MAT 645: Pseudoholomorphic Curves
Stony Brook            Spring 2022 |
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[Z4], 05/30/22: Extensive updates described in Section 1.1
[Z1], 04/24/22: Section 6.2 added (bubbling on thin necks)
        
03/26/22: Proposition 6.2 added (bubbling with marked points colliding)
        
03/15/21: Section 6.1 added
        
03/14/21: Section 2.2 and Examples 2.7,2.8 added
         03/10/21: statement and proof of Lemma 5.4 sharpened;
Section 5.3 redone, justifying the termination in finitely many steps carefully.
Date | Topic | Read |
01/24, M | Introduction lecture notes |
[MS04]: Preface, Chapter 1 [MS98]: Introduction, Chapter 1 [Z1]: Section 1 |
01/26, W | Energy of J-holomorphic curves | [Z1]: Sections 2,4.1 [MS04]: Sections 2.0-2.2,4.0,4.1 |
01/31, M | Mean Value Inequality | [Z1]: Sections 4.1 [MS04]: Section 4.3 |
02/02, W | Removal of Singularities | [Z1]: Section 5.1 [MS04]: Sections 4.1,4.5 |
02/07, M | Carleman Similarity Principle | [Z1]: Sections 3.1,3.2 [MS04]: Section 2.3 |
02/09, W | The Monotonicity Lemma | [Z1]: Section 3.3 |
02/14, M | Bubbling | [Z1]: Section 5.2 [MS04]: Sections 4.2,4.6 |
02/16, W | Isoperimetric Inequality | [Z1]: Section 4.2 [MS04]: Section 4.4 |
02/21, M | Energy distribution | [Z1]: Section 4.4 [MS04]: Section 4.7 |
02/23, W | Gromov's Convergence | [Z1]: Section 5.3 [MS04]: Section 4.7 |
02/28, M | Stable curves | [Z1]: Section 1.1 [Z6]: Section 4.1 [MS04]: Sections 5.1-5.4 |
03/02, W | Sequences and topologies | [Z1]: Section 5.5 [MS04]: Section 5.6 |
03/07, M | Moduli spaces of stable curves | [MS04]: Appendix D |
03/09, W | Convergence of stable maps | [Z1]: Section 1.2 [MS04]: Sections 5.0-5.3 |
03/21, M | Topology of moduli space of stable maps | |
03/23, W | Implicit Function Theorem for Banach manifolds | [MS04]: Appendix A.3 |
03/28, M | Linearization of dbar-operator and examples | [Z1]: Sections C.3-4 [MS04]: Section 3.1 |
03/30, W | Expansion of dbar-operator | |
04/04, M | Analytic properties of linearization of dbar-operator | |
04/06, W | Serre Duality | [ISh]: Section 2 |
04/11, M | Transversality at reduced maps | [MS04]: Section 3.2 [Z2]: Section 3 |
04/13, W | Universal moduli space | |
04/18, M | The determinant line bundle | [Z4] |
04/20, W | Pseudocycles and integral homology | [Z3] |
04/25, M | GW-invariants for semipositive manifolds | [MS04]: Sections 6.4,7.0,7.1 |
04/27, W | Gromov's nonsqueezing theorem | [MS04]: Section 9.3 |
05/02, M | Quantum cohomology
and enumerative geometry by Shuhao and Spencer |
[MS]: Sections 11.0,11.1; [Z6] |
05/04, W |
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