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# Texas A&M Number Theory Seminar

##
Department of Mathematics

Milner 317

Wednesdays, 12:30-1:30 PM

Yaacov
Kopeliovich

Abstract in
PDF Slides
in PDF

**Wednesday, November 15**

Milner 317, 12:30 PM

**Title: ** Theta
function identities at periods of covers of order 3 and representation
theory of symmetric groups

**Abstract:** At the end of
nineteenth century Thomae discovered a formula connecting the values of
theta functions evaluated at periods of algebraic curves that, are
double covers of the sphere branched over r points (these are called
hyper-elliptic curves). Frobenius used these formulas to construct
special identities for theta functions evaluated at periods of such
curves. In 1988 Bershadsky and Radul discovered a similar formula for
curves that are cyclic covers of the sphere of degree n. We combine
Bershadsky and Radul formula and representation theory of symmetric
groups to obtain special identities among theta functions evaluated at
period matrices of cyclic covers of order 3. We present an evidence of
similar formulas in many instances for moduli spaces of branched covers
of the sphere. The talk will be self-contained and we encourage Ph.D.
students to attend.