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# Geometric Methods in Representation Theory Seminar – Tom Gannon (UCLA)

## August 30 @ 4:00 pm - 5:00 pm

**Quantization of the Ngô morphism**

**Abstract:** We will discuss work, joint with Victor Ginzburg, which proves a conjecture of Nadler on the existence of a quantization (non-commutative deformation) of the Ngô morphism, a morphism of group schemes constructed by Ngô in his proof of the fundamental lemma in the Langlands program. We will first explain the construction of the Ngô morphism and discuss an extended example of this map for the group of invertible n x n complex matrices. Then, we will give a precise statement of our main theorem and discuss some of the tools used in proving this theorem, including a quantization of Moore-Tachikawa varieties.

Time permitting, we will also discuss how the tools used to construct this morphism can be used to prove conjectures of Ben-Zvi—Gunningham, which predict a “spectral decomposition” of DG categories with an action of a reductive group.