Abstract:
Paul L\'evy's classical arcsine law states that the occupation time ratio of one-dimensional Brownian motion for the positive side is arcsine-distributed. The arcsine law has been generalized to a variety of classes of stochastic processes and dynamical systems.

Title: An intrinsic characterization of cofree representations of reductive groups

Abstract.
The realization of m.p automorphisms as transfer on the space of the
paths on the graded graphs allows to use new kind of encoding
of one-sided Bernoulli shift.
I will start with simple example how to realize Bernoulli shift in
the locally finite space (graph) $\prod_n {1,2,\dots n}$ (triangle
compact.)
Much more complicated example connected to old papers by
S.Kerov-Vershik and recent by Romik-Sniady in which one-sided
Bernoulli shift is
realized as Schutzenberger transfer on the space of infinite Young

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.

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

אשנב למתמטיקה

חן מרגלית (תלמיד שנה ג') : סייטסוואפ - המתמטיקה של הג'אגלינג

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Speaker: Uri Rabinovich (U. Haifa)
Title: SOME EXTREMAL PROBLEMS ABOUT SIMPLICIAL COMPLEXES
Abstract:
We shall discuss the following three issues:
* The existence of Hamiltonian d-cycles, i.e., simple d-cycles containing a spanning d-hypertree of a complete d-complex K_n^d;
* The existence of a distribution D over spanning d-hypertrees T of K_n^d, so that for ANY
(d-1)-cycle C there, the expected size of the d-filling of C with respect to a random T from D is Omega(n^d);

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

Speaker: Doron Puder, TAU
Title: Aldous' spectral gap conjecture for normal sets
Abstract:
Aldous' spectral gap conjecture, proved in 2009 by Caputo, Liggett and Richthammer, states the following a priori very surprising fact: the spectral gap of a random walk on a finite graph is equal to the spectral gap of the interchange process on the same graph.

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.

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.