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).

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

**Focus for Fall 2018: Hochschild homology**

Meetings: Tuesdays, 11-12:30pm, 939 Evans.

- 9/4 & 9/11 Alex Takeda, "Intro to Hochschild homology"
- 9/18 & 9/25 German Stefanich, "Morita invariance/HH of a category"
- 10/2 & 10/9, Aaron Brookner, "Hochschild-Kostant-Rosenberg"
- 10/16 & 10/23 Danny Chupin, "Homology of loop spaces"
- 10/30, Dmitry Vaintrob, "Infinity-categories"
- 11/6 & 11/13, Joe Stahl, "Derived algebraic geometry"
- 11/20 No talk (classes cancelled due to smoke)
- 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.

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

Some references

- Gelfand and Manin, Methods of Homological Algebra
- Bondal and Kapranov, Enhanced triangulated categories
- Keller, On differential graded categories
- Toen, Lectures on DG-categories
- Kontsevich, Homological Algebra of Mirror Symmetry
- Kashiwara and Schapira, Sheaves on Manifolds
- 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.

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

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

- Tuesday, January 20: An introduction to stacks, D. Nadler (Berkeley).
- Tuesday, January 27: Vect_n(P^1), D. Nadler (Berkeley).
- Tuesday, February 3: Satake isomorphism, D Appel (Berkeley).
- Tuesday, February 10: Perverse sheaves, A. Zorn (Berkeley).
- Tuesday, February 17: Perverse exercises, A. Zorn (Berkeley).
- Tuesday, February 24: D-modules, S. Agrawal (Berkeley).
- Tuesday, March 3: Category O, B. Gammage (Berkeley)
- Tuesday, March 10: Local systems, H. Chen (Berkeley)
- Tuesday, March 17: Geometric Satake isomorphism, Q. Yuan (Berkeley)
- Tuesday, March 24: no seminar.
- Tuesday, March 31: Canonical bases, Q. Zhou (Berkeley)
- Tuesday, April 7: no seminar.
- Tuesday, April 14: Elliptic cohomology, C. Ray.
- Tuesday, April 21: Adjoint quotient, X. Jin (Berkeley)
- Tuesday, April 28: Springer theory, M. Monks Gillespie (Berkeley).
- 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.

- Thursday, February 6: What is the affine Grassmannian?, D. Nadler (Berkeley).
- Thursday, February 13: What is a groupoid?, Q. Yuan (Berkeley).
- Thursday, February 20: No seminar.
- Thursday, February 27: What is the Geometric Satake Correspondence?, C. Koppensteiner (Northwestern).
- Thursday, March 6: What is the exponential map?, P. Li (Berkeley).
- Thursday, March 20: What is a Poisson-Lie group?, N. Reshetikhin (Berkeley).
- Thursday, March 27: No seminar.
- Thursday, April 3: What is a Bott-Samelson resolution?, Q. Zhou (Berkeley).
- Thursday, April 10: What is an arithmetic D-module?, S. Agrawal (Berkeley).
- Thursday, April 17: No seminar.
- 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.

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

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

Further references

- Postnikov, Total positivity, Grassmannians, and networks.
- Postnikov, lecture notes by Morales.
- 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.

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