Extremal combinatorics concerns itself with problems about how large or small a finite collection of objects can be while satisfying certain conditions. Questions of this type arise naturally across mathematics, so this area has close connections and interactions with a broad array of other fields, including number theory, group theory, model theory, probability, statistical physics, optimization, and theoretical computer science.
The area has seen huge growth in the twenty-first century and, particularly in recent years, there has been a steady stream of solutions to important longstanding problems and many powerful new methods have been introduced. These advances include improvements in absorption techniques which have facilitated the proof of the existence of designs and related objects, the breakthrough on the sunflower conjecture whose further development eventually led to the proof of the Kahn–Kalai conjecture in discrete probability and the discovery of interactions between spectral graph theory and the study of equiangular lines in discrete geometry. These and other groundbreaking advances will be the central theme of the semester program on “Extremal Combinatorics” at SLMath.
In this program, we will bring together experts as well as enthusiastic young researchers to learn from each other, to initiate and continue collaborations, to communicate recent work, and to further advance the field by making progress on fundamental open problems and developing further connections with other branches of mathematics. We trust that younger mathematicians will greatly contribute to the success of the program with their new ideas. It is our hope that this program will provide a unique opportunity for women and underrepresented groups to make outstanding contributions to the field and we strongly encourage their participation.Show less
extremal set theory
extremal graph theory
structural graph theory
05C25 - Graphs and abstract algebra (groups, rings, fields, etc.) [See also 20F65]
05C50 - Graphs and linear algebra (matrices, eigenvalues, etc.)
05C51 - Graph designs and isomomorphic decomposition [See also 05B30]
11P70 - Inverse problems of additive number theory, including sumsets
52C10 - Erdős problems and related topics of discrete geometry [See also 11Hxx]
52C35 - Arrangements of points, flats, hyperplanes [See also 32S22]