Random Discrete Structures Seminar

Seminarium Losowe Struktury Dyskretne

Meetings are held on Wednesdays, 13:13-14:14 in room A.0.8, building C-19 (Map of the university campus), Faculty of Pure and Applied Mathematics, Wroclaw University of Science and Technology. Hosts:      prof. dr hab. Krzysztof Bogdan                 dr hab. Kamil Kaleta                 dr hab. Grzegorz Serafin                 dr hab. Pawel Sztonyk Secretary: dr Tomasz Skalski.

Referaty w roku akademickim 2023/24
12.12.2023	dr hab. Bartosz Trojan	Compactifications of affine buildings Abstract: In this talk I am going to introduce affine buildings and indicate what are the analytic problems one can be interested in. In particular, I describe several compactification procedures and motive the study of random walks. I am going to formulate what is Martin compactification and explain why it is important.
20.03.2024	lic. Wojciech Michalczuk	CTG dla liczby izomorficznych kopii hipergrafu w uogolnionym modelu Erdosa-Renyia Abstract: Podczas wykladu opowiem o modelu hipergrafu losowego, ktory, choc w naturalny sposob uogolnia dobrze znany model Erdosa-Renyia, wciaz pozostaje slabo zbadany. Przedstawie rezultaty badan pod kierunkiem dr. hab. inz. Grzegorza Serafina dotyczace zmiennej zliczajacej podgrafy izomorficzne z danym hipergrafem. Podam charakteryzacje asymptotycznej normalnosci, pare nierownosci typu Berry-Esseena oraz ujawnie, ze kwestia optymalnego oszacowania nadal pozostaje otwarta, tak jak przez wiele lat bylo z wersja dla grafow.
27.03.2024	prof. Wojciech Samotij	Stability of large cuts in random graphs Abstract: A cut in a graph G is the set of edges that cross some partition of the vertices of G into two sets and a maximum cut of G is a cut with the largest size among all cuts. We will prove that the family of largest cuts in the binomial random graph G(n,p) exhibits the following stability property: If 1/n << p ≤ 1-Ω(1), then, with probability 1-o(1), there is a set of n-o(n) vertices that is partitioned in the same manner by all maximum cuts of G(n,p). Moreover, the analogous statement remains true when one replaces maximum cuts with nearly-maximum cuts. We will then demonstrate how one can use this statement as a tool for showing that certain properties of G(n,p) that hold in a fixed cut hold simultaneously in all maximum cuts. This talk is based on a joint work (https://arxiv.org/abs/2402.14620) with Ilay Hoshen (Tel Aviv University) and Maksim Zhukovskii (University of Sheffield).

Archiwum:                                                                                                                                                       Rok akademicki 2018/19, Rok akademicki 2019/20, Rok akademicki 2020/21, Rok akademicki 2021/22, Rok akademicki 2022/23.