Talks

The standard structure formation model is based on the Cold Dark Matter (CDM) hypothesis where non-gravitational dark matter interactions are irrelevant for the formation and evolution of galaxies. Surprisingly, current observations allow for significant departures from the CDM hypothesis,

which could potentially leave signatures of the dark matter particle nature in the properties of galaxies. In this talk, I will describe a framework we have proposed that generalizes the theory of structure formation (in both the linear and non-linear regimes) to include new dark matter physics in order to explore galaxy formation and evolution in the broadest sense.

In my talk, I will briefly review the representation theoretical construction of conformal blocks attached to an affine Kac-Moody algebra and a smooth algebraic curve with marked points. I will focus on the case when the algebraic curve is an elliptic curve. The bundle of conformal blocks carries a canonical flat connection: the Knizhnik-Zamolodchikov-Bernard (KZB) equation. There are various generalizations of the KZB equation. I will talk about one generalization that constructed by myself and Toledano Laredo recently: the elliptic Casimir connection. It is a holonomic system of differential equations with regular singularities on elliptic curve with marked points, taking values in a deformation of the double current algebra g[u, v] defined by Guay. The monodromy of elliptic Casimir connection leads to interesting representations of the elliptic braid groups.