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Weekly research seminar
2023-03-30, 12:15, 3160
Witold Bednorz (Uniwersytet Warszawski)
Smoothed Analysis of the Komlos Conjecture
Last year, a new result appeared towards the solution of the well-known Komlos conjecture. The conjecture says that given n vectors in R^d with Euclidean norm at most one, there is always a coloring ± 1 such that the norm ℓ_1 of a signed-sum vector is constant independent of n and d. The ...
2023-03-23, 12:15, 3160
Adam Osękowski (Uniwersytet Warszawski)
Teoria operatorów wieloliniowych jest prężnie rozwijającym się działem analizy harmonicznej. W szczególności, oszacowania z wagą dla wieloliniowych funkcji maksymalnych, kwadratowych oraz operatorów singularnych były intensywnie badane w ciągu ostatnich dziesięciu lat....
2023-03-16, 12:15, 3160
Maciej Wiśniewolski (Uniwersytet Warszawski)
On bivariate distributions of the local time of It\^o-McKean diffusions
Denote as $L$ the local time at $0$ of an It\^o-McKean diffusion $X$. We present a new explicit description of the distribution of $L_t$ in terms of convolution exponent and, using the excursion theory, we describe the transition density of the pair $(X,L)$. We provide a simple connection formula fo...
2023-03-09, 12:15, 5820 (please note the change of room)
Stanisław Cichomski (Uniwersytet Warszawski)
Coherent Distributions on the Square
Let C denote the family of coherent distributions on [0,1]^2, i.e. all those probability measures m for which there exists a random vector (X,Y)~m such that X=P(E|G), Y=P(E|H) a.s. for some event E and sigma fields G,H. During the talk, we will: 1) examine the set of extreme points of C and p...
2023-03-02, 12:15, 5820
Samer Dweik (Uniwersytet Warszawski)
Sharp Poincaré and trace inequalities via Optimal Transport
In this talk, we study some Optimal Transport problems and we also find their corresponding minimal flow formulations. Then, we show that some sharp Poincaré and trace inequalities in BV space on bounded sets can be obtained by means of Optimal Transport. ...
2023-01-26, 12:15, 3160
Rafał Latała (Uniwersytet Warszawski)
Spectral norm bounds for Rademacher matrices
We will discuss bounds for the mean spectral norm of unhomogenous Rademacher matrices. We will recall a general conjecture formulated together with Witold Światkowski and show that it is satisfied in few particular cases. ...
2023-01-12, 12:15, 5060 (note the change of room)
Michał Kotowski (Uniwersytet Warszawski)
Large deviations for the interchange process on the interval and incompressible flows
In the talk I will explain how large deviations for the one-dimensional interchange process are related to incompressible Euler equations. I will sketch how to obtain matching large deviation lower and upper bounds for processes which are energy-minimizing (under certain additional regularity assump...
2022-12-15, 12:15, 3160
Radosław Adamczak (Uniwersytet Warszawski)
Isoperimetric inequalities for certain star-shaped bodies
I will present isoperimetric type inequalities for star-shaped sets that interpolate between intersection bodies and dual Lp centroid bodies, two classes of convex bodies studied in geometry. This provides a bridge between two well-known inequalities: the Busemann intersection inequality and the Lut...
2022-11-10, 12:15, 3160
Katarzyna Pietruska-Pałuba (Uniwersytet Warszawski)
Lp identities and inequalities related to certain Levy proceses
I will present recent results, concerned with generators and forms (acting on Lp) related to Levy processes. We establish the Hardy-Stein identity in Lp and related multivariate identities. If time permits, we will also present the optimal Hardy inequality for stable processes. All these results req...
2022-11-03, 12:15, 3160
Rémy Poudevigne-Auboiron (University of Cambridge)
Macroscopic cycles for the interchange process on random regular graphs
The interchange process can be seen as a random walk on permutations of a graph: at rate 1, independently on every edge, we exchange the value on both endpoints of the edge. This model was introduced as a way to study the quantum Heisenberg model. For this model, progress had been made on some speci...
