# Talk by Ángel González Prieto (18/5)

May 16, 2022

(to honour the memory of Marc Herault)

Next Wednesday 18/5 Ángel González-Prieto is offering a talk at the CRM.

**Title:** Quantum sledgehammers to crack character nuts

**Speaker:** Ángel González Prieto (Universidad Complutense de Madrid)

**Time:** Wednesday 18/5 at 12:30.

**Location:** Room A1

**Remote connection:** Zoom link: https://zoom.us/j/98878683945?pwd=OGRxNm9XWHhVamt2K2hCTHJvRjYrdz09

**Abstract:** Despite their close relation with moduli spaces of Higgs bundles and flat connections through the non-abelian Hodge correspondence, the algebraic structure of moduli spaces of representations of surfaces groups, aka character varieties (our hard nut), remains being a mystery in many cases. To address this problem, in this talk we shall explain how to construct Topological Quantum Field Theories (our sophisticated and very powerful sledgehammer) to crack this problem and others in algebraic topology.Topological Quantum Field Theories were introduced by Witten to interpret the Jones polynomial, a knot invariant, in terms of Chern-Simmons theory. This construction, which also involves character varieties, was carried out through geometric quantization. In sharp contrast, our quantization will be inspired by Fourier-Mukai transformations of sheaves, which leads to new and exciting ways of computing motivic information of the character variety. Time permitting, we shall also discuss the emerging interference phenomena arising in parabolic character varieties.

*Marc Herault was a member of the Lab of Geometry and Dynamics. A charismatic double Math-Phys student of CFIS at UPC who was about to start his TFG in cosupervision with Sergei Gukov at Caltech. His endless passion for mathematics and physics remains an inspiration for our team. His smile and enthusiasm accompany and encourage our daily research. This talk is the second talk to honor his memory.*

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