Department of Mathematics

Details

Categorified Heisenberg Actions on Hilbert Schemes

by Sabin Cautis | Columbia
Time: 14:00  (Tuesday, Nov. 23, 2010)
Location: BA6180, Bahen Center, 40 St George St
Abstract:
I will describe an action of a quantized Heisenberg algebra on the (derived) categories of coherent sheaves on Hilbert schemes of ALE spaces (crepant resolutions of $C^2/G$). This action essentially lifts the actions of Nakajima and Grojnowski on the cohomology of these spaces. (joint with Tony Licata)

Dates in this series

· Friday, Feb. 05, 2010: Harmonic analysis on spherical varieties in terms of the wonderful compactification (Yiannis Sakellaridis)

· Friday, Feb. 12, 2010: String polytopes of Littelmann-Bernstein-Zelevinsky and Newton-Okounkov bodies (Kuimars Kaveh)

· Friday, Feb. 19, 2010: Tate's proof of the Residue Formula (Mikhail Mazin)

· Monday, Mar. 01, 2010: The 2-group of a linear auto-equivalences of an abelian category and its Lie 2-algebra (Xinwen Zhu)

· Friday, Mar. 05, 2010: Braid group actions in geometry (Sabin Cautis)

· Friday, Mar. 26, 2010: The hidden smoothness of the space of stable maps ()

· Friday, Mar. 26, 2010: The hidden smoothness of the space of stable maps ()

· Friday, Mar. 26, 2010: The hidden smoothness of the space of stable maps ()

· Friday, Mar. 26, 2010: The hidden smoothness of the space of stable maps ()

· Tuesday, Mar. 30, 2010: Local duality and polarized Hodge modules (Christian Schnell)

· Friday, Apr. 09, 2010: Quantum cohomology of symplectic resolutions and derived auto-equivalences (Alexander Braverman)

· Tuesday, Sep. 21, 2010: Multiplicity Spaces in Classical Symplectic Branching (Oded Yacobi)

· Wednesday, Sep. 22, 2010: Modular tensor categories and modular functors: braided tensor categories and quantum groups (Joel Kamnitzer)

· Tuesday, Sep. 28, 2010: Cluster categories and higher-dimensional analogues (Hugh Thomas)

· Tuesday, Oct. 05, 2010: Categorification and geometric representation theory (Joel Kamnitzer)

· Tuesday, Oct. 12, 2010: Idempotents in $R$-trivial monoids (Chris Burg)

· Tuesday, Oct. 26, 2010: Webs and the Affine Grassmannian (Bruce Fontaine)

· Thursday, Nov. 04, 2010: Quantum insertion and Schur-Weyl duality (Sonya Berg)

· Thursday, Nov. 11, 2010: Geometrization of Principal Series Representation of $GL_N$ (Travis Schedler)

· Tuesday, Nov. 16, 2010: Symmetries of stability conditions (Parker Lowrey)

· Tuesday, Nov. 23, 2010: Categorified Heisenberg Actions on Hilbert Schemes (Sabin Cautis)

· Thursday, Jan. 20, 2011: Polynomial representation of general linear groups and categorifications of Fock space (Oded Yacobi)

· Tuesday, Jan. 25, 2011: The antigravity method in cyclotomic quotients of KLR algebras (Alex Hoffnung)

· Thursday, Jan. 27, 2011: Crystal models for the basic representation of the affine special linear Lie algebras (Chris Berg)

· Thursday, Feb. 03, 2011: Derived completion, derived descent and semi-infinite cohomology of quantum groups (Sergey Arkhipov)

· Tuesday, Feb. 08, 2011: Affine Mirkovic-Vilonen Polytopes (Joel Kamnitzer)

· Thursday, Feb. 24, 2011: Degenerations of Kazhdan-Lusztig varieties, and applications (Allen Knutson)

· Tuesday, Mar. 08, 2011: The derived category and the singularity category (Umut Isik)

· Tuesday, Mar. 15, 2011: The combinatorics of the affine Satake isomorphism (Alexander Braverman)

· Thursday, Mar. 24, 2011: 2-representation theory (Raphael Rouquier)

· Thursday, Apr. 07, 2011: Turaev--Viro invariants, Kitaev's model and extended TQFTs (Alexander Kirillov)

· Wednesday, May. 04, 2011: A brief introduction to the theory of descent,  (Omar Anatolin Camarena)

· Monday, Jul. 18, 2011: Gindikin-Karpelevich formulas and Plancherel Theorems (James Parkinson)

· Wednesday, Aug. 03, 2011: Quotient-closed subcategories of representations of quivers and sorting order on reflection groups (Hugh Thomas)

· Friday, Sep. 16, 2011: Equivariant coherent sheaves and categorifications of Affine Hecke algebras (Chris Dodd)

· Friday, Sep. 30, 2011: Quiver Representations in the Super-Category (Jaimie Thind)

· Friday, Oct. 07, 2011: Nilpotent semi-infinite homology of quantum groups and categorical completion (Sergey Akhipov)

· Friday, Oct. 21, 2011: The blob complex (Scott Morrison)

· Friday, Oct. 28, 2011: Equivariant map algebras: irreducible representations and block decompositions (Alistair Savage)

· Friday, Nov. 04, 2011: Graded Expansions of Groups (Peter Lee)

· Friday, Nov. 04, 2011: `Quadraticity' of Groups (Peter Lee)

· Friday, Nov. 11, 2011: Spin Networks (Roland van der Veen)

· Friday, Nov. 18, 2011: On the structure of intrinsic topological order in 2D (Oliver Buerschaper)

· Friday, Nov. 25, 2011: Jacobi Factors of Quasihomogeneous Plane Curve Singularities (Mikhail Mazin)

· Friday, Dec. 02, 2011: Promotion Operators and Crystal Bases (Tom Denton)

· Tuesday, Dec. 13, 2011: Quantum affine algebras, Braid groups, and Heisenberg categorification (Tony Licata)

· Friday, Jan. 13, 2012: Bruhat cells and atlases thereof (Allen Knutson)

· Friday, Jan. 20, 2012: The classification of irreducible mod p representations of a p-adic GL_n (Florian Herzig)

· Friday, Jan. 27, 2012: Categorifications of the characteristic polynomial of hyperplane arrangements (Zsuzsanna Dancso)

· Friday, Mar. 02, 2012: L-functions and their generating functions (Avner Segal)

· Monday, Mar. 12, 2012: Laminations, Affine Buildings, and Invariants of Tensor Products of Representations (Ian Le)

· Friday, Mar. 23, 2012: Combinatorics of twisted Higgs bundles: g=0 and beyond (Steven Rayan)

· Monday, Mar. 26, 2012: Real variations of stability conditions and representation theory (Roman Bezrukavnikov)

· Thursday, Apr. 05, 2012: Coherent DG-modules over the de Rham DG-algebra (Sergey Rybakov)

· Thursday, Sep. 27, 2012: Classifying subfactors (Dave Penneys)

· Thursday, Oct. 04, 2012: Introduction to Geometric Complexity Theory (Josh Grochow)

· Thursday, Oct. 11, 2012: Crystals, geometric Satake, and non-negative tropical flag variety (Joel Kamnitzer)

· Friday, Oct. 19, 2012: Ramified Satake Isomorphisms (Masoud Kamgarpour)

· Friday, Oct. 26, 2012: Combinatorial rules for branching to symmetric subgroups (Allen Knutson)

· Thursday, Nov. 01, 2012: Crystals, geometric Satake, and the non-negative tropical flag variety II (Joel Kamnitzer)

· Thursday, Nov. 08, 2012: Crystals, geometric Satake, and non-negative tropical flag variety III (Joel Kamnitzer)

· Thursday, Nov. 08, 2012: Character varieties as completely integrable systems (Adam Sikora)

· Thursday, Nov. 22, 2012: Crystals, geometric Satake, and non-negative tropical flag variety III (Joel Kamnitzer)

· Thursday, Nov. 29, 2012: Crystals, geometric Satake, and the non-negative tropical flag variety IV (Joel Kamnitzer)

· Friday, Nov. 30, 2012: The colored HOMFLY polynomial is q-holonomic (Stavros Garoufalidis)

· Thursday, Jan. 17, 2013: Twisted Geometric Satake Equivalence (Bhairav Singh)

· Thursday, Jan. 24, 2013: Extended conformal field theories (Andre Henriques)

· Thursday, Feb. 07, 2013: Quantum cohomology of hypertoric spaces, Bethe equations and mirror formulae (Michael McBreen)