Join us for coffee and tea at 15.45 p.m.
Date: Tuesday, November 1st 2011
Speaker: Prof. S. Shadrin (UvA)
Room: 5161.0267 (Bernoulliborg),
Title:"Hurwitz numbers: relations with the moduli of curves and with the integrable hierarchies"
Hurwitz numbers emerged originally in the representation theory of the symmetric groups and a simplest example would be an answer to the following question:
How many ways are there to represent a given permutation as the product of a given number of transposition?
There was an enormous interest in Hurwitz numbers in recent years due to two different connections that were discovered about 10 years ago:
One, due to Okounkov, connects Hurwitz theory to a very special hierarchy of PDEs called the Kadomtsev-Petviashvili hierarchy. It has a very beautiful and simple description via a semi-infinite matrix, and I'll explain both the description of the hierarchy and relation to Hurwitz theory in these terms.
A second connection, due to Ekadahl-Lando-Shapiro-Vainshtein, relates Hurwitz numbers to the intersection theory on the moduli spaces of curves. I'll explain that as well.
I hope to be very basic, but still indicate some open direction in this theory.
are Prof.dr. A.C.D. van Enter (e-mail : A.C.D.van.Enter@rug.nl) and
Dr. A.V. Kiselev (e-mail: email@example.com)
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