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Seminars

Algebraic Geometry Seminar

Trace map on chiral Weyl algebras

2025/06/25 (Wed.) 15:00~16:00
  • Date : 2025/06/25 (Wed.) 15:00~16:00
  • Location : online
  • Speaker : Zhengping Gui (SIMIS)
  • Abstract : We investigate a two-dimensional chiral analogue of the algebraic index theorem using the theory of chiral algebras developed by Beilinson and Drinfeld. Within the BV quantization framework, we construct a trace map on the elliptic chiral homology of the free βγ-bc system. Evaluating this trace on the unit constant chiral chain recovers the formal Witten genus in Lie algebra cohomology. For any smooth Riemann surface, we extend this construction to the chiral homology of chiral Weyl algebras, where the trace map serves as a chiral analogue of the deformed HKR quasi-isomorphism. We calculate examples of trace maps with single insertions and find they are closely related to the variation of analytic torsion for holomorphic bundles on Riemann surfaces.
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