Symplectic duality and (generalized) affine Grassmannian slices

Abstract: Under the geometric Satake equivalence, slices in the affine Grassmannian give a geometric incarnation of dominant weight spaces in representations of reductive groups. These affine Grassmannian slices are quantized by algebras known as truncated shifted Yangians. From this perspective, we expect to categorify these weight spaces using category O for these truncated shifted Yangians.

The slices in the affine Grassmannian and truncated shifted Yangians can also be defined as special cases of the Coulomb branch construction of Braverman-Finkelberg-Nakajima. From this perspective, we find many insights. First, we can generalize affine Grassmannian slices to the case of non-dominant weights and arbitrary symmetric Kac-Moody Lie algebras. Second, we establish a link with modules for KLRW algebras. Finally, we defined a categorical g-action on the categories O, using Hamiltonian reduction.

commutative algebraalgebraic geometryanalysis of PDEsalgebraic topologydifferential geometrygeneral topologygeometric topologymetric geometryoperator algebrasquantum algebrarings and algebrassymplectic geometry

Audience: researchers in the topic

( video )

---

Algebra Seminar (presented by SMRI)

Series comments: Algebra Seminar:

'Homological comparison of resolution and smoothing'

Will Donovan (Tsinghua University)

Friday Sep 23, 12:00-1:00PM

Online via Zoom

Register here: uni-sydney.zoom.us/meeting/register/tZEpd-isqD0iGdLoqtmNEEQKxmg0xlakSdCq

Abstract: A singular space often comes equipped with (1) a resolution, given by a morphism from a smooth space, and (2) a smoothing, namely a deformation with smooth generic fibre. I will discuss work in progress on how these may be related homologically, starting with the threefold ordinary double point as a key example.

Biography: Will Donovan is currently an Associate professor at Yau MSC, Tsinghua University, Beijing. He is also a member of the adjunct faculty at BIMSA, Yanqi Lake, Huairou, Beijing and a visiting associate scientist at Kavli IPMU, University of Tokyo. He received his PhD in Mathematics in 2011 from Imperial College London. His interests are algebraic geometry, noncommutative geometry, representation theory, string theory and symplectic geometry.

www.maths.usyd.edu.au/u/AlgebraSeminar/

Note: These seminars will be recorded, including participant questions (participants only when asking questions), and uploaded to the SMRI YouTube Channel www.youtube.com/c/SydneyMathematicalResearchInstituteSMRI

Other upcoming SMRI events can be found here: mathematical-research-institute.sydney.edu.au/news-events/

---