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Extremal Combinatorics January 21, 2025 to May 16, 2025
Organizers LEAD David Conlon (California Institute of Technology), LEAD Jacob Fox (Stanford University), Penny Haxell (University of Waterloo), Janos Pach (Alfréd Rényi Institute of Mathematics), Maya Stein (Universidad de Chile), Andrew Suk (University of California, San Diego)
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.
Keywords and Mathematics Subject Classification (MSC)
  • extremal combinatorics

  • extremal set theory

  • extremal graph theory

  • hypergraphs

  • designs

  • Ramsey theory

  • positional games

  • random graphs

  • thresholds

  • probabilistic combinatorics

  • combinatorial probability

  • statistical physics

  • percolation

  • structural graph theory

  • graph minors

  • chromatic number

  • arithmetic combinatorics

  • arithmetic progressions

  • discrete geometry

  • combinatorial geometry

  • incidence theorems

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
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Programmatic Workshops
February 06, 2025 - February 07, 2025 Connections Workshop: Extremal Combinatorics
February 10, 2025 - February 14, 2025 Introductory Workshop - Graph Theory: Extremal, Probabilistic and Structural
March 17, 2025 - March 21, 2025 Algebraic and Analytic Methods in Combinatorics