2017 Nov 27

# HD-Combinatorics: Irit Dinur, "PCPs and high dimensional expansion"

2:00pm to 4:00pm

## Location:

Room 130, Feldman Building (IIAS), Givat Ram
The "PCP theorem" says that problems in NP are hard in a robust or stable way. I will give a brief intro to PCPs (and explain the acronym) and then try to outline a proof of the PCP theorem based on "agreement expansion" which is a form of high dimensional expansion. My aim is to show how high dimensional expansion is inherently present in PCP type questions.
2017 Dec 04

# HD-Combinatorics: Tali Kaufman, "High dimensional expanders imply PCP-agreement expansion"

2:00pm to 4:00pm

## Location:

Room 130, Feldman Building (IIAS), Givat Ram
Abstract: I will introduce the notion of (PCP)-agreement expansion which is an important building block in PCPs constructions. I will then show that a high dimensional expanders imply PCP-agreement expanders. based on Joint work with Irit Dinur
2017 Sep 05

# IIAS Seminar: Tatiana Nagnibeda - Infinite Ramanujan graphs and completely dissipative actions

4:00pm to 5:00pm

## Location:

Math room 209
Speaker : Tatiana Nagnibeda (University of Geneva) Abstract: The definition of a Ramanujan graph extends naturally to infinite graphs: an infinite graph is Ramanujan if its spectral radius is not larger than (and hence equal to) the spectral radius of its universal covering tree. As with infinite families of finite graphs, it is interesting and non-trivial to understand, how much Ramanujan graphs resemble trees. I will discuss some results in this direction obtained in a joint work with Vadim Kaimanovich, by investigating ergodic properties of boundary actions of free groups.
2017 Dec 18

# HD-Combinatorics: Steven Damelin, "Approximate and exact alignment of data, extensions and interpolation in R^D--parts"

2:00pm to 4:00pm

## Location:

Sprinzak Building, Room 28
Speaker: Steven Damelin (The American Mathematical Society) Abstract: A classical problem in geometry goes as follows. Suppose we are given two sets of $D$ dimensional data, that is, sets of points in $R^D$. The data sets are indexed by the same set, and we know that pairwise distances between corresponding points are equal in the two data sets. In other words, the sets are isometric. Can this correspondence be extended to an isometry of the ambient Euclidean space? In this form the question is not terribly interesting; the answer has long known
2017 Nov 20

# Andreas Thom, "C*-algebras and group theory"

9:00am to 11:00am

## Location:

Room 130, Feldman Building (IIAS), Givat Ram
2017 Nov 27

# Andreas Thom, "C*-algebras and group theory (continued)"

9:00am to 11:00am

## Location:

Room 130, Feldman Building (IIAS), Givat Ram
2017 Dec 25

# HD-Combinatorics: Shai Evra, "Bounded degree high dimensional expanders"

2:00pm to 4:00pm

In the recent theory of high dimensional expanders, the following open problem was raised by Gromov: Are there bounded degree high dimensional expanders? For the definition of high dimensional expanders, we shall follow the pioneers of this field, and consider the notions of coboundary expanders (Linial-Meshulam) and topological expanders (Gromov). In a recent work, building on an earlier work of Kaufman-Kazhdan-Lubotzky in dimension 2, we were able to prove the existence of bounded degree expanders according to Gromov, in every dimension.
2017 Nov 20

# Leonard Schulman, "Analysis of a Classical Matrix Preconditioning Algorithm"

2:00pm to 3:00pm

## Location:

Room 130, Feldman Building, Givat Ram
There are several prominent computational problems for which simple iterative methods are widely preferred in practice despite an absence of runtime or performance analysis (or "worse", actual evidence that more sophisticated methods have superior performance according to the usual criteria). These situations raise interesting challenges for the analysis of algorithms. We are concerned in this work with one such simple method: a classical iterative algorithm for balancing matrices via scaling transformations. This algorithm, which goes back to Osborne and
2017 Oct 23

# HD-Combinatorics: Nati Linial, "High-dimensional permutations"

2:00pm to 4:00pm

## Location:

Israel Institute for Advanced Studies (Feldman building, Givat Ram), Eilat Hall
This is a survey talk about one of the main parts of what we call high-dimensional combinatorics. We start by equating a permutation with a permutation matrix. Namely, an nxn array of zeros and ones where every line (=row or column) contains exactly one 1. In general, a d-dimensional permutation is an array [n]x[n]x....x[n] (d+1 factors) of zeros and ones in which every line (now there are d+1 types of lines) contains exactly one 1. Many questions suggest themselves, some of which we have already solved, but many others are still wide opne. Here are a few examples:
2018 Jan 10

# Logic Seminar - Alex Lubotzky - "First order rigidity of high-rank arithmetic groups"

11:00am to 1:00pm

## Location:

Ross 63
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 Jan 15

# NT&AG: Dmitry Vaintrob (IAS), "The log-coherent category and Hodge theory of open varieties"

2:00pm to 3:00pm

## Location:

Room 70A, Ross Building, Jerusalem, Israel
I will talk about a new Abelian category associated to an open variety with normal-crossings (or more generally, logarithmic) choice of compactification, which behaves in remarkable (and remarkably nice) ways with respect to changes of compactification and duality, and which first appeared in work on mirror symmetry.
2018 Jan 01

# NT&AG: Alexander Polischchuk (University of Oregon), "Associative Yang-Baxter equation and related 1-CY categories"

3:00pm to 4:00pm

## Location:

Room 70A, Ross Building, Jerusalem, Israel
The talk is based on the joint work with Yanki Lekili. The associative Yang-Baxter equation is a quadratic equation related to both classical and quantum Yang-Baxter equations. It appears naturally in connection with triple Massey products in the derived category of coherent sheaves on elliptic curve and its degenerations. We show that all of its nondegenerate trigonometric solutions are obtained from Fukaya categories of some noncompact surfaces. We use this to prove that any two simple vector bundles on a cycle of projective lines are related by a sequence of spherical twists.
2017 Dec 13

# Logic seminar - Omer Mermelstein - "Template structures for the class of Hrushovski ab initio geometries"

11:00am to 1:00pm

## Location:

Math 209
Zilber's trichotomy conjecture, in modern formulation, distinguishes three flavours of geometries of strongly minimal sets --- disintegrated/trivial, modular, and the geometry of an ACF. Each of these three flavours has a classic template'' --- a set with no structure, a projective space over a prime field, and an algebraically closed field, respectively. The class of ab initio constructions with which Hrushovski refuted the conjecture features a new flavour of geometries --- non-modular, yet prohibiting any algebraic structure.
2017 Dec 28

# Amitsur Algebra: Ari Shnidman (Boston College), "The behavior of rational points in one-parameter families"

12:00pm to 1:00pm

## Location:

Ross 70, Math Building, Givat Ram
Title: The behavior of rational points in one-parameter families Abstract: How often does a "random" algebraic plane curve f(x,y) = 0 have a solution with rational coordinates? In one-parameter "twist" families of elliptic curves, Goldfeld conjectured that there should be a rational point exactly half of the time. Recent progress towards this conjecture makes use of Selmer groups, and I'll explain the geometric idea underlying their construction. I'll also describe results for families of curves of higher genus, and abelian varieties of higher dimension.
2017 Nov 01

# Logic Seminar - Immanuel BenPorat - "Cardinal conditions for strong Fubini theorems"

11:00am to 1:00pm

## Location:

Math209
This talk will be largely based on a paper by Joseph Shipman with the same title. We will discuss some variations of Fubini type theorems. The focus will be on what is known as "strong Fubini type theorems". Apparently these versions were proved to be independent of ZFC,and our main aim will be to sketch a proof of this result. We will assume basic knowledge in measure theory. Aside from that, the material is rather self contained.