NCMW - Contact and Symplectic Geometry (2018)

Speakers and Syllabus

Syllabus to be covered in terms of modules of 6 lectures each :

Name of the Speakers with affiliation.

No. of Lectures

Detailed Syllabus

Outstation Speakers

Dr. Somnath Basu, IISER Kolkata. (SB)

5 (1.5 hrs each) = 7.5 hrs

Knot Contact Homology, Cord Algebras.

Dr. Mahuya Datta, ISI Kolkata. (MD)

5 (1.5 hrs each) = 7.5 hr

Introduction to Contact Geometry, Eliashberg’s Theorem for classification of overtwisted contact structures in dimension three.

Dr. Ritwik Mukherjee, NISER Bhubaneshwar. (RM)

6 (1.5 hrs each) = 9.0 hrs

Introduction to J-holomorphic curves, Moduli Spaces of J-holomorphic curves, Gromov-Witten Invariants.

Dr. Sushmita Venugopalan, IMSc., Chennai. (SV)

5 (1.5 hrs each) = 7.5 hrs

Hamiltonian Floer Homology and Lagrangian Floer Homology. Proof of Arnold’s conjecture in some cases.

Local Speakers

Dr. D. Divakaran, IISER Bhopal. (DD)

4 (1.5 hrs each) = 6 hrs

Donaldson’s construction of Approximately Holomorphic sections, Existence of Symplectic Submanifolds, Lefschetz Pencils on symplectic 4-manifolds.

Dr. Atreyee Bhattacharya, IISER Bhopal. (AB)

3 (1.5 hrs each) +2 (1 hr each) = 6.5 hrs

Riemannian Geometry of Contact Manifolds, Contact Sphere Theorem. Some open problems in contact metric manifolds.

Dr. Anandateertha Mangasuli, IISER Bhopal. (AM)

3 (1.5 hrs each) + 2 (1 hr) = 6.5 hrs

Introduction to Symplectic Topology, Classical Mechanics and symplectic structures, Contact structures in PDE’s.

Dr. Kashyap Rajeevsarathy, IISER Bhopal. (KR)

2 (1.5 hrs each) = 3 hrs

Introduction to Mapping Class Groups, Primitivity of Mapping classes and contact structures

Dr. Dheeraj Kulkarni, IISER Bhopal. (DK)

2 (1.5 hrs each) = 3 hrs

Giroux correspondence relating open book decompositions and contact structures, Fillability of contact structures.

References:

Books:

  1. McDuff, Dusa, and Dietmar Salamon. Introduction to symplectic topology. Oxford University Press, 2017.

  2. McDuff, Dusa, and Dietmar Salamon. J-holomorphic curves and symplectic topology. Vol. 52. American Mathematical Soc., 2012.

  3. Geiges, Hansjörg. An introduction to contact topology. Vol. 109. Cambridge University Press, 2008.

  4. Farb, Benson, and Dan Margalit. A primer on mapping class groups (pms-49). Princeton University Press, 2011.

  5. Eliashberg, Yakov, and Nikolai M. Mishachev. Introduction to the h-principle. No. 48. American Mathematical Soc., 2002.

  6. Audin, Michèle, and Jacques Lafontaine, eds. Holomorphic curves in symplectic geometry. Vol. 117. Birkhäuser, 2012.

  7. Audin, Michèle, and Mihai Damian. Morse theory and Floer homology. London: Springer, 2014.

 Articles:

  1. Ekholm, Tobias, John B. Etnyre, Lenhard Ng, and Michael G. Sullivan. "Knot contact homology." Geometry & Topology 17, no. 2 (2013): 975-1112.

  2. Basu, Somnath, Jason McGibbon, Dennis Sullivan, and Michael Sullivan. "Transverse string topology and the cord algebra." arXiv preprint arXiv:1210.5722 (2012).

Time Table

Tentative time-table with names of the speakers and tutors with their affiliation:

Time

Lecture 1
9.30
to
11.00

Tea
11.05
to
11.25

 

Lecture 2
11.30
to
1.00

Lunch
1.00
to
2.00

 

Lecture 3
2.00
to
3.30

3.35
to
3.55

 

Discussion
4.00
to
5.00

5.05
to
5.35

 

 Day/Date

(name of the speaker)

(name of the speaker)

(name of the speaker)

(Name of the speaker/tutor)

Mon
3/12/2018

Introduction to Symplectic Geometry-I. (AM)

 T

E

A

Introduction to Contact Geometry- I . (MD)

L

U

N

C

H

Introduction to J-holomrophic curves-I. (RM)

T

E

A

Symplectic structures and Classical Mechanics (AM)

S

N

A

C

K

S

Tue
4/12/2018

Introduction to Symplectic Geometry-II. (AM)

Introduction to Contact Geometry-II. (MD)

Introduction to J-holomrophic curves-II. (RM)

Contact Structures in PDEs (AM)

Wed
5/12/2018

Introduction to Symplectic Geometry-III. (AM)

Introduction to Contact Geometry-III. (MD)

Introduction to J-holomrophic curves-III. (RM)

Reeb Flow and geodesic flow. (AB)

Thu
6/12/2018

Introduction to Mapping Class groups. (KR)

The Giroux Correspondence. (DK)

Moduli Spaces Of J-holomorphic curves-IV. (RM)

Gromov’s Compactness - I (1.5 hrs) (DD)

Fri
7/12/2018

Approximately Holomorphic Geometry (DD)

Eliashberg’s Classification of Overtwisted Contact Structures in dimension 3. Part-1 (MD)

Gromov-Witten Invariants, Enumerative Geometry (RM)

Gromov’s Compactness - II. (1.5 hrs) (DD)

Sat
8/12/2018

Approximately Holomorphic Geometry (DD)

Eliashberg’s Classification of Overtwisted Contact Structures in dimension 3.Part-2. (MD)

Gromov-Witten Invariants, Enumerative Geometry (RM)

Enumerative Geometry

Mon
10/12/2018

Knot Contact homology (SB)

Open Books and Fillability of contact structures. (DK)

Arnold’s Conjecture and Floer Theories (SV)

Primitivity in the mapping class group and related open problems. (KR)

Tue
11/12/2018

Knot Contact homology (SB)

Riemannian geometry of Contact manifolds. (AB)

Arnold’s Conjecture and Floer Theories (SV)

Open Problems in Riemannian geometry of Contact manifolds (AB)

Wed
12/12/2018

Knot Contact homology (SB)

Riemannian geometry of Contact manifolds. (AB)

Arnold’s Conjecture and Floer Theories (SV)

Open Problems in Rigidity Side of Symplectic and Contact Structures.

Thu
13/12/2018

Knot Contact homology (SB)

Riemannian geometry of Contact manifolds. (AB)

Arnold’s Conjecture and Floer Theories (SV)

Open Problems in Rigidity Side of Symplectic and Contact Structures.

Fri
14/12/2018

Knot Contact homology (SB)

Arnold’s Conjecture and Floer Theories (SV)

Conclusion.

 
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