Speaker: Elad Levi
Algebraic regularity lemma for hypergraphs
Abstract: Szemer´edi’s Regularity Lemma is a fundamental tool in graph theory. It states that for every large enough graph, the set of vertices has a partition A1,..,Ak, such that for almost every two subsets Ai,Aj the induced bipartite graph on (Ai,Aj) is regular, i.e. similar to a random bipartite graph up to a given error.
It is a familiar fact (sometimes attributed to Ahlbrandt-Ziegler, though it is possibly older) that two aleph0-categorical theories are bi-interpretable if and only if their countable models have isomorphic topological isomorphism groups. Conversely, groups arising in this manner can be given an abstract characterisation, and a countable model of the theory (up to bi-interpretation, of course) can be reconstructed.
Dependent theories have now a very solid and well-established collection of results and applications. Beyond first order, the development of "dependency" has been rather scarce so far. In addition to the results due to Kaplan, Lavi and Shelah (dependent diagrams and the generic pair conjecture), I will speak on a few lines of current research around the extraction of indiscernibles for dependent diagrams and on various forms on dependence for abstract elementary classes. This is joint work with Saharon Shelah.
A special class among the countably infinite relational structures is the class of homogeneous structures. These are the structures where every finite partial isomorphism extends to a total automorphism. A countable set, the ordered rationals, and the random graph are all homogeneous.
We will present briefly the "multiverse view" of set theory, advocated by Hamkins, that there are a multitude of set-theoretic universes, and not one background universe, and his proposed "Multiverse Axioms". We will then move on to present the main result of Gitman and Hamkins in their paper "A natural model of the multiverse axioms" - that the countable computably saturated models of ZFC form a "toy model" of the multiverse axioms.
Chang's Conjecture is a strengthening of Lowenheim-Skolem-Tarski theorem. While Lowenheim-Skolem-Tarski theorem is provable in ZFC, any instance of Chang's Conjecture is independent with ZFC and has nontrivial consistency strength. Thus, the question of how many instances of Chang's Conjecture can consistently hold simultaneously is natural.
I will talk about some classical results on the impossibility of some instances of Chang's Conjecture and present some results from a joint work with Monroe Eskew.
Speaker: Shira Zerbib Gelaki (MSRI, University of Michigan)
Title: Colorful coverings of polytopes -- the hidden topological truth behind different colorful phenomena
The topological KKMS Theorem is a powerful extension of the Brouwer's Fixed-Point Theorem, which was proved by Shapley in 1973 in the context of
We prove a colorful and polytopal generalization of the KKMS Theorem, and show that our theorem implies some seemingly unrelated results in
discrete geometry and combinatorics involving colorful settings.
Using the endoscopic classification
of automorphic forms for unitary groups,
I will prove conjecturally sharp upper
bounds for the growth of Betti numbers
in congruence towers of complex
hyperbolic manifolds. This is
joint work with Sug Woo Shin.
האירוע הזה כולל שיחת וידאו ב-Google Hangouts.
Abstract: In modern algebraic geometry we encounter the notion of derived intersection of subschemes. This is a sophisticated way to encode what happens when two subschemes Y_1 and Y_2 of a given scheme X intersect non-transversely. The classical intersection multiplicity can be extracted from the derived intersection.
We prove cases of Rietsch mirror conjecture that the quantum
connection for projective homogeneous varieties is isomorphic to the
pushforward D-module attached to Berenstein-Kazhdan geometric crystals.
The idea is to recognize the quantum connection as Galois and the
geometric crystal as automorphic. In particular we link the purity of
Berenstein-Kazhdan crystals to the Ramanujan property of certain Hecke
The isomorphism of D-modules comes from global rigidity results where a
Hecke eigenform is determined by its local ramification. We reveal
This talk is in natural in the context of the Zagier conjecture.
We express values of the Kronecker double series at CM points in
terms of values some version (Bloch-Wigner) of dilogarithm in algebraic
numbers. As zeta-function of the Hilbert class field of quadratic field can
be expressed as combination of the Kronecker double series at CM points
my result gives explicit form of the Zagier conjecture.
My technique is rather elementary and the proof is based on the introduction
some new function (elliptic (1,1)-logarithm) and comparisons with it.
In this talk, I present an analogue of the Hardy-Littlewood conjecture on the asymptotic distribution of prime constellations in the setting of short intervals in function fields of smooth projective curves over finite fields.
I will discuss the definition of a "short interval" on a curve as an additive translation of the space of global sections of a sufficiently positive divisor E by a suitable rational function f, and show how this definition generalizes the definition of a short interval in the polynomial
In this talk we discuss some aspects concerning the arithmetic of
systems of quadratic forms. This includes a result on the frequency of
counterexamples to the Hasse principle for del Pezzo surfaces of degree
four (joint work with J. Jahnel), and a result on the representability of
integers by systems of three quadratic forms (joint work with L. B. Pierce
and M. M. Wood).
Motivated by understanding the action of Hecke operators on special sub-varieties of Shimura varieties, we consider the simplest possible case: the action of Hecke operators on the j-line, namely on the moduli space of elliptic curves, and in particular the action on singular moduli. Our interest is in this action considered in the p-adic topology. The emerging picture is surprisingly rich and the answers involve Serre-Tate coordinates, the Gross-Hopkins period map and finally involves random walks on GL_n.
This is joint work with Payman Kassaei (King's College).