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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Maths HEP Lunchtime Seminars: CFTs on Riemann surfaces of genus greater than or equal to 1: Modular forms and beyond

Presented by Marianne Leitner, Dublin Institute of Advanced Studies

2 May 2014 13:00 in CM221

The Rogers-Ramanujan functions arise as partition (or zero-point)
functions in a conformal field theory (CFT) on the torus. More
generally, we can study such a theory on arbitrary genus compact Riemann
surfaces. A CFT is considered to be solved once all of its N-point
functions are known. Explicit formulas have been obtained for the two-
and three-point functions of the Virasoro field on any hyperelliptic
Riemann surface, using methods from complex analysis and algebraic
geometry. The formulas involve a finite number of parameters (notably
the zero- and one-point functions) which depend on the moduli of the
surface and can be determined using differential equations. We present
an algebraic-geometric approach that is designed to work for
hyperelliptic surfaces of arbitrary genus, thus giving new access to
higher genus automorphic forms. First results for genus two will be addressed.
This is joint work in progress with Werner Nahm.

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