Geometric Representation Theory

These seminars focus on research in representation theory and algebraic geometry.  

More information on these seminars can be found at the following link:


The combinatorics of the affine Satake isomorphism

by Alexander Braverman | Brown University
Time: 15:00 — 16:30  (Tuesday, Mar. 15, 2011)
Location: BA3000, Bahen Center, 40 St. George St.
I am going to explain the generalizations of the so called "Macdonald formula for the spherical function" to the case of affine Kac-Moody groups. Time permitting I will also explain the connection of these formulas with the theory of affine Eisenstein series (initiated by Kapranov and studied by Garland) and with the work of Fishel-Grojnowski-Teleman on the de Rham cohomology of the affine Grassmannian.

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)