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Alexander Razborov: Continuous Combinatorics

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Time: Wed 2015-03-18 15.15 - 16.15

Lecturer: Alexander Razborov, University of Chicago

Location: Room Oskar Klein, AlbaNova

14.00-15.00 Pre-colloquium by PhD student Sangxia Huang (Room FB52, AlbaNova)
15:15-16:15 Colloquium lecture by Alexander Razborov (Room Oskar Klein, AlbaNova)
16:15-17:00 SMC social get together with refreshments

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. Moreover, the numerical characteristics researchers are normally interested in are "continuous" in the sense that small perturbations in the structure do not change the output very much. This makes it very natural to try to think of the "limit theory" of such objects by pretending that "very large" actually means "infinite". It turns out that this mathematical abstraction is very useful and instructive and leads to unexpected connections with many other things, both in mathematics and computer science.

Two complementing approaches to constructing such a theory and applying it elsewhere are known as graph limits and flag algebras, and in our talk we review as much of it as the time permits.

Titel Datum
Dmitry Khavinson: "Between two truths of the real domain, the easiest and shortest path quite often passes through the complex domain." P. Painleve, 1900. A variation on the theme of analytic continua 2015‑12‑12
Kathryn Hess: A calculus for knot theory 2015‑11‑06
Gregory F. Lawler: Self-avoiding motion 2015‑10‑09
Claudio Procesi: Analytic and combinatorial aspects of the Non Linear Schroedinger equation (NLS) on a torus 2015‑05‑27
Alexander Razborov: Continuous Combinatorics 2015‑03‑18
Christiane Tretter: Operator theory and applications: a successful interplay 2015‑02‑04