MTH 996 Special topics in topology
A topological introduction to microlocal sheaf theory
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)
Sheaves on manifolds, M. Kashiwara and P. Schapira
Methods of Homological Algebra, S. Gelfand and Y. Manin
Papers (further topics)
Legendrian knots and constructible sheaves, V. Shende, D. Treumann and E. Zaslow
Sheaf quantization of Hamiltonian isotopies and applications to non displaceability problems, S. Guillermou, M. Kashiwara, and P. Schapira
Non-squeezing property of contact balls, S.-F. Chiu
The three cusps conjecture, S. Guillermou
T-Duality and Homological Mirror Symmetry of Toric Varieties, B. Fang, C.-C. M. Liu, D. Treumann and E. Zaslow
A categorification of Morelli's theorem, B. Fang, C.-C. M. Liu, D. Treumann and E. Zaslow
Cluster varieties from Legendrian knots, V. Shende, D. Treumann, H. Williams and E. Zaslow
Cluster structures on double bott-samelson cells, D. Weng and L. Shen
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.