## Departmental PhD Thesis Exam – Siddarth Sankaran

Everybody welcome.  Refreshments will be served in the Math Lounge
before the exam.

Thursday, June 14, 2012, 2:10 p.m., in BA 2135, 40 St. George Street

PhD Candidate:  Siddarth Sankaran

Thesis Title:  Special cycles on Shimura curves and the Shimura lift
http://www.math.utoronto.ca/~sankaran/thesis.pdf

Thesis Abstract:

The main theorem of this thesis describes a relationship between two families
of arithmetic divisors on an integral model of a Shimura curve. The first family,
studied by Kudla, Rapoport and Yang, parametrizes abelian surfaces with specified
endomorphism structure. The second family arises via the  pullbacks of divisors
on integral models of Shimura varieties associated to unitary groups of signature
(1,1). In the thesis, we describe the construction of these families of cycles,
and prove the theorem relating them, which is expressed in terms of the
"Shimura lift", a classical tool in the theory of modular forms of half-integral
weight. This theorem can be viewed as further evidence for the modularity of
generating series of arithmetic "special cycles" for U(1,1), and fits broadly
into Kudla's programme for unitary groups.