Date: Monday, September 11, 2017
Location: 4096 East Hall (4:00 PM to 6:00 PM)
Title: Dbrane masses and the motivic Hodge conjecture
Abstract: We consider the one parameter mirror family W of the quintic in P^4. By mirror symmetry the even Dpbrane masses of the quintic M can be identified with four periods w.r.t to an integral symplectic basis of H_3(W,Z) at the point of maximal unipotent monodromy. We establish that the masses of the D4 and D2 branes at the conifold are given by the two algebraically independent values of the Lfunction of the weight four holomorphic Hecke eigenform with eigenvalue one of \Gamma_0(25), that was found by Chad Schoen in this context and whose coefficients a_p count the number of solutions of the mirror quintic at the conifold over the finite number field F_p as was discovered by del la Ossa, Candelas and Villegas. Using the theory of periods and quasiperiods of \Gamma_0(N) and the special geometry pairing on CalabiYau 3 folds we can fix further values in the connection matrix between the maximal unipotent monodromy point and the conifold point.
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Speaker: Albrecht Klemm
Institution: Bonn
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