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 15

# HD-Combinatorics: Alexander Gamburd, "Arithmetic and Dynamics on Markoff-Hurwitz Varieties"

2:00pm to 4:00pm

## Location:

IIAS, Feldman Building, Givat Ram
Markoff triples are integer solutions to Markoff equation $x^2+y^2+z^2=3xyz$ which arose in Markoff's spectacular and fundamental work (1879) on diophantine approximation and has been henceforth ubiquitous in a tremendous variety of different fields in mathematics and beyond.
2017 Nov 06

4:00pm to 6:00pm

Room 130
2017 Nov 13

# HD-Combinatorics: Shmuel Weinberger, "L^2 cohomology"

2:00pm to 4:00pm

## Location:

Room 130, Feldman Building, Givat Ram
Abstract: I will give an introduction to the cohomology of universal covers of finite complexes. These groups are (for infinite covers) either trivial or infinite dimensional, but they have renormalized real valued Betti numbers. Their study is philosophically related to the topic of our year, and they have wonderful applications in geometry, group theory, topology etc and I hope to explain some of this.
2017 Nov 30

# Fedor Manin, "Introduction to quantitative topology"

9:00am to 10:00am

## Location:

Room 115, Feldman Building (IIAS), Givat Ram
2017 Oct 23

# Alex Lubotzky: High-Dimensional expanders and stability in group theory (course)

9:00am to 11:00am

## Location:

Feldman building, Eilat Hall
2017 Nov 20

# HD-Combinatorics: Ran Levi, "Neuro-Topology: An interaction between topology and neuroscience"

3:00pm to 4:00pm

## Location:

Room 130, Feldman Building, Givat Ram
Abstract: While algebraic topology is now well established as an applicable branch of mathematics, its emergence in neuroscience is surprisingly recent. In this talk I will present a summary of an ongoing joint project with mathematician and neuroscientists. I will start with some basic facts on neuroscience and the digital reconstruction of a rat’s neocortex by the Blue Brain Project in EPFL.
2018 Mar 26

# NG&AT: Stephan Ehlen, TBA

2:00pm to 3:00pm

## Location:

Room 70A, Ross Building, Jerusalem, Israel
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.
2016 Dec 27

# Special logic seminar - Itaï BEN YAACOV, "Baby version of the asymptotic volume estimate"

10:00am to 12:00pm

## Location:

Shprinzak 102
I'll show how the Vandermonde determinant identity allows us to estimate the volume of certain spaces of polynomials in one variable (or rather, of homogeneous polynomials in two variables), as the degree goes to infinity. I'll explain what this is good for in the context of globally valued fields, and, given time constraints, may give some indications on the approach for the "real inequality" in higher projective dimension.
2017 Dec 27

# Logic Seminar - Omer Ben-Neria - "Singular Stationarity and Set Theoretic Generalizations of Algebras"

11:00am to 1:00pm

## Location:

Ross 63
Abstract: The set theoretic generalizations of algebras have been introduced in the 1960s to give a set theoretic interpretation of usual algebraic structures. The shift in perspective from algebra to set theory is that in set theory the focus is on the collection of possible algebras and sub-algebras on specific cardinals rather than on particular algebraic structures. The study of collections of algebras and sub-algebras has generated many well-known problems in combinatorial set theory (e.g., Chang’s conjecture and the existence of small singular Jonsson cardinals).