Martin Hils will speal about Classification of imaginaries in valued fields with automorphism.
Title: Classification of imaginaries in valued fields with automorphism
Abstract: The imaginaries in the theory ACVF of non-triviallally valued algebraically closed valued fields are classified by the so-called 'geometric' sorts. This is a fundamental result due to Haskell-Hrushovski-Macpherson. We show that the imaginaries in henselian equicharacteristic 0 valued fields may be reduced, under rather general
In the mid-18th century,Euler derived his famous equations of motion of an incompressible fluid, one ofthe most studied equations in hydrodynamics. More than 200 years later, in1966, Arnold observed that they are, in fact, geodesic equations on the(infinite dimensional) Lie group of volume-preserving diffeomorphisms of amanifold, endowed with a certain right-invariant Riemannian metric.
A countable group is said to be homogeneous if whenever tuples of elements u, v satisfy the same first-order formulas there is an automorphism of the group sending one to the other. We had previously proved with Rizos Sklinos that free groups are homogeneous, while most surface groups aren't. In a joint work with Ayala Dente-Byron, we extend this to give a complete characterization of torsion-free hyperbolic groups that are homogeneous.
Yatir Halevi will speal about Coloring Stable Graphs.
Title: Coloring Stable Graphs
Abstract: Given a graph G=(V,E), a coloring of G in \kappa colors is a map c:V\to \kappa in which adjacent vertices are colored in different colors. The chromatic number of G is the smallest such \kappa. We will briefly review some questions and conjectures on the chromatic number of infinite graphs and will mainly concentrate on the strong form of Taylor's conjecture:
Abstract: I will explain what measure distal transformations are
and describe some new constructions obtained with Eli Glasner.
These answer, inter alia, a question recently raised by Ibarlucia and Tsankov
concerning the existence of strongly ergodic non compact distal actions of the
free group.
In this talk we study a natural generalization of the classical \eps-net problem (Haussler-Welzl 1987), which we call 'the \eps-t-net problem': Given a hypergraph on n vertices and parameters t and \eps , find a minimum-sized family S of t-element subsets of vertices such that each hyperedge of size at least \eps n contains a set in S. When t=1, this corresponds to the \eps-net problem.
