Speaker
Anton Mellit
Description
Character varieties parametrize local systems on punctured Riemann surfaces with prescribed monodromies around
punctures. Hausel, Letellier and Rodriguez-Villegas studied character varieties from a motivic point of view
and guessed a formula which should compute the mixed Hodge structures of all character varieties. The formula
is quite complicated: it has infinite products, infinitely many variables, and Macdonald polynomials. However
in the case when all but two monodromies have ramification index 1, I discovered that their formula can be
reduced to an elementary expression with a sum over graphs of certain type, which I call the B-formula. This
case can be seen as an analogue of the famous Hurwitz number problem (ELSV formula), and I hope it to have
some connection to physics.
