This is joint work with M. Vlasenko. The notion of motivic gamma function is due to V. Golyshev. Basically, a motivic gamma function is the Mellin transform of the solution of a linear differential equation on the Riemann sphere. Using work of Golyshev and Zagier on inhomogeneous Frobenius solutions, we show that the Mellin integrand in this case has a canonical primitive. As a consequence, certain particularly interesting motivic gammas have Taylor coefficients which are given by the variation of the solution around a conifold singularity. Again following Golyshev and Zagier, this has consequences for mirror symmetry. This talk will be for non-experts!!!

Spencer Bloch is an American mathematician known for his contributions to algebraic geometry and algebraic K-theory. Bloch is a R. M. Hutchins Distinguished Service Professor Emeritus in the Department of Mathematics of the University of Chicago. He is a member of the U.S. National Academy of Sciences and a Fellow of the American Academy of Arts and Sciences and of the American Mathematical Society. At the International Congress of Mathematicians he gave an invited lecture in 1978 and a plenary lecture in 1990. He was a visiting scholar at the Institute for Advanced Study in 1981-82. He received a Humboldt Prize in 1996.