AF/NT seminar

Krakow, Poznań

Automorphic Forms/ Number Theory seminar is a recurrent meeting wandering between Jagiellonian University in Krakow (JU)  and Adam Mickiewicz University in Poznań (AMU), typically on the first Monday of the month. We plan to have two invited speakers per session preceded by  introductory talks by junior faculty or graduate students. 

We have limited funds to support travel for the participants from Poland to the seminar venue. 

Talks in Krakow will take place in the Conference Hall B  under the library at the Faculty of Mathematics and Computer Science of JU . Talks in Poznań will take place in the seminar room B1-37 at the Faculty of Mathematics and Computer Science of AMU. 

Upcoming Meetings

Jan 13th, 2025 (Kraków) 

Introductory talks:

11:00-12:00 Dominik Kwietniak (UJ) 

Title:  An introduction to Ratner's theorems on unipotent flows I.

Abstract: Abstract: Unipotent flows are well-behaved dynamical systems. In particular, Marina Ratner has shown that the closure of every orbit for such a flow is of a nice algebraic (or geometric) form. This is known as the Ratner Orbit Closure Theorem. The other two closely related results are the Ratner Measure-Classification Theorem and the Ratner Equidistribution Theorem. These theorems resolve long-standing conjectures in ergodic theory and have applications in number theory, particularly in proving density results for integer points on homogeneous varieties. Their strength comes from complete classification of orbit closures and invariant measures for a whole class of important flows, something rare in the theory of dynamical systems.

The two introductory lectures are intended for a fairly general audience. Our aim is to provide an elementary introduction to the subject, explain these important theorems and some of their consequences. We concentrate on examples that illustrate the theorems and applications. The lectures are based on excellent lecture notes "Ratner’s Theorems on Unipotent Flows" written by Dave Witte Morris, see https://arxiv.org/pdf/math/0310402

12:0-13:30 Lunch break

13:30-14:30 Dominik Kwietniak (UJ)  

Title An introduction to Ratner's theorems on unipotent flows II

14:30-15:00 Coffee break 

15:00-16:00 Alex Gorodnik (University of Zurich)

Title: Equidistribution of unipotent periods and randomness of counting functions

Abstract: We study the limiting behavior of measures supported on unipotent orbits and discuss quantitative estimates for correlations of these measures. As an application we analyze statistical properties of counting functions representing the number of solutions of multiplicative Diophantine problems and show that they behave like sums of independent random variables. This is a joint work with Björklund and Fregolli.


March 3rd, 2025 (Poznań) 

Abhishek Saha (Queen Mary University of London)

May 5th, 2025 (Poznań) 

Kathrin Maurischat (RWTH Aachen University)