The first half of the semester will be introductory, focusing on the example of G = SL(2) and learning how to describe this space in many of the guises mentioned above. In the second half of the semester, we will go deeper into the theory of J, possibly including applications to representation theory, 3d mirror symmetry, or whatever topics are of interest to participants in this seminar.

E-mail me (Ben G.) if you want on the mailing list.

The seminar meets

Date |
Speaker |
Topic |

Sept. 2 | Benjamin Gammage | Introduction and organization |

Sept. 9 | David Yang | Toda lattice |

Sept. 16 | [No seminar] | [No seminar] |

Sept. 23 | [Postponed] | [Postponed] |

Sept. 30 | Keeley Hoek | Quantum Toda lattice |

Oct. 7 | Sanath Devalapurkar | Bi-Whittaker D-modules |

Oct. 14 | Grant Barkley | The BFM calculation |

Oct. 21 | Jianqiao Xia | Regular centralizers in the Fundamental Lemma |

Oct. 28 | Charles Fu | (???) |

Nov. 4 | Jae Hae Lee | QH*(G/B) |

- Multiplicative universal centralizers, q-difference quantum Toda lattice
- Quantum cohomology of the flag variety
- "Instanton counting via affine Lie algebras" papers
- Mirrors of flag varieties à la Teleman

[2] Bezrukavnikov-Finkelberg, Equivariant Satake category and Kostant-Whittaker reduction

[3] Braverman-Finkelberg-Nakajima, Towards a mathematical definition of Coulomb branches of 3-dimensional N=4 gauge theories, II

[4] Braverman-Finkelberg, Coulomb branches of 3-dimensional gauge theories and related structures

[5] Teleman, Gauge theory and mirror symmetry

[6] Ngô, Le lemme fondamental pour les algèbres de Lie

[7] Ginzburg, Nil Hecke algebras and Whittaker D-modules

[8] Lonergan, A Fourier transform for the quantum Toda lattice

[9] Kazhdan-Kostant-Sternberg, Hamiltonian group actions and dynamical systems of Calogero type

[10] Kostant, The solution to a generalized Toda lattice and representation theory

[11] Givental-Kim, Quantum cohomology of flag manifolds and Toda lattices

[12] Kostant, Flag manifold quantum cohomology, the Toda lattice, and the representation with highest weight ρ

[13] Rietsch, A mirror symmetric solution to the quantum Toda lattice

[14] Ben-Zvi–Gunningham, Symmetries of categorical representations and the quantum Ngô action

[15] Jin, Homological Mirror Symmetry for the universal centralizers I: The adjoint group case

[16] Balibanu, The partial compactification of the universal centralizer

Organized by Ben G. (that's me!)