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:
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?
The existence of sharply 2-transitive groups without regular normal subgroup was a longstanding open problem. Recently constructions have been given, at least in certain characteristics. We will survey the current state of the art and explain some constructions and their limitations. (joint work with E. Rips)
Title: On groups with quadratic Dehn functions
Abstract: This is a joint work with A. Olshanskii. We construct a finitely presented group with quadratic Dehn function and undecidable conjugacy problem.
Title: Approximations of groups and equations over groups.
The talk is largely based on the paper which may be found here:
Abstract: Let G be a group and K a class of groups. I define a notion of approximation of G by K and give several characterizations of approximable by K groups. For example, the sofic groups, defined by B. Weiss, are the groups approximable by symmetric (or alternating) groups. In the case of sofic groups we have that the following are equivalent:
Title: Old and New Results on Subgroup Growth in Pro-p Groups.
Abstract: I will survey our current knowledge about subgroup growth in pro-p growth. In particular I will present new solutions to long standing open problems in the area:
1. What is the minimal subgroup growth of non-$p$-adic analytic pro-$p$ groups? (Joint work with Benjamin Klopsch and Jan-Christoph Schlage-Puchta.)
2. What are the subgroup growths of the Grigorchuk group and the Gupta-Sidki groups? (Joint work with Jan-Christoph Schlage-Puchta.)