Jorge Duque - Hodge cycles and Gauss hypergeometric function

Speaker: Jorge Duque
Title: Hodge cycles and Gauss hypergeometric function
Date: 31/07/2020

Abstract:
In this talk, we will explain how to calculate periods on affine cycles. This will allow us to consider a subspace of the Hodge cycles defined by "simple" arithmetic conditions in the family $x_1^{m_1}+x_2^{m_2}+\cdots+x_n^{m_n}+P(y)$. We will explore some examples and we will give an upper bound of the dimension of this subspace. As an application of the above, we will find expressions involving the hypergeometric function such that they algebraic.