Abstract: The metaplectic geometric Langlands program can be understood in two ways: as a twisted analogue of the geometric Langlands program, and as a geometric analogue of the Langlands program for covering groups, namely the metaplectic Langlands program. One of the key structures in the geometric Langlands program is the spectral action, which roughly says that the spectral side acts on the automorphic side, allowing one to spectrally decompose the automorphic category over the moduli of \check{G}-local systems. This can be viewed as a geometric incarnation of the automorphic-to-Galois direction.

One may hope that the spectral action carries over to the metaplectic setting, and this expectation was formulated by Gaitsgory and Lysenko under the name “metaplectic vanishing conjecture.” In this talk, I will discuss my recent work on constructing the spectral action in the Betti metaplectic context. I will focus on what changes in the metaplectic setting and on the categorical framework for studying factorizable actions of local systems of symmetric monoidal categories.

Geometric Representation Theory Seminar: https://sites.google.com/view/yale-grt-seminar/home

In this talk, I will discuss a joint work with Samuel J. Taylor, where we consider embedded non-fiber surfaces in a closed hyperbolic 3-manifold transverse to a pseudo-Anosov flow. Utilizing foundational work on Kleinian surface groups, we connect the hyperbolic geometry of the surface to the dynamics of the flow via the curve graph. More specifically, the flow gives a pair of special multicurves on the surface, and we show that they are also geometrically distinguished, enabling us to extract geometric information, such as the position of short curves and the volume, from the relation of the pair of multicurves in the curve graph. Our result also connects to recent study of the geometry of endperiodic mapping tori.