Victor Ginzburg

About

Victor Ginzburg is a professor in the Department of Mathematics at The University of Chicago. His research primarily focuses on geometric representation theory and noncommutative geometry. In geometric representation theory, he applies methods of algebraic geometry to study representations of various algebras, including the classification of irreducible representations of Hecke algebras, applications of D-modules and perverse sheaves to representations of complex or real reductive groups and semisimple Lie algebras, the study of integrable representations of quantum groups via the geometry of quiver varieties, and the geometric Langlands program. In recent years, Ginzburg has also developed interests in noncommutative geometry, drawing inspiration from the theory of quivers, mirror symmetry, Calabi-Yau categories, and the mathematics appearing in string theory. He has authored lectures and survey articles on these topics and has contributed to the understanding of noncommutative symplectic geometry, symplectic reflection algebras, Calogero-Moser space, and deformed Harish-Chandra homomorphism. Ginzburg supervises graduate students, encouraging them to pursue research topics of their choosing, and collaborates on joint projects with some of his students.

Research topics

• Mathematics
• Pure mathematics
• Mathematical analysis
• Physics

Selected publications

• Isospectral commuting variety, the Harish-Chandra D-module, and principal nilpotent pairs

  Duke Mathematical Journal · 2012-07-24 · 29 citations

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  Let g be a complex reductive Lie algebra with Cartan algebra t. Hotta and Kashiwara defined a holonomic D-module M, on g×t, called the Harish-Chandra module. We relate grM, an associated graded module with respect to a canonical Hodge filtration on M, to the isospectral commuting variety, a subvariety of g×g×t×t which is a ramified cover of the variety of pairs of commuting elements of g. Our main result establishes an isomorphism of grM with the structure sheaf of Xnorm, the normalization of th…

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• Quantization of line bundles on lagrangian subvarieties

  Selecta Mathematica · 2015-08-06 · 20 citations

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• DIFFERENTIAL OPERATORS ON AND THE AFFINE GRASSMANNIAN

  Journal of the Institute of Mathematics of Jussieu · 2014-04-07 · 20 citations

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  We describe the equivariant cohomology of cofibers of spherical perverse sheaves on the affine Grassmannian of a reductive algebraic group in terms of the geometry of the Langlands dual group. In fact we give two equivalent descriptions: one in terms of $\mathscr{D}$ -modules of the basic affine space, and one in terms of intertwining operators for universal Verma modules. We also construct natural collections of isomorphisms parameterized by the Weyl group in these three contexts, and prove tha…

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• Nil-Hecke Algebras and Whittaker 𝔇-Modules

  Progress in mathematics · 2018-01-01 · 18 citations

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• Hamiltonian reduction and nearby cycles for mirabolic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi mathvariant="script">D</mml:mi></mml:math>-modules

  Advances in Mathematics · 2014-10-28 · 17 citations

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Recent grants

• Moduli Spaces, Quivers, and Duality

  NSF · $230k · 2016–2020

• Symplectic algebraic geometry and representation theory

  NSF · $351k · 2013–2017

• Symplectic Reflection Algebras and their Generalizations

  NSF · $171k · 2006–2009

Frequent coauthors

• Pavel Etingof

  36 shared

• Michael Finkelberg

  21 shared

• Simon Riche

  Université Clermont Auvergne

  17 shared

• Yuri Berest

  15 shared

• Vladimir Baranovsky

  University of California, Irvine

  15 shared

• Travis Schedler

  11 shared

• Gwyn Bellamy

  11 shared

• Wee Liang Gan

  University of California, Riverside

  10 shared

Similar researchers at University of Chicago

• Jiajie Chenh-98
• Vladimir Drinfeldh-39
• Guillaume Balh-37