SMRI Algebra and Geometry Online: Kamnitzer -- ’Symplectic duality and (generalized) affine Grassmannian slices’

SMRI Algebra and Geometry Online 
’Symplectic duality and (generalized) affine Grassmannian slices’ 
Joel Kamnitzer (University of Toronto) 

Thursday Oct 21, 10:00am-11:30am (AEDT) 

Register:
https://uni-sydney.zoom.us/meeting/register/tZAudeqrqzkuGt2PXvWH1xyoWASjAZfiGiEG 

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.  

Biography: Joel Kamnitzer is a Professor of Mathematics at the University of Toronto.
His research concerns complex reductive groups and their representations, focusing on
canonical bases, categorification, and geometric constructions.  His 2005 Ph.D.  thesis
from UC Berkeley focused on the study of Mirkovic-Vilonen cycles in Affine
Grassmannians.  He received the 2011 Andre Aisenstadt Prize, a 2012 Sloan Research
Fellowship, a 2018 E.W.R.  Steacie Memorial Fellowship, a 2018 Poincare Chair, and the
2021 Jeffrey-Williams Prize.  

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

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https://mathematical-research-institute.sydney.edu.au/news-events/