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. 

Abstract: An observation by Jens Marklof shows that the primitive rational points of a fixed denominator along the periodic unipotent orbit of volume equal to the square of the denominator equidistribute inside a proper submanifold of the modular surface. This concentration as well as the equidistribution are intimately related to classical questions of number theoretic origin. We discuss the distribution of the primitive rational points along periodic orbits of intermediate size. In this case, we can show joint equidistribution with polynomial rate in the modular surface and in the torus.

Title:
Dilations of q-commuting unitaries
Abstract:
Let (u,v) be a pair of unitary operators on a Hilbert space H such that vu=quv for a complex number q of modulus 1. For q' another complex number of modulus 1, we determine the smallest constant c>0 for which there exists a pair of q' commuting unitaries (U,V) on a larger Hilbert space K containing H such that (u,v) is the compression of (cU,cV) to H.

As it was observed a few years ago, there exists a certain signed count of real lines on real projective hypersurfaces of degree 2n+1 and dimension n that, contrary to the honest "cardinal" count, is independent of the choice of a hypersurface, and by this reason provides, as a consequence, a strong lower bound on the honest count. Originally, in this invariant signed count the input of a line was given by its local contribution to the Euler number of an appropriate auxiliary universal vector bundle.

The 26th Amitsur Memorial Symposium will be held at the Einstein Institute of Mathematics, the Hebrew University of Jerusalem.

Coordinators: Avinoam Mann, Aner Shalev