Colloquium Mathematics, Prof. S. Shadrin

Join us for coffee and tea at 15.45 p.m.

 

 

Date: Tuesday, November 1^st 2011

Speaker: Prof. S. Shadrin (UvA)

Room: 5161.0267 (Bernoulliborg),

Time: 16.15

 

 

Title:"Hurwitz numbers: relations with the moduli of curves and with the integrable
hierarchies"



Abstract:

 

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.

 

 

  

 

 

Colloquium coordinators are Prof.dr. A.C.D. van Enter (e-mail : A.C.D.van.Enter@rug.nl) and

Dr. A.V. Kiselev (e-mail: a.v.kiselev@rug.nl)