Meetings

Monday/Thursday, 4:10-5:30pm, Eastern Time.

• The first lecture is on Jan 21

• The last lecture is on Apr 19

References

Books (foundations)

1. Sheaves on manifolds, M. Kashiwara and P. Schapira

2. Methods of Homological Algebra, S. Gelfand and Y. Manin

Papers (further topics)

3. Legendrian knots and constructible sheaves, V. Shende, D. Treumann and E. Zaslow

4. Sheaf quantization of Hamiltonian isotopies and applications to non displaceability problems, S. Guillermou, M. Kashiwara, and P. Schapira

5. Non-squeezing property of contact balls, S.-F. Chiu

6. The three cusps conjecture, S. Guillermou

7. T-Duality and Homological Mirror Symmetry of Toric Varieties, B. Fang, C.-C. M. Liu, D. Treumann and E. Zaslow

8. A categorification of Morelli's theorem, B. Fang, C.-C. M. Liu, D. Treumann and E. Zaslow

9. Cluster varieties from Legendrian knots, V. Shende, D. Treumann, H. Williams and E. Zaslow

10. Cluster structures on double bott-samelson cells, D. Weng and L. Shen

11. Legendrain weaves, R. Casals and E. Zaslow

Modules

(Request the accesss to lecture notes by sending me an email)

Module 1 Introduction

• Lecture 1 (Jan 21, Thur): sheaves, example of constructible sheaves in dimension 1, micro-support

• Lecture 2 (Jan 25, Mon): Fourier-Sato transform, microlocal Morse lemma, involutivity, constructible sheaves, GKS theorem

• Lecture 3 (Jan 28, Thur): GKS theorem (cont.), the three cusp conjecture, contact non-squeezing

• Lecture 4 (Feb 1, Mon ): HMS for complex P^1, Legendrain weaves

Module 2 Sheaves and categories

Lecture 5 (Feb 4, Thur): KS 1.1, 1.2, 2.1

• Lecture 6 (Feb 11, Thur): KS 2.1, 2.2

• Lecture 7 (Feb 15, Mon): KS 2.2, 2.3

• Lecture 8 (Feb 18, Thur): KS 2.3, 2.5

• Lecture 9 (Feb 22, Mon): KS 2.5, 1,4

• Lecture 10 (Feb 25, Thur): GM 2.4, 3.1, 3.2 / KS 1.5, 1.6, 1.7

• Lecture 11 (Mar 1, Mon): KS 1.8, 2.6

• Lecture 12 (Mar 4, Thur): KS 3.1

Module 3 Microlocalization

• Lecture 13 (Mar 8, Mon): KS 3.1, 3.6, 3.7

• Lecture 14 (Mar 11, Thur): KS 3.7

• Lecture 15 (Mar 15, Mon): KS 3.7, 4.1

• Lecture 16 (Mar 18, Thur): KS 4.2

• Lecture 17 (Mar 22, Mon): KS 4.3, 4.4

• Lecture 18 (Mar 25, Thur): KS 5.1, 5.3

Module 4 Further Topics

• Lecture 19 (Mar 29, Mon): Student presentation by Tristan Wellsfilbert, STZ sections 2, 3

• Lecture 20 (Apr 1, Thur): STZ section 4

• Lecture 21 (Apr 5, Mon): STZ section 5

• Lecture 22 (Apr 8, Thur): Student presentation by Orsola Capovilla-Searle, GKS section 3

• Lecture 23 (Apr 13, Mon): three cusp conjecture part I

• Lecture 24 (Apr 15, Thur): Student presentation by Wenyuan Li, three cusp conjecture part II

• Lecture 25 (Apr 19, Mon): Student presentation by Chen Zhang.