In this talk, we shall discuss the theta series associated with positive definite integral quadratic forms and some of its applications in getting formulas for the number of representations of positive integers by quadratic forms, using the theory of modular forms. The second part of this talk...

Given a holomorphic map between compact Riemann surfaces, Hurwitz's formula relates the genera of the domain and range with the degree and ramification of the map. Hence, given two compact Riemann surfaces we get a restriction on the possible types of holomorphic maps between them. In particular...