2018 Jun 11

# HD-Combinatorics: Roy Meshulam, "Homology and Expansion of the spherical building"

9:00am to 9:50am

## Location:

Feldman Building, Givat Ram
Let X be the spherical building associated to the group G=GL(n,F) , where F is a finite field. We will survey some results on the homology of X with constant and twisted coefficients, and on the corresponding expansion properties.
2018 Jun 04

# HD-Combinatorics: Prahladh Harsha, "Local Testability and Expansion"

10:00am to 10:50am

## Location:

Feldman Building, Givat Ram
Locally testable codes are error-correcting codes that admit super-efficient checking procedures. In the first part of the talk, we will see why expander based codes are NOT locally testable. This is in contrast to typical "good" error correcting properties which follow from expansion. We will then see that despite this disconnect between expansion and testability, all known construction of locally testable codes follow from the high-dimensional expansion property of a related complex leaving open an intriguing connection between local-testability and high-dimension
2018 Jun 04

# HD-Combinatorics: Eli Shamir, "Almost optimal Boolean matrix multiplication[BMM] - By Multi-encoding of rows and columns"

9:00am to 9:50am

## Location:

Feldman Building, Givat Ram
Computing R=P.Q ,the product of two mXm Boolean matrices [BMM] is an ingredient of many combinatorial algorithms. Many efforts were made to speed it beyond the standard m^3 steps, without using the algebraic multiplication. To divide the computation task, encoding of the rows and column indices were used (1.1) j by (j1,j2) k by (k1,k2) e.g. using integer p j2=j mod p ,j1=ceiling of j/p. Clearly, the product of the ranges of the digits= m1.m2 - is approximately m. L.Lee’s article reduced BMM to parsing substrings of a fixed string u with
2018 Jun 04

# HD-Combinatorics: Shai Evra, "Gromov-Guth embedding complexity"

2:00pm to 3:50pm

## Location:

Feldman Building, Givat Ram
In this talk we shall review a paper by Gromov and Guth, in which they introduced several ways to measure the geometric complexity of an embedding of simplicial complexes to Euclidean spaces. One such measurement is strongly related to the notion of high dimensional expanders introduced by Gromov, and in fact, it is based on a paper of Kolmogorov and Barzadin from 1967, in which the notion of an expander graph appeared implicitly. We shall show one application of bounded degree high dimensional expanders, and present many more open questions arising from the above mentioned paper.
2018 May 29

# Logic Seminar - Martin Goldstern - "Higher Random Reals"

1:30pm to 3:00pm

The set of real numbers is often identified with
Cantor Space 2^omega, with which it shares many important
properties: not only the cardinality, but also other
"cardinal characteristics" such as cov(null), the smallest
number of measure zero sets needed to cover the whole space,
and similarly cov(meager), where meager="first category";
or their "dual" versions non(meager) (the smallest
cardinality of a nonmeager set) and non(null).

Many ZFC results and consistency results (such as
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 May 28

# HD-Combinatorics: Special Day on "Locally testable codes" (organized by Dorit Aharonov and Noga Ron-Zewi)

(All day)

## Location:

Eilat Hall, Feldman Building, Givat Ram
09:00 - 10:50 Noga Ron-Zewi, "Locally testable codes"

14:00 - 14:50 Dorit Aharonov, "Quantum error correcting codes"
​15:00 - 15:50 Dorit Aharonov, " Quantum Locally Testable codes and High dimensional expansion"

Abstract for Noga Ron-Zewi's talk:
2018 May 31

# Basic Notions: Mike Hochman - "Furstenberg's conjecture on transversality of semigroups and slices of fractal sets" Part I

4:00pm to 5:30pm

## Location:

Ross 70
In 1970, Furstenberg made a number of conjectures about the expansions of real numbers in non-comensurable bases, e.g. bases 2 and 3. The most difficult remains wide open, but several related problems, which can be stated in terms of the dimension theory of certain fractal sets, were recently settled. In the first talk I will try to describe the conjectures and some of what was known. In the second talk I will present Meng Wu's proof of the "slice conjecture" (it was also proved independently by Pablo Shmerkin, and I will try to also say a little about that proof too).
2018 Jun 07

# Basic Notions: Mike Hochman - "Furstenberg's conjecture on transversality of semigroups and slices of fractal sets" Part II

4:00pm to 5:30pm

## Location:

Ross 70
Second part of the talk from the previous week.
2018 May 30

# Special Wolf Prize lecture: Vladimir Drinfeld (Chicago): Slopes of irreducible local systems

## Lecturer:

11:00am to 12:00pm

## Location:

Kaplan building, Rothberg hall
2018 May 21

# HD-Combinatorics Special Day on "Stability in permutations" (organized by Oren Becker)

(All day)

## Location:

Room 130, IIAS, Feldman Building, Givat Ram

Both talks will be given by Oren Becker.
9:00 - 10:50
Title: Proving stability via hyperfiniteness, graph limits and invariant random subgroups

Abstract: We will discuss stability in permutations, mostly in the context of amenable groups. We will characterize stable groups among amenable groups in terms of their invariant random subgroups. Then, we will introduce graph limits and hyperfinite graphings (and some theorems about them), and show how the aforementioned characterization of stability follows.

14:00 - 16:00
2018 May 17

# Basic Notions - Benjamin Weiss: "All ergodic systems have the Weak Pinsker property" Part 2

4:00pm to 5:30pm

## Location:

Ross 70
Second part of the talk from last week: An ergodic system (X;B; μ; T) is said to have the weak Pinsker property if for any ε > 0 one can express the system as the direct product of two systems with the first having entropy less than ε and the second one being isomorphic to a Bernoulli system. The problem as to whether or not this property holds for all systems was open for more than forty years and has been recently settled in the affirmative in a remarkable work by Tim Austin. I will begin by describing why Jean-Paul formulated this prob-
2018 May 22

# T&G: Elisheva Adina Gamse (Toronto), The moduli space of parabolic vector bundles over a Riemann surface

12:00pm to 1:30pm

## Location:

Room 110, Manchester Buildling, Jerusalem, Israel
Let $\Sigma$ be a Riemann surface of genus $g \geq 2$, and p be a point on $\Sigma$. We define a space $S_g(t)$ consisting of certain irreducible representations of the fundamental group of $\Sigma \setminus p$, modulo conjugation by SU(n). This space has interpretations in algebraic geometry, gauge theory and topological quantum field theory; in particular if Σ has a Kahler structure then $S_g(t)$ is the moduli space of parabolic vector bundles of rank n over Σ.
2018 May 29

# T&G: Tristan Collins (Harvard), Geometric flows and algebraic geometry

12:00pm to 1:30pm

## Location:

Room 110, Manchester Buildling, Jerusalem, Israel
I will discuss the inverse Monge-Ampere flow and its applications to the existence, and non-existence, of Kahler-Einstein metrics. To motivate this discussion I will first describe the classical theory of the Donaldson heat flow on a Riemann surface, and its relationship with the Harder-Narasimhan filtration of an unstable vector bundle.
2018 May 31

# Groups & Dynamics: Anish Gosh (TIFR) - The metric theory of dense lattice orbits

10:30am to 11:30am

Abstract: The classical theory of metric Diophantine approximation is very well developed and has, in recent years, seen significant advances, partly due to connections with homogeneous dynamics. Several problems in this subject can be viewed as particular examples of a very general setup, that of lattice actions on homogeneous varieties of semisimple groups. The latter setup presents significant challenges, including but not limited to, the non-abelian nature of the objects under study.