• 2018 Jun 25

# HD-Combinatorics Special Day: "Quantum ergodicity and spectral theory with a discrete flavour" (organized by Elon Lindenstrauss and Shimon Brooks)

(All day)

## Location:

Feldman Building, Givat Ram
Title for the day: "Quantum ergodicity and spectral theory with a discrete flavour"

9:00-10:50: Shimon Brooks (Bar Ilan), "Delocalization of Graph Eigenfunctions"
14:00-15:50: Elon Lindenstrauss (HUJI), "Quantum ergodicity on graphs and beyond"

See also the Basic Notions by Elon Lindenstrauss @ Ross 70 (16:30).

Abstract for morning session:
• 2018 Jun 25

# Combinatorics: Roman Glebov (HU) "Perfect Matchings in Random Subgraphs of Regular Bipartite Graphs"

11:00am to 12:30pm

## Location:

IIAS, room 130, Feldman bldg, Givat Ram
Speaker: Roman Glebov (HU) Title: Perfect Matchings in Random Subgraphs of Regular Bipartite Graphs Abstract: Consider the random process in which the edges of a graph $G$ are added one by one in a random order. A classical result states that if $G$ is the complete graph $K_{2n}$ or the complete bipartite graph $K_{n,n}$, then typically a perfect matching appears at the moment at which the last isolated vertex disappears. We extend this result to arbitrary $k$-regular bipartite graphs $G$ on $2n$ vertices for all $k=\Omega(n)$.
• 2018 Jun 25

# NT&AG: Gal Porat (HUJI), "Induction and Restriction of $(\varphi,\Gamma)$-Modules"

2:00pm to 3:00pm

## Location:

Room 70A, Ross Building, Jerusalem, Israel
Abstract. Let L be a non-archimedean local field of characteristic 0. In this talk we will present a variant of the theory of (\varphi,\Gamma)-modules associated with Lubin-Tate groups, developed by Kisin and Ren, in which we replace the Lubin-Tate tower by the maximal abelian extension \Gamma=Gal (L^ab/L). This variation allows us to compute the functors of induction and restriction for (\varphi,\Gamma)-modules, when the ground field L changes. If time permits, we will also discuss the Cherbonnier-Colmez theorem on overconvergence in our setting. Joint work with Ehud de Shalit.
• 2018 Jun 25

# Elon Lindenstrauss (HUJI) - Effective Equidistribution and property tau

4:30pm to 5:45pm

This is the second of two lectures on the paper Einseidler,, Margulis, Mohammadi and Venkatesh https://arxiv.org/abs/1503.05884. In this second lecture I will explain how the authors obtain using property tau (uniform spectral gap for arithmetic quotient) quantitaive equidistribution results for periodic orbits of maximal semisimple groups. Surprisingly, one can then use this theorem to establish property tau...
• 2018 Jun 26

# Amitsur Symposium: Alex Lubotzky - "First order rigidity of high-rank arithmetic groups"

10:00am to 11:00am

## Location:

Manchester House, Lecture Hall 2
The family of high rank arithmetic groups is a class of groups playing an important role in various areas of mathematics. It includes SL(n,Z), for n>2 , SL(n, Z[1/p] ) for n>1, their finite index subgroups and many more. A number of remarkable results about them have been proven including; Mostow rigidity, Margulis Super rigidity and the Quasi-isometric rigidity.
• 2018 Jun 26

# Amitsur Symposium: Malka Schaps - "Symmetric Kashivara crystals of type A in low rank"

11:30am to 12:30pm

## Location:

Manchester House, Lecture Hall 2
The basis of elements of the highest weight representations of affine Lie algebra of type A can be labeled in three different ways, my multipartitions, by piecewise linear paths in the weight space, and by canonical basis elements. The entire infinite basis is recursively generated from the highest weight vector of operators f_i from the Chevalley basis of the affine Lie algebra, and organized into a crystal called a Kashiwara crystal. We describe cases where one can move between the different labelings in a non-recursive fashion, particularly when the crystal has some symmetry.
• 2018 Jun 26

# Dynamics Lunch: Jasmin Matz (Huji) ״Distribution of periodic orbits of the horocycle flow״

12:00pm to 1:00pm

## Location:

Manchester lounge
An old result of Hedlund tells us that there are no closed orbits for the horocycle flow on a compact Riemann surface M. The situation is different if M is non-compact in which case there is a one-parameter family of periodic orbits for every cusp of M. I want to talk about a result by Sarnak concerning the distribution of the such orbits in each of these families when their length goes to infinity. It turns out that these orbits become equidistributed in M and the rate of convergence can in fact be quantified in terms of spectral properties of the Eisenstein series on M.
• 2018 Jun 26

# Amitsur Symposium: Arye Juhasz - "On the center of Artin groups"

2:00pm to 3:00pm

## Location:

Manchester House, Lecture Hall 2
Let A be an Artin group. It is known that if A is spherical (of finite type) and irreducible (not a direct sum), then it has infinite cyclic center. It is conjectured that all other irreducible Artin groups have trivial center. I prove this conjecture under a stronger assumption that not being spherical namely, if there is a standard generator which is not contained in any 3-generated spherical standard parabolic subgroup. The main tool is relative presentations of Artin groups.
• 2018 Jun 26

# Sieye Ryu (BGU): Predictability and Entropy for Actions of Amenable Groups and Non-amenable Groups

2:15pm to 3:15pm

Suppose that a countable group $G$ acts on a compact metric space $X$ and that $S \subset G$ is a semigroup not containing the identity of $G$. If every continuous function $f$ on $X$ is contained in the closed algebra generated by $\{sf : s \in S\}$, the action is said to be $S$-predictable. In this talk, we consider the following question due to Hochman: When $G$ is amenable, does $S$-predictability imply zero topological entropy? To provide an affirmative answer, we introduce the notion of a random invariant order.
• 2018 Jun 26

# Amitsur Symposium: Aner Shalev - "The length and depth of finite groups, algebraic groups and Lie groups"

3:00pm to 4:00pm

## Location:

Manchester House, Lecture Hall 2
The length of a finite group G is defined to be the maximal length of an unrefinable chain of subgroups going from G to 1. This notion was studied by many authors since the 1940s. Recently there is growing interest also in the depth of G, which is the minimal length of such a chain. Moreover, similar notions were defined and studied for important families of infinite groups, such as connected algebraic groups and connected Lie groups.