First talk: Speaker: Madeleine Weinstein (Berkeley) Title: Voronoi Cells of Varieties Abstract:

Speaker: Shira Zerbib (U. Michigan, Iowa State University) Title: Envy-free division of a cake without the “hungry players" assumption Abstract: The fair division theorem due to Stromquist (1980) ensures that under some conditions it is possible to divide a rectangular cake into n pieces and assign one piece to each of n players such that no player strictly prefers a piece that has not been assigned to him.

Speaker: Omri Ben Eliezer, TAU Title: Finding patterns in permutations Abstract: For two permutations sigma and pi, we say that sigma contains a copy of pi, if there is a subset (not necessarily consecutive) of elements in sigma, whose relative order is the same as in pi. For example, if pi = (1,2,3), then a copy of pi in sigma amounts to an increasing subsequence in sigma of length 3. As shown by Guillemot and Marx, a copy of a constant length pi can be found in sigma in linear time. However, how quickly can one find such a

Hilbert's 12th problem (Kronecker's Jugendtraum) is one of the major open problems

Speaker: Eyal Karni (BIU) Title: Combinatorial high dimensional expanders Abstract: An eps-expander is a graph G=(V,E) in which every set of vertices X where |X|<=|V|/2 satisfies |E(X,X^c)|>=eps*|X| . There are many edges that "go out" from any relevant set.

Hilbert's 12th problem (Kronecker's Jugendtraum) is one of the major open problems

Abstract: Any birational geometer would agree that the best algorithm for resolution of singularities should run by defining a simple invariant of the singularity and iteratively blowing up its maximality locus. The only problem is that already the famous example of Whitney umbrella shows that this is impossible, and all methods following Hironaka had to use some history and resulted in more complicated algorithms. Nevertheless, in a recent work with Abramovich and Wlodarczyk we did construct such an algorithm, and an independent description of a similar

Liftings mod p² and the Nygaard filtration

Abstract: I will revisit old results on liftings mod p² and decompositions of de Rham complexes in positive characteristic (Deligne-I.) at the light of relations recently discovered independently by Bhargav Bhatt and myself between cotangent complexes, de Rham-Witt, and derived de Rham complexes.

Abstract: In this talk, I shall present a generalization of the lattice point counting problem for Euclidean balls in the context of a certain type of homogeneous groups, the so-called Heisenberg groups.

Abstract: A Markov chain over a finite state space is said to exhibit the total variation cutoff phenomenon if, starting from some Dirac measure, the total variation distance to the stationary distribution drops abruptly from near maximal to near zero. It is conjectured that simple random walks on the family of $k$-regular, transitive graphs with a two sided $\epsilon$ spectral gap exhibit total variation cutoff (for any fixed $k$ and $\epsilon). This is known to be true only in a small number of cases.