Time: Friday afternoon, 14:00
Place: Zoom
This seminar is intended to understand the construction of the chiral algebra given by Beilinson & Drinfeld. We plan to go through the following topics:
The definition of the chiral algebra and its construction.
The construction of the chiral differential operators and the CDO over a complex Lie group.
Chiral homology, its definition and the way to compute it.
Elliptic trace map on the chiral homology.
Chiral categories and the D-modules over the semi-infinite flags.
Beilinson A, Drinfeld V, Drinfeld V G. Chiral algebras[M]. American Mathematical Soc., 2004.
Hilburn J, Raskin S. Tate's thesis in the de Rham Setting[J]. arXiv preprint arXiv:2107.11325, 2021.
Raskin S. Chiral categories[J]. preprint available at http://math. mit. edu/~ sraskin, 2015.
van Ekeren J, Heluani R. Chiral homology of elliptic curves and the Zhu algebra[J]. Communications in Mathematical Physics, 2021, 386(1): 495-550.
Gui Z, Li S. Elliptic Trace Map on Chiral Algebras[J]. arXiv preprint arXiv:2112.14572, 2021.
Raskin S. Chiral principal series categories I: finite dimensional calculations[J]. Advances in Mathematics, 2021, 388: 107856.
Raskin S. Chiral principal series categories II: the factorizable Whittaker category[J]. Preprint. Available at math. mit. edu/~ sraskin/cpsii. pdf, 2016.
2022/3/25 Tianqing Zhu. Introduction to the chiral algebra.
2022/4/2 Tianqing Zhu. Factorization algebra, and the chiral Koszul duality.
2022/4/7 Tianqing Zhu. Chiral envelope for the Lie* algebra.
2022/4/15 Tianqing Zhu. Chiral envelope for the Lie* algebra.
2022/4/24 Keyou Zeng. Chiral homology.