Hershel M. Farkas

Professor of Mathematics

telephone: 972 2 6584386

email: farkas@math.huji.ac.il


My research interests revolve around function theory on compact Riemann surfaces, Jacobi varieties and the theory of theta functions.

The research in the area of function theory on compact Riemann surfaces has focused on the Schottky problem which asks for a description of the space of Jacobians of compact Riemann surfaces of genus g in the Siegel upper half plane of degree g.

Contributions have been made to Schottky-Jung theory.

More recently, I have been studying modular forms and their applications to geometry and number theory. Here the main contribution has been obtaining concrete representations of holomorphic mappings of modular curves into projective spaces of low dimensions and the realization of their automorphism groups as the restriction of global isometries of the projective space to the image of the curve. In addition, these mappings have given generalizations of the Platonic solids, interesting theta constant identities, and connections with classical combinatorial number theory.