Algomanet - spring 2024

Basic information

The two Algomanet courses given by Pablo Candela and Joel Moreira, which are scheduled for the spring 2024, will take place in the week May 20-24 at the Jagiellonian University in Kraków. The courses will be delivered on site only, starting at 9am on Monday May 20 and concluding in late afternoon on Friday May 24. In the following week, i.e., the week May 27-31, the workshop Dynamics and Number Theory, which is likely to be of interest to a substantial number of Algomanet participants, will take place at the Jagiellonian University.

The registration for the Algomanet courses is now open. You can register by sending an e-mail to both Jan Grebík (grebikj@mail.muni.cz) and Dan Kráľ (dkral@fi.muni.cz) before the deadline noted below. It is possible to register for both or just one of the two courses offered. The courses are primarily intended for those affiliated with the participating universities, however, we are able to offer a limited number of places to students from other universities, too.

Registration deadline: Monday March 25, 2024

Unfortunately, there is no financial support available in addition to that offered by individual sites to their own students. However, if the absence of financial support can prevent you from participating, please get in touch to discuss possible options.

Pablo Candela: Higher-order Fourier analysis

Arithmetic combinatorics is a vibrant area of contemporary mathematics, combining ideas and tools from fields including harmonic analysis, graph theory and probability, in order to study the structure of various types of subsets of abelian groups. We will explore arithmetic combinatorics through a particularly interesting theory which emerged from this area in the late 1990s, namely the analysis of Gowers norms. This theory is now known as higher-order Fourier analysis. We will discuss some central aspects of this theory and study some of its important combinatorial applications, in particular those related to Szemerédi's famous theorem on arithmetic progressions. We will also provide an introduction to a more recent development that has led to further progress in higher-order Fourier analysis: the theory of nilspaces.

Joel Moreira: Ergodic Ramsey theory

Ergodic Ramsey theory is a relatively new subject which applies ideas and techniques from ergodic theory to problems arising in Ramsey theory, combinatorics and number theory. The course will introduce the basics of ergodic theory and show how it can be used to study problems arising in Ramsey theory via the so-called Furstenberg correspondence principle. We will look at some of the classical applications, including Furstenberg-Sarkozy theorem, Roth's theorem and Szemeredi's theorem; and by the end we will look at some of the more modern applications.

Schedule

All lectures and discussion sessions will take place in the room 1016 of the building of the Faculty of Mathematics and Computer Science located at ul. Prof. S. Łojasiewicza 6, 30-348 Kraków.

Please note that the schedule is preliminary and the individual lectures may still be rescheduled within the week.

Monday May 20

Tuesday May 21

Wednesday May 22

Thursday May 23

Friday May 24