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Noncommutative geometry in applied math
Prof. Andrei Okounkov (Princeton)
Abstract: I will explain how some basic algebraic ideas help us study linear difference equations of probabilistic interest.
Alexander Zabrodsky / The Mathematics Genealogy Project
The continuation of the Zabrodsky lecture of A.Okounkov will be on Monday and Tuesday [rm 209].The general outline of the problem and the argument was given in the first talk.
In the remaining talks Professor Okounkov will discuss the following topics:
- the classical Kasteleyn theory of dimers and how it applies to stepped surfaces
- why discrete holomorphic functions in polygonal domains satisfy additional difference equations
- how does the additional equation depends on the domain, this is really the theory of noncommutative shifts on the Jacobian, or discrete Painleve equations
- how to take the continuous limit in part (3)
- what does this has to do with things like mirror symmetry and other advanced topics for the next year's program