Abstract: I will review the research about dp-minimal expansions of (Z,+), and then present a recent result classifying (Z,+,<) as the unique dp-minimal expansion of (Z,+) defining an infinite subset of N. All the relevant notions will be defined in the talk.
Abstract: The rel foliation is a foliation of the moduli space of abelian differentials obtained by "moving the zeroes of the one form while keeping all absolute periods fixed". It has been studied in complex analysis and dynamics under different names (isoperiodic foliation, Schiffer variation, kernel foliation). Until recent years the question of its ergodicity was wide open. Recently partial results were obtained by Calsamiglia-Deroin-Francaviglia and by Hamenstadt. In our work we completely resolve the ergodicity question.
Universal functions, strong colourings and ideas from PID
A construction of Shelah will be reformulated using the PID to provide alternative models of the failure of CH and the existence of a universal colouring of cardinality. The impact of the range of the colourings will be examined. An application to the theory of strong colourings over partitions will also be given.
On generating ideals by additive subgroups of rings and an application to Bohr compactifications of some matrix groups
Abstract: I will present several fundamental results about generating ideals in finitely many steps inside additive groups of rings from my very recent joint paper with T. Rzepecki. I will also mention an application to computations of definable and classical Bohr compactifications of the groups of upper unitriangular and invertible upper triangular matrices
Title: Gross' Canonical and Quasi-canonical Liftings
Abstract: The goal of this talk is to give an account on Gross' seminal paper on canonical and quasi-canonical liftings of formal modules. Except for basic notions on formal groups, this talk is intended to be self-contained.
Results in Borel chromatic numbers using Infinite games and Borel determinacy
Abstract: (Based on the paper “A determinacy approach to Borel combinatorics” by Andrew Marks) A Borel graph on a standard Borel space X is a symmetric irreflexive relation G on X that is Borel as a subset of X×X.
A Borel coloring of a Borel graph G on X is a Borel function c from X to a standard Borel space Y such that if xGy then c(x)!=c(x)
The meeting will be open from 16.15 (local time) *NOTE UNUSUAL TIME* for a virtual coffee with the speaker.
Title: Short exponential sums and their applications over function fields
In joint work with Will Sawin, we obtain (square-root) cancellation in quite general incomplete exponential sums for the ring F_q[x] of polynomials over a finite field. This has applications to problems in analytic number theory such as the Chowla conjecture, Bateman-Horn conjecture, and the number of real quadratic function fields with a huge class group.
Solving equations in finite groups and complete amalgamation
Abstract: Roth's theorem on arithmetic progression states that a subset $A$ of the natural numbers of positive upper density contains an arithmetic progression of length 3, that is, the equation $x+z=2y$ has a solution in $A$.
Abstract: We present measures on product spaces with Markovian type of dependence. We discuss questions like how they should be defined; in what way they are less understood than product measures; and, what nice properties of product measures we may hope to have also in Markov measures. We will assume knowledge in probability in an undergraduate level, as well as general familiarity with the fact that measures on product spaces can be specified on cylinders.