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.

Speaker: Lukas Kühne (University of Bonn) Title: Heavy hyperplanes in multiarrangements and their freeness Abstract: One of the central topics among the theory of hyperplane arrangements is their freeness. Terao's conjecture tries to link the freeness with the combinatorics of an arrangement. One of the few categories of arrangements which satisfy this conjecture consists of 3-dimensional arrangements with an unbalanced Ziegler restriction. This means that the arrangement contains a lot of hyperplanes intersecting in one single line

Speaker 1: Sria Louis Title: Asymptotically Almost Every 2r-regular Graph has an Internal Partition Abstract: An internal partition of a graph is a partitioning of the vertex set into two parts such that for every vertex, at least half of its neighbors are on its side. It is easy to notice that such a partition doesn't always exist (e.g. - cliques), though, both the existence and finding of such a partition - are open problems. Stiebitz (1996), responding to a problem of Thomassen (1983), made a breakthrough in this area, but the question and some interesting generalizations are still open.

Speaker: Zilin Jiang (Technion) Title: Relations between Tverberg points and central points Abstract: Given 3n lines in general position in the plane, it is always possible to partition them into n triples of lines so that all the triangles, formed by the triples, share a common point. This result is known back in 1988 by J.P. Roudneff. Strangely, in higher dimensions, it is only proved by Roman Karasev for n that is a prime power.

NOTE THE SPECIAL TIME: 11:00--12:30 Speaker: Eyal Ackerman, University of Haifa at Oranim Title: Coloring points with respect to squares Abstract: Is there an absolute constant $m$ such that any finite planar point set can be 2-colored such that every axis-parallel square that contains at least $m$ points contains points of both colors? I will discuss this problem and related ones.

Speaker: Klim Efremenko (TAU) Title: Testing Equality in Communication Graphs Abstract: Let G=(V,E) be a connected undirected graph with k vertices. Suppose that on each vertex of the graph there is a player having an n-bit string. Each player is allowed to communicate with its neighbors according to a (static) agreed communication protocol and the players must decide, deterministically, if their inputs are all equal. What is the minimum possible total number of bits transmitted in a protocol solving this problem? We determine this minimum up to a lower order

Speaker: Elchanan Mossel (MIT) Title: Lower Bounds on Same-Set Inner Product in Correlated Spaces Abstract: Suppose we pick X uniformly from {0,1,2}^n and Y is picked by letting each Y(i) = X(i) or X(i) + 1 mod 3 with probability 0.5 each independently. Is it true that for every set S with |S| > c 2^n it holds that the probability that both X and Y are in S is at least g(c) > 0, where g does not depend on the dimension n? Similar questions were asked before in different contexts. For example,

Speaker: Dmitry Faifman (U Toronto) Title: The integral geometry of indefinite signature.

Speaker: David Ellis, Queen Mary Title: Some applications of the $p$-biased measure to Erd\H{o}s-Ko-Rado type problems Abstract:

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 = −.