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 = −.

* 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 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: Ron Holzman, Technion Title: Edge-covers in d-interval hypergraphs

Title: Shellability is NP-complete

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: Bram Petri, Max Planck Institute, Bonn Title: The length spectrum of a random surface

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.

Speaker: Thilo Weinert, BGU Title: The Ramsey Theory of ordinals and its relation to finitary combinatorics Abstract: Ramsey Theory is a branch of mathematics which is often times summed up by the slogan “complete disorder is impossible”. An important branch of finitary Ramsey Theory lies in the determination of Ramsey Numbers. Infinitary Ramsey Theory on the other hand is an important branch of set theory. Whereas the Ramsey Theory of the Uncountable often times features independence phenomena, the Ramsey Theory of the Countably Infinite provides many interesting combinatorial challenges.

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.