretic properties of G. A classic example of this is the Luck approximation theorem which says that the growth of the ordinary Betti numbers of sequence G_i is given by the L^2-Betti number of (the classifying space) of G.

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