Jun

07

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 SankaranPhD Advisor:Stephen KudlaThesis Title:Special cycles on Shimura curves and the Shimura lift http://www.math.utoronto.ca/~sankaran/thesis.pdfThesis 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.

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