By Pedro Pinto (Technische Universitat Darmstadt).

We wish to investigate circumstances where the solutions of (naturally given) ordinary differential equations have integer coefficients.

We start from Zagier's paper "Arithmetic and Topology of Differential Equations" and try to understand some of its features. We will then look at various examples (Apéry's recursion, hypergeometric equation,...).

Por Alexandre Tavares Baraviera (Universidade Federal do Rio Grande do Sul).

Por Gonçalo Oliveira (Universidade Federal Fluminense - UFF).

By Sean Lawton (George Mason Univ.)

Por Gabrielle Nornberg (University of São Paulo and Sapienza Università di Roma).

Por Ederson Moreira dos Santos (Universidade de São Paulo - São Carlos - Brazil).

Por Tom Sutherland (Grupo de Física Matemática).

Abstract: I will give an explicit description of the space of stability conditions of a set of Calabi-Yau-3 triangulated categories labelled by the Painlevé equations. We will see how the Painlevé equations appear in a Riemann-Hilbert problem motivated by the enumerative geometry of Calabi-Yau-3 categories whose solution is related to the study of the monodromy of opers.

Por Mário Edmundo (FCUL e CMAFcIO, Universidade de Lisboa).

Por Angelo Aliano Filho (Universidade Estadual de Campinas - UNICAMP).