There are exponentially many triangulations of a fixed manifold extremely distant from each other in some natural metric. I will discuss similar results for contractible 2-complexes. In order to prove these for the manifold being the sphere (or a contractible complex) one needs to create topology out of nothing. This is done by studying group theory of the trivial group.
Speaker: Ilan Karpas, HU
Tilte: Families with forbidden intersection patterns
Abstract:
Let l, n be even natural numbers. A pattern p of length l is an element
p = (p1, . . . , pl) ∈ {−, +}^l. Given such a pattern and two sets A, B ⊂ [n], we say that the pair (A, B) forms pattern p if the following conditions are satisfied:
1. A \Delta B = {i_1, . . . , i_l}, where i_1 < i_2 < . . . < i_l,
2. For 1 ≤ j ≤ l, we have i_ j ∈ A \ B if p_ j = + and i_ j ∈ B \ A if p_ j = −.
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
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Speaker: László Babai (University of Chicago)
Title: Finite permutation groups and the Graph Isomorphism problem
Updated abstract:
The Graph Isomorphism (GI) problem is the algorithmic problem
Title: Polynomials vanishing on Cartesian products
Abstract:
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
Abstract:
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.
