The Painlevé I equation and the A2 quiver

Speaker: Davide Masoero (Grupo de Física Matemática, FCUL).

Abstract: We study a second-order linear differential equation known as the deformed cubic oscillator, whose isomonodromic deformations are controlled by the first Painlevé equation. We use the generalised monodromy map for this equation to give solutions to the Bridgeland's Riemann-Hilbert problem arising from the Donaldson-Thomas theory of the A2quiver.

Noncommutative Weil conjectures

Speaker: Gonçalo Tabuada (FCTUNL).

Abstract: The Weil conjectures (proved by Deligne in the 70's) played a key role in the development of modern algebraic geometry. In this talk, making use of some recent topological "technology", I will extended the Weil conjectures from the realm of algebraic geometry to the broad noncommutative setting of differential graded categories. Moreover, I will prove the noncommutative Weil conjectures in some interesting cases.