abstract.pdfPanorama Lectures by Pavel Etingof
Professor Pavel Etingof who is visiting the School of Mathematics is giving a series of eight lectures. This is not part of the conference but participants might be interested.
Panorama Lectures by Professor Pavel Etingof
Title: Hitchin Systems and their Quantization
Plan of lectures: Professor Etingof will give a series of 8 lectures each of 1 hour and 15 mins during the period 19th - 22nd January 2026 at the Tata Institute of Fundamental Research, Mumbai. Two lectures will be given on each day of the program, one in the morning and one in the afternoon.
The topics covered will include Principal G-bundles, Moduli stacks of G-bundles on smooth projective curves and their double quotient realization, stable bundles and Higgs fields, Hitchin integrable systems, parabolic structures and quantization of Hitchin systems. The relationship with Knizhnik–Zamolodchikov connections, monodromy representations and quantum groups will also be discussed.
Professor Patrick Brosnan who is visiting the School of Mathematics is giving a seminar on January 21. This is not part of the conference.
Title: The geometry of Hessenberg and Lusztig varieties
Abstract: Hessenberg and Lusztig varieties are two families of closed subvarieties of generalized flag varieties with representation theoretic significance. In the case of Hessenberg varieties, one associates to a combinatorial piece of data a family of varieties living over the Lie algebra of a reductive group G. (For the general linear group, that combinatorial piece of data is just an integer-valued function. In general, it can be thought of as a G-equivariant subbundle of the tangent bundle of the flag variety.) In the case of Lusztig varieties, one associates to each element of the Weyl group of G a family of varieties over G. I'll talk about some basic results on the geometry of Hessenberg varieties. Then I'll state a theorem on the automorphisms of deformations of Hessenberg varieties. Finally, I'll state a theorem about the
relationship between Hesssenberg and Lusztig varieties.