IMPAN Colloquium
Wednesdays at 14:15 in Room 321, before the lecture there are cookies and tea in room 409 at 13:45
Organizers:
Marcin Lara, Grigor Sargsyan, Mateusz Wasilewski, Aneta Wróblewska-Kamińska
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UPCOMING MEETINGS
UPCOMING MEETINGS
OCTOBER 15
Jakub Byszewski (Jagiellonian University)
Algebraic Approaches to Generalised Polynomials
Generalised polynomials are functions obtained from ordinary polynomials by allowing the use of the floor function, together with addition, multiplication, and composition. Such expressions arise naturally in number theory and dynamics. Despite their simple definition, they exhibit a rich and rather subtle arithmetic, combinatorial, and dynamical behaviour.
In this talk, I will discuss several algebraic methods that are used to study these properties. These include techniques based on nilmanifolds and the algebra of ultrafilters, as well as tools of a more Diophantine nature, such as those related to S-unit equations.
The talk is based on joint work with Jakub Konieczny (Kyiv).
OCTOBER 22
Joachim Jelisiejew (University of Warsaw)
OCTOBER 29
Ryszard Rudnicki (IMPAN Katowice)
NOVEMBER 5
Krzysztof Oleszkiewicz (University of Warsaw)
NOVEMBER 12
Damian Osajda (University of Copenhagen/University of Wrocław)
PAST MEETINGS
OCTOBER 8
Błażej Miasojedow (University of Warsaw)
Sampling as optimisation over the space of measures
Sampling from probability distributions that are only known up to a constant is a key challenge in computational statistics and machine learning. A common method is to use stochastic processes such as Langevin dynamics, which form the basis of many MCMC (Markov chain Monte Carlo) algorithms. In this talk, we present an alternative view: sampling can be seen as an optimisation problem in the space of probability measures equipped with a specific metric, the so-called Wasserstein space W2. From this perspective, sampling algorithms approximate gradient flows in the W2 metric. This approach provides a clearer interpretation of existing methods, extends their use to a wider range of distributions, and allows for more precise convergence guarantees.
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