Israel Institute for Advanced Studies, Safra campus, Givat Ram
* This talk is joint with the 20th Midrasha Mathematicae: 60 faces to groups, celebrating Alex Lubotzky's 60th birthday.
The full program for AlexFest, Nov. 6--11, is detailed here: http://www.as.huji.ac.il/ias/public/121/the20thMidrashaMa2016/program.pdf
Speaker: László Babai (University of Chicago)
Title: Finite permutation groups and the Graph Isomorphism problem
The Graph Isomorphism (GI) problem is the algorithmic problem
Title: Polynomials vanishing on Cartesian products
Let F(x,y,z) be a real trivariate polynomial of constant degree, and let A,B,C be three sets of real numbers, each of size n. How many roots can F have on A x B x C?
Speaker: Doron Puder, TAU
Title: Meanders and Non-Crossing Partitions
Abstract: Imagine a long river and a closed (not self-intersecting) racetrack that crosses the river by bridges 2n times. This is called a meander. How many meanders are there with 2n bridges (up to homeomorphisms of the plane that stabilizes the river)? This challenging question, which is open for several decades now, has connections to several fields of mathematics.
Speaker: Zur Luria (ETH)
Title: Hamiltonian spheres in random hypergraphs
Hamiltonian cycles are a fundamental object in graph theory, and combinatorics in general. A classical result states that in the random graph model G(n,p), there is a sharp threshold for the appearance of a Hamiltonian cycle. It is natural to wonder what happens in higher dimensions - that is, in random uniform hypergraphs?
Title: Gaussian Random Links
Abstract: A model for random links is obtained by fixing an
initial curve in some n-dimensional Euclidean space and
projecting the curve on to random 3 dimensional subspaces. By
varying the curve we obtain different models of random
knots, and we will study how the second moment of the average crossing
number change as a function of the initial curve.
This is based on work of Christopher Westenberger.
Speaker: Ehud Fridgut (Weizmann Institute)
Title: Almost-intersecting families are almost intersecting-families.
Abstract: Consider a family of subsets of size k from a ground set of size n (with k < n/2). Assume most (in some well defined sense) pairs of sets in the family intersect. Is it then possible to remove few (in some well defined sense) sets, and remain with a family where every two sets intersect?
We will answer this affirmatively, and the route to the answer will pass through a removal lemma in product graphs.
Speaker: Elon Lindenstrauss (HU)
Title: On the spectral gap of Cayley graphs for the group of affine transformations
Abstract: Joint work with P. Varju.
One of the most important open questions regarding spectral gap of Cayley graphs is the dependence of the gap on the choice of generators.
The Theta Number of Simplicial Complexes
The celebrated Lovász theta number of a graph is an efficiently computable upper bound for the independence number of a graph, given by a semidefinite program. This talk presents a generalization of the theta number to simplicial complexes of arbitrary dimension, based on real simplicial cohomology theory, in particular higher dimensional Laplacians.
Title: Labeling and Eliminating Geometric Realization Spaces
Abstract: I will introduce a Moduli-space of Shapes of Polyhedra, and show how they may be eliminated by labeling their underlying combinatorial data. I discuss how this relates to geometric realization problems and in particular to flexibility of polyhedra.