Скачать или смотреть Pt. 2 – Sublinear expander graphs | Matija Bucić, University of Vienna | IAS/PCMI

Title: Sublinear expander graphs - part 2
Presented to PCMI by Matija Bucić, University of Vienna
Abstract: Expander graphs are certainly one of the most widely useful classes of graphs ever considered. In this course, we will explore a (weaker) notion of sublinear expansion due to Komlós and Szemerédi from the early 90's which has found a remarkable number of impressive applications in recent years.

We will start with a brief introduction to the theory of expander graphs, introduce the sublinear notion, show the pass to expander and expander decomposition lemma, establish a number of properties, and illustrate how they were used in some of the aforementioned recent applications.

Prerequisites: Familiarity with basic notions from graph theory, probability theory, and linear algebra.--
Lecture notes & problem sets
https://www.ias.edu/pcmi/pcmi-2025-gs...
PCMI 2025 GSS Lecture Notes and Problem Sets - IAS/Park City Mathematics Institute
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PCMI 2025 Research Topic: Probabilistic and Extremal Combinatorics
Organized by Julia Böttcher (LSE), Jacob Fox (Stanford University), Penny Haxell (University of Waterloo), Robert Morris (IMPA), and Wojciech Samotij (Tel Aviv University).

Extremal and probabilistic combinatorics are two central branches of contemporary discrete mathematics. The first of these two branches studies how large (or how small) a discrete structure can be given that it satisfies a certain set of restrictions; the second investigates random combinatorial objects using a blend of combinatorial methods and tools of probability theory. These two fields have been growing at a stunning rate over the last few decades and are nowadays considered to be an important part of mainstream mathematical research.
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The aim of the planned summer graduate program at PCMI is to provide in-depth introduction to several preeminent themes and methods in extremal and probabilistic combinatorics, with particular emphasis on strong connections of these fields with other areas of mathematics such as analysis, geometry, number theory, statistical physics, and theoretical computer science. The core of the program will be nine graduate mini-courses taught by a diverse group of leading researchers in the field renowned for their clear and engaging lecturing styles. In parallel, we plan thematic workshops aimed at more senior researchers as well as activities for undergraduate students.