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Cotygodniowe seminarium badawcze.
2023-10-05, godz. 12:15, 3160
Kunal Dutta (Uniwersytet Warszawski)
Dimensionality Reduction for Persistent Homology with Gaussian Kernels
Computing persistent homology using Gaussian kernels is useful in the domains of topological data analysis and machine learning. We consider a power distance version of the Gaussian kernel distance (GKPD) given by Phillips, Wang and Zheng, and show that for high-dimensional datasets, the persistent ...
2023-05-25, godz. 12:15, 3160
Rafał Latała (Uniwersytet Warszawski)
We will present a Chevet-type inequality for subexpontial Weibull processes and show how it may be applied to find two-sided bounds for operator \ell_p to \ell_q norms of random rectangular matrices with iid Weibull entries. We will also discuss lower and upper bounds for operator norms of other iid...
2023-05-18, godz. 12:15, 5820 (please note the change of room)
Alexandros Eskenazis (Sorbonne Université)
Discrete logarithmic Sobolev inequalities in Banach spaces
We shall discuss certain aspects of vector-valued harmonic analysis on the discrete hypercube. After presenting the geometric motivation behind such investigations, we will survey known results on the Poincaré inequality and Talagrand’s influence inequality. Then we will proceed to pres...
2023-05-11, godz. 12:15, 3160
Dominik Kutek (Uniwersytet Warszawski)
On Orlicz spaces satisfying the Hoffmann-Jørgensen inequality
We say that an Orlicz function \Psi satisfies the H-J inequality, if \| \sum_{k=1}^n X_k \|_{\Psi} \le C_{\Psi} ( \| \sum_{k=1}^n X_k \|_{L_1} + \| \max_{k \le n}\|X_k\| \|_{\Psi}) for any collection \{X_k\}_{k \le n} of zero mean and independent random variables taking values in any separable Banac...
2023-04-27, godz. 12:15, 3160
Piotr Nayar (Uniwersytet Warszawski)
Maximal sections of l_p^n balls for large values of p.
Let B_p^n be the unit ball in the standard p-th norm in R^n. Suppose we intersect this ball with a codimension one hyperplane H and ask the following question: for which H is the volume of this section maximal and minimal? The first result concerning this problem is due to Hadwiger and Hensley who i...
2023-04-13, godz. 12:15, 3160
Michał Strzelecki (Uniwersytet Warszawski)
The s-numbers of Schatten class embeddings
Roughly speaking, the s-numbers of a linear operator between two Banach spaces are certain quantities which indicate how compact this operator is. One can introduce various sequences of s-numbers (classical examples include the approximation and Gelfand numbers of an operator). Then one can wonder w...
2023-03-30, godz. 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, godz. 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, godz. 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, godz. 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...
