|Date: Monday, September 11, 2017
Location: 4096 East Hall (4:00 PM to 6:00 PM)
Title: D-brane 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 Dp-brane 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 L-function 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 quasi-periods of \Gamma_0(N) and the special geometry pairing on Calabi-Yau 3 folds we can fix further values in the connection matrix between the maximal unipotent monodromy point and the conifold point.
Speaker: Albrecht Klemm