Geometric Representation Theory Seminar

This will be an ongoing learning seminar devoted to current research directions where infinitesimal symmetries play a distinguished role.

Focus for Fall 2019: Geometry of flag varieties

Meetings, 732 Evans, Tuesdays 12:30-2pm.

Course number: 15363(8).

  1. Tuesday, September 3: Survey of flag varieties, D. Nadler (Berkeley).

Focus for Fall 2018: Hochschild homology

Meetings: Tuesdays, 11-12:30pm, 939 Evans.
  1. 9/4 & 9/11 Alex Takeda, "Intro to Hochschild homology"
  2. 9/18 & 9/25 German Stefanich, "Morita invariance/HH of a category"
  3. 10/2 & 10/9, Aaron Brookner, "Hochschild-Kostant-Rosenberg"
  4. 10/16 & 10/23 Danny Chupin, "Homology of loop spaces"
  5. 10/30, Dmitry Vaintrob, "Infinity-categories"
  6. 11/6 & 11/13, Joe Stahl, "Derived algebraic geometry"
  7. 11/20 No talk (classes cancelled due to smoke)
  8. 11/27 & 12/4, Chris Kuo, "HKR via loop spaces"

Focus for Fall 2017: Derived geometry of sheaves

Meetings, 732 Evans, Wednesdays 11am-12:30pm.

Course control number: 16977.

  1. Wednesday, September 6: Abelian Categories of Sheaves, M. Jeffs (Berkeley).
  2. Wednesday, September 13: Localization of Categories, I. Huq-Kuruvilla (Berkeley).
  3. Wednesday, September 20: Cones, Cylinders and Model Categories, M. Jeffs (Berkeley).
  4. Wednesday, September 27: Derived Categories, I. Huq-Kuruvilla (Berkeley).
  5. Wednesday, October 4: Ext and Derived Functors, Yixuan Li (Berkeley).
  6. Wednesday, October 11: Derived Functors on Derived Categories, (Berkeley).
  7. Wednesday, October 18: Spectral Sequences I, Yixuan Li (Berkeley).
  8. Wednesday, October 25: Spectral Sequences II, Yixuan Li (Berkeley).
  9. Wednesday, November 1: Steenrod Operations and the Coulomb Branch, Gus Lonergan (MIT).
  10. Wednesday, November 8: Derived Functors on Sheaves, I. Huq-Kuruvilla (Berkeley).
  11. Wednesday, November 15: Triangulated Categories, M. Jeffs (Berkeley).
  12. Wednesday, November 22: no seminar.
  13. Wednesday, November 29: Microlocal Mirror Symmetry, Dmitry Vaintrob (IAS).
  14. Wednesday, December 6: Verdier Duality I, Danny Chupin (Berkeley).
  15. Wednesday, December 13: Verdier Duality II, Danny Chupin (Berkeley).

Some references

  1. Gelfand and Manin, Methods of Homological Algebra
  2. Bondal and Kapranov, Enhanced triangulated categories
  3. Keller, On differential graded categories
  4. Toen, Lectures on DG-categories
  5. Kontsevich, Homological Algebra of Mirror Symmetry
  6. Kashiwara and Schapira, Sheaves on Manifolds
  7. Bernstein, Algebraic Theory of D-modules

Focus for Fall 2016: Symplectic manifolds and Lagrangian subvarieties

Meetings, 891 Evans, Tuesdays 2-3:30pm.

Course control number: 18817.

  1. Tuesday, August 29: Overview, D. Nadler (Berkeley).
  2. Tuesday, September 6: Basics of symplectic/contact geometry, B. Gammage (Berkeley).
  3. Tuesday, September 13: Lagrangian/Legendrian neighborhood theorems, B. Gammage (Berkeley).
  4. Tuesday, September 20: Ribbon graphs, A. Zorn (Berkeley).
  5. Tuesday, September 27: no seminar.
  6. Tuesday, October 4: Elliptic surfaces, M. Weiler (Berkeley).
  7. Tuesday, October 11: Singular fibers of elliptic surfaces, M. Weiler (Berkeley).
  8. Tuesday, October 18: no seminar.
  9. Tuesday, October 25: Weinstein manifolds, D. Nadler (Berkeley)
  10. Tuesday, November 1: Lagrangian skeleta, A. Komatsuzaki (Berkeley).
  11. Tuesday, November 8: Legendrian knots, T. Su (Berkeley).
  12. Tuesday, November 15: Isotropic triples, A. Weinstein (Berkeley).
  13. Tuesday, November 22: More on Legendrian knots, T. Su (Berkeley).

Focus for Fall 2015: Singular hypersurfaces

Meetings, 939 Evans, Thursdays 12:30-2pm.

Course control number: 54584.

  1. Thursday, September 3: Hypersurface singularities, D. Nadler (Berkeley).
  2. Thursday, September 10: Morse singularities, D. Nadler (Berkeley).
  3. Thursday, September 17: Parity of complex Morse singularities, D. Nadler (Berkeley).
  4. Thursday, September 24: x^3=y^2, A. Zorn (Berkeley).
  5. Thursday, October 1: Kleinian surface singularities, David Nadler (Berkeley).
  6. Thursday, October 8: Isolated hypersurface singularities, Ben Gammage (Berkeley).
  7. Thursday, October 15: More on isolated hypersurface singularities, Ben Gammage (Berkeley).
  8. Thursday, October 22: Thom-Sebastiani theorems, Alex Sherman (Berkeley).
  9. Thursday, October 29: More about Thom-Sebastiani theorems, Alex Sherman (Berkeley).
  10. Thursday, November 5: no seminar.
  11. Thursday, November 12: Non-isolated hypersurface singularities, David Nadler (Berkeley).
  12. Thursday, November 19: Degeneration of moduli of Higgs bundles, Vikraman Balaji, (Chennai Mathematical Institute)
  13. Thursday, November 26: no seminar, Happy Thanksgiving!
  14. Thursday, December 3: Nearby and vanishing cycles, Penghui Li (Berkeley).

Focus for Spring 2015: Key tools in geometric representation theory.

Meetings, 740 Evans, Tuesdays 12:30pm-2pm.
  1. Tuesday, January 20: An introduction to stacks, D. Nadler (Berkeley).
  2. Tuesday, January 27: Vect_n(P^1), D. Nadler (Berkeley).
  3. Tuesday, February 3: Satake isomorphism, D Appel (Berkeley).
  4. Tuesday, February 10: Perverse sheaves, A. Zorn (Berkeley).
  5. Tuesday, February 17: Perverse exercises, A. Zorn (Berkeley).
  6. Tuesday, February 24: D-modules, S. Agrawal (Berkeley).
  7. Tuesday, March 3: Category O, B. Gammage (Berkeley)
  8. Tuesday, March 10: Local systems, H. Chen (Berkeley)
  9. Tuesday, March 17: Geometric Satake isomorphism, Q. Yuan (Berkeley)
  10. Tuesday, March 24: no seminar.
  11. Tuesday, March 31: Canonical bases, Q. Zhou (Berkeley)
  12. Tuesday, April 7: no seminar.
  13. Tuesday, April 14: Elliptic cohomology, C. Ray.
  14. Tuesday, April 21: Adjoint quotient, X. Jin (Berkeley)
  15. Tuesday, April 28: Springer theory, M. Monks Gillespie (Berkeley).
  16. Tuesday, May 5: Character sheaves, P. Li (Berkeley)

Focus for Spring 2014: Introductory talks about central objects, in the spirit of the Notices of the AMS series "What is...?"

Meetings, 891 Evans, Thursdays 9:30am-11:00am.
  1. Thursday, February 6: What is the affine Grassmannian?, D. Nadler (Berkeley).
  2. Thursday, February 13: What is a groupoid?, Q. Yuan (Berkeley).
  3. Thursday, February 20: No seminar.
  4. Thursday, February 27: What is the Geometric Satake Correspondence?, C. Koppensteiner (Northwestern).
  5. Thursday, March 6: What is the exponential map?, P. Li (Berkeley).
  6. Thursday, March 20: What is a Poisson-Lie group?, N. Reshetikhin (Berkeley).
  7. Thursday, March 27: No seminar.
  8. Thursday, April 3: What is a Bott-Samelson resolution?, Q. Zhou (Berkeley).
  9. Thursday, April 10: What is an arithmetic D-module?, S. Agrawal (Berkeley).
  10. Thursday, April 17: No seminar.
  11. Thursday, April 24: What is a blowup in symplectic geometry?, X. Jin (Berkeley).

Focus for Fall 2013: Student research.

Meetings, 891 Evans, Thursdays 12:30pm-2:00pm.
  1. Thursday, September 5: Moduli of semistable G-bundles on an elliptic curve, P. Li (Berkeley).
  2. Thursday, September 12: An historical introduction to the Cobordism Hypothesis, D. Appel (Berkeley).
  3. Thursday, September 19: Springer theory, H. Chen (Berkeley).
  4. Thursday, September 26: Dehn twists, X. Jin (Berkeley).
  5. Thursday, October 3: Deformation theory and the cotangent complex, S. Agrawal (Berkeley).
  6. Thursday, October 10: No seminar.
  7. Thursday, October 17: Compactified Jacobians, Q. Zhou (Berkeley).
  8. Thursday, October 24: Beilinson-Bernstein localization, A. Zorn (Berkeley).
  9. Thursday, October 31: No seminar.
  10. Thursday, November 7: No seminar.
  11. Thursday, November 14: Log geometry, J. McIvor (Berkeley).
  12. Thursday, November 21: Adoint quotients, P. Li (Berkeley).
  13. Thursday, November 28: No seminar.
  14. Thursday, December 5: Cobordism Hypothesis with singularities, D. Appel (Berkeley).

Focus for Spring 2013: N. Arkani-Hamed, J. Bourjaily, F. Cachazo, A. Goncharov, A. Postnikov, and J. Trnka, Scattering Amplitudes and the Positive Grassmannian.

Lectures, 891 Evans, Wednesdays 11:00am-12:30pm.
  1. Wednesday, January 30: Introduction to positive Grassmannians, D. Nadler (Berkeley).
  2. Wednesday, February 13: Plabic networks and the positive Grassmannian, S. Karp (Berkeley).
  3. Wednesday, February 20: Decorated permutations and the positive Grassmannian, S. Karp (Berkeley).
  4. Wednesday, February 27: G(2, 4), Q. Zhou (Berkeley).
  5. Wednesday, March 6: Reduced plabic graphs and cluster transformations I, S. Brodsky (Berkeley).
  6. Wednesday, March 13: Reduced plabic graphs and cluster transformations II, S. Brodsky (Berkeley).
  7. Wednesday, March 20: Cluster Algebras and the Grassmannian I, H. Williams (Berkeley).
  8. Wednesday, March 27: Spring break.
  9. Wednesday, April 3: Cluster Algebras and the Grassmannian II, H. Williams (Berkeley).
  10. Wednesday, April 10: Introduction to QFT and Scattering I, A. Zorn (Berkeley).
  11. Wednesday, April 17: No seminar.
  12. Wednesday, April 24: Introduction to QFT and Scattering II, A. Zorn (Berkeley).
  13. Wednesday, May 1: No seminar.
  14. Wednesday, May 8: Introduction to QFT and Scattering III, A. Zorn (Berkeley).

Further references

  1. Postnikov, Total positivity, Grassmannians, and networks.
  2. Postnikov, lecture notes by Morales.
  3. Talaska, A formula for Plucker coordinates associated with a planar network.

Focus for Fall 2012: Relation of infinitesimal symmetries to microlocal structures.

Lectures, 891 Evans, Tuesdays 12:30-2pm.
  1. Tuesday, August 28: Introduction to infinitesimal descent, D. Nadler (Berkeley).
  2. Tuesday, September 4: Introduction to microlocal structures, D. Nadler (Berkeley).
  3. Tuesday, September 11: Example oriented introduction to D-modules, Penghui Li (Berkeley).
  4. Tuesday, September 18: Symplectic geometry of holonomic D-modules, Penghui Li (Berkeley).
  5. Tuesday, September 25: D-modules on the affine line, Harrison Chen (Berkeley).
  6. Tuesday, October 2: Constructible sheaves on the affine line, David Nadler (Berkeley).
  7. Tuesday, October 9: Nearby and vanishing cycles, David Nadler (Berkeley).
  8. Tuesday, October 16: No meeting.
  9. Tuesday, October 23: Introduction to the Riemann-Hilbert Correspondence, Owen Gwilliam (Berkeley).
  10. Tuesday, October 30: Regularity of algebraic D-modules, Owen Gwilliam (Berkeley).
  11. Tuesday, November 6: No meeting.
  12. Tuesday, November 13: Riemann-Hilbert correspondence on the affine line, David Nadler (Berkeley).
  13. Tuesday, November 20: Introduction to semisimple perverse sheaves, Xin Jin (Berkeley).
  14. Tuesday, November 27: Examples of the Decomposition Theorem, Xin Jin (Berkeley).
  15. Tuesday, December 4: Towards Koszul duality for D-modules, Daniel Appel (Berkeley).