In this talk, I will discuss the curved Koszul duality for associative algebras presented by quadratic-linear-constant (QLC) relations. Let A be a QLC algebra, the Koszul dual coalgebra of the associated quadratic algebra qA is a curved DG coalgebra. Moreover, this curved DG coalgebra gives rise to resolutions of A which can be used to compute the Hochschild and cyclic homology of A. I will describe the cyclic (co)homology of a QLC algebra and its Koszul dual curved DG algebra, and extend a result due to Feigin and Tsygan.

Curved Koszul duality and cyclic (co)homology

Thu, Nov. 4 3pm (Zoom)

Probability

Konstantin Matetski (Columbia University)

X

The KPZ universality class includes random growing interfaces, which, after rescaling, are conjectured to converge to the KPZ fixed point. The latter is a Markov process, which has been characterized through the exact solution of TASEP, a particular model in the class. The KPZ equation plays a special role and is conjectured to be the only model connecting the Edwards-Wilkinson (Gaussian) and the KPZ fixed points. In the talk, I will introduce the KPZ fixed point and review recent progress on the KPZ universality.