Speaker: Raphy Yuster, U. Haifa
Title: On some Ramsey type problems in tournaments
Abstract:
I will talk about several Ramsey type problems in tournaments guaranteeing the existence of subgraphs with certain chromatic properties.
Here are two such problems which attracted some attention recently:
1. Let g(n) be the smallest integer such that every tournament with more than g(n) vertices has an *acyclic subgraph* with chromatic number larger than n.

Speaker: Arindam Banerjee, RMVERI
Title: Castelnuovo-Mumford Regularity, Combinatorics and Edge Ideals.
Abstract:

From Raphy Yuster: On Monday 17 June, 2019 we will hold a one day mini conference in memory of Professor Yossi Zaks
(see attached poster or updated information in
http://sciences.haifa.ac.il/math/wp/?page_id=1382 )
Mini conference: Yossi Zaks Memorial Meeting – Monday, June 17, 2019
list of speakers
Noga Alon, Princeton University and Tel Aviv University
Gil Kalai, Hebrew University
Nati Linial, Hebrew University
Rom Pinchasi, The Technion
Organizers

Speaker: Karthik C. Srikanta (Weizmann Institute)
Title: On Closest Pair Problem and Contact Dimension of a Graph
Abstract: Given a set of points in a metric space, the Closest Pair problem asks to find a pair of distinct points in the set with the smallest distance. In this talk, we address the fine-grained complexity of this problem which has been of recent interest. At the heart of all our proofs is the construction of a family of dense bipartite graphs with special embedding properties and are inspired by the construction of locally dense codes.

Speaker: Kim Minki, Technion
Title: The fractional Helly properties for families of non-empty sets
Abstract:
Let $F$ be a (possibly infinite) family of non-empty sets.
The Helly number of $F$ is defined as the greatest integer $m = h(F)$ for which there exists a finite subfamily $F'$ of cardinality $m$ such that every proper subfamily of $F'$ is intersecing and $F'$ itself is not intersecting.
For example, Helly's theorem asserts that the family of all convex sets in $d$-dimensional Euclidean space has Helly number $d+1$.

Speaker: Roy Meshulam (Technion)
Title: Topology and combinatorics of the complex of flags
Abstract:

Abstract: We first survey a recent progress related to the nonsingular Bernoulli transformations. Then we construct inductively new examples of conservative Bernoulli maps of type III. They appear as a limit of a sequence of Bernoulli maps of type II_1.

Poisson suspensions are random sets of points endowed with a transformation that displaces each point according to a single transformation of the sigma-finite space where the points lie. In this ongoing work, instead of dealing with measure-preserving transformations (which is the classical case), we are going to present our attempt to explore the non-singular case. The difficulties are counterbalanced by new tools that are trivial in the measure-preserving case but highly informative in the non-singular one.

Abstract:
The Minimal Tower Problem was one of most famous question in Cardinal
Invariants. We will present a combinatorial argument of this proof, which without using model theory
and forcing, motivated by Malliaris and Shelah's proof.

Yun and Zhang compute the Taylor series expansion of an automorphic L-function over a function field, in terms of intersection pairings of certain algebraic cycles on the so-called moduli stack of shtukas. This generalizes the Waldspurger and Gross-Zagier formulas, which concern the first two coefficients.

Zlil Sela and Alex Lubotzky "Model theory of groups"
In the first part of the course we will present some of the main results in the theory of free,
hyperbolic and related groups, many of which appear as lattices in rank one simple Lie groups
We will present some of the main objects that are used in studying the theory of these groups,
and at least sketch the proofs of some of the main theorems.
In the second part of the course, we will talk about the model theory of lattices in high rank simple Lie groups.

Abstract: The ultrafilter lemma, saying that every filter can be extended to an ultrafilter, is one of the fundamental consequences of the axiom of choice. By adding closure assumptions, and asking for extension of $\kappa$-complete filters to $\kappa$-complete ultrafilters, we obtain the notion of strongly compact cardinal, which has a very high consistency strength.