Speaker: Micha Sharir (Tel Aviv University) Title: Eliminating depth cycles for lines and triangles, with applications to bounding incidences Abstract: --------- The talk presents three related results. We first consider the problem of eliminating all depth cycles in a set of n lines in 3-space. For two lines l_1, l_2 in 3-space (in general position), we say that l_1 lies below l_2 if the unique vertical line that meets both lines meets l_1 at a point below the point where it meets l_2. This depth relationship typically has cycles, which can be eliminated if we cut the lines into

Speaker: Gil Kalai, HU Title: Algebraic-topological invariants of hypergraphs and extremal combinatorics Abstract: We will discuss some algebraic invariants of hypergraphs and some connection to algebraic topology. We will present some conjectural (rather speculative) relations with two central problems in extremal combinatorics: The Turan (4,3) conjecture and the Erdos-Rado sunflower conjecture.

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.)

Title: Inp-minimal ordered groups. Abstract. The main goal of the talk is to present the proof of the theorem stating that inp-minimal (left)-ordered groups are abelian. This generalizes a previous result of P. Simon for bi-ordered inp-minimal groups.

Title: Random integer matrices Abstract: I will discuss various models of random integer matrices, and their (occasionally surprising) properties. Some of the work discussed is joint with E. Fuchs.

Title: A tale of three elliptic curves. Abstract: We will show how the arithmetic of three elliptic curves answers three old questions in the Euclidean geometry.

Title: Fixed points of finite groups on modules Abstract: Suppose G is a finite group, p is a prime, S is a Sylow p-subgroup of G, and V is a G-module over a field of characteristic p. In some situations, an easy calculation shows that the fixed points of G on V are the same as the fixed points of the normalizer of S in G. Generalizations of this result have been obtained previously to study the structure of G for p odd. We plan to describe a new generalization for p = 2. (This is part of joint work with J. Lynd that removes the classification of finite simple groups

Title: Almost Congruence Extension Property for subgroups of free groups. Abstract. The talk essentially based on: https://arxiv.org/abs/1606.02345 Let G be a group and H

Title: The spectral method for geometric colouring problems

Title: Stability patterns in representation theory and applications Abstract: Many natural sequences of objects come equipped with group actions, e.g. the symmetric group on n letters acting on a space X_n. This leads to fundamental instability of invariants, such as homology, arising from the representation theory of the sequence of groups. Representation stability is a new and increasingly important set of ideas that describe a sense in which such sequence of representations (of different groups) stabilizes.

Title: Semisimply degenerate quadratic forms and a conjecture of Grothendieck and Serre (joint work with E. Bayer-Fluckiger) Abstract:

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: Pseudo-finite groups containing an involution with a finite centralizer.

Title: Approximations of groups and equations over groups. Abstract: The talk is largely based on the paper which may be found here: https://authors.elsevier.com/a/1UN3b4~FOr6ze 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: