Past Seminars
September 2022- May 2023
Floer Homology and the Fukaya Category
We read A beginner's introduction to Fukaya categories by Denis Auroux and parts of Sectorial Descent for wrapped Fukaya categories by Ganatra-Pardon-Shende.
Talk 1: 30 September An overview of Floer theory
Talk 2: 14 October Hutchings 1-2.2 Morse theory
Talk 3: 28 October Hutchings 2.3-2.4 and 4 Morse homology
Talk 4: 4 November Auroux 1.2-1.5 The Floer complex
Talk 5: 11 November Seidel 9 Products and A-infinity structure
Talk 6: 25 November GPS 3.1-3.3 Localization in the Fukaya category
Talk 7: 6 December Legendrian contact homology
Talk 8: 7 December Smith 5 Examples of Fukaya categories
Talk 9: 14 December Morse flow trees
Talk 10: 21 March GPS II Section 2 Liouville sectors
Talk 11: 5 April GPS II Section 2 Wrapped Fukaya category
Talk 12: 18 April GPS II Section 1 Theorems about the wrapped Fukaya category
Talk 13: 9 May Setup of Heegaard Floer homology
Talk 14: 16 May Cylindrical reformulation of Heegaard Floer
November 2022- April 2023
Microlocal Sheaf Theory: The Tamarkin Category
We read Quantitative Tamarkin Category by Jun Zhang.
Talk 1: 3 November An Overview of the Tamarkin Category
Talk 2: 17 November Viterbo 9.1-9.2 Singular support, propagation, and the Morse lemma
Talk 3: 1 December Zhang 3.1-3.5 The Tamarkin Category
Talk 4: 15 December Zhang 3.6-3.8 Torsion and the Separation Theorem
Talk 5: 25 April Zhang 4.1 Sheaf Quantization
Talk 6: Zhang 4.10 Gromov non-squeezing
February 2022- April 2022
Introduction to J-holomorphic curves
We covered Chapters 4-5 of Lectures on Holomorphic Curves in Symplectic and Contact Geometry by Chris Wendl.
Talk 1: 9 February, Section 4.1 - Moduli space of closed curves - Ikshu Neithalath
Talk 2: 16 February, Section 4.2 - Riemann surfaces - Konstantin Wernli
Talk 3: 23 February, Section 4.3 - Fredholm regularity - Chris Kuo
Meeting 4: 2 March, Section 4.4.1 - Transversality for generic J
Meeting 5: 9 March, Section 4.4.2 - Dense implies generic
Meeting 6: 23 March, Sections 4.5-4.6 - Generic families and transversality of the evaluation map
Meeting 7: 30 March, Section 4.7 - Generic curves are immersed
Meeting 8: 6 April, Section 5.1 - Nonsqueezing
Meeting 9: 20 April, Sections 5.2-5.3 - Bubbling
September - December 2021
Introduction to J-holomorphic curves
We covered Chapters 1-3 of Lectures on Holomorphic Curves in Symplectic and Contact Geometry by Chris Wendl.
Talk 1: 24 September, Section 1 - Introduction to symplectic geometry - Ikshu Neithalath (video)
Talk 2: 1 October, Sections 2.3-2.4 - The delbar operator - Emil Hössjer
Talk 3: 8 October, Sections 2.5-2.6.1 - Sobolev spaces - Tim Henke
Talk 4: 19 October, Section 2.6.2-2.6.3 - The basic delbar estimate - Calvin Pfeiffer (video)
Talk 5: 22 October, Sections 2.7-2.10 - Properties of J-holomorphic curves - Zhongyu Zhang
Talk 6: 29 October, Section 2.11 - Nonlinear regularity - Chris Kuo
Talk 7: 5 November, Sections 2.11-2.13 - Nonlinear regularity and local existence of curves - Chris Kuo, In IMADA Conference room (Ø18-509-2)
Talk 8: 12 November, Section 2.14 - Isolated intersections - Ikshu Neithalath
Talk 9: 19 November, Sections 2.15-2.16 - Multiply covered curves and positivity of intersections - Ikshu Neithalath
Talk 10: 26 November, Sections 3.1-3.2 - Banach manifolds - Emil Hössjer
Talk 11: 8 December, Sections 3.3-3.4 - Fredholm operators and Riemann-Roch - Zhongyu Zhang, In IMADA Conference room
Talk 12: mid-January, specific date TBD, Section 4.1 - Moduli space of closed curves