- Series
- School of Mathematics Colloquium
- Time
- Thursday, September 5, 2024 - 11:00am for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Alexander Razborov – The University of Chicago – https://people.cs.uchicago.edu/~razborov/
- Organizer
- Alex Dunn, Xiaoyu He, Rose McCarty, Dmitrii Ostrovskii, and Wei Zhu
Combinatorics was conceived, and then developed over centuries as a discipline about finite structures. In the modern world, however, its applications increasingly pertain to structures that, although finite, are extremely large: the Internet network, social networks, statistical physics, to name just a few. This makes it very natural to try to think of the "limit theory" of such objects by pretending that "very large" actually means "infinite". This mathematical abstraction turns out to be very useful and instructive.
After briefly reviewing the basics of the theory (graphons and flag algebras), I will report on some more recent developments. Time permitting, we will discuss the most general form of the theory suitable for arbitrary combinatorial structures (peons and theons), its applications to the theory of quasi-randomness and its applications to machine learning.
The first two topics are based on joint work with L. Coregliano, and the third one on a recent paper by Coregliano and Malliaris.