Introduction to J-holomorphic curves and Gromov-Witten Invariants

July 10 - 22, 2017

About School and Workshop
For the last twenty years, the theory of Gromov-Witten invariants and Mirror Symmetry has been an active area of research in the interface of Mathematics and Theoretical Physics (particularly String Theory). We are therefore organizing an introductory school at NISER in J-holomorphic curves and Gromov-Witten invariants with connections to Mirror Symmetry. Young mathematicians (PhD stduents and postdocs) who are interested in Differential Topology, Differential Geometry, Complex Algebraic Geometry and Symplectic Geometry are particularly encouraged to apply.
Workshop Speakers
Samik Basu (RKMVU Belur)
Somnath Basu (IISER Kolkata)
Chitrabhanu Chaudhuri (IISER Pune)
Utsav Chaudhury (IISER Kolkata)
Mahuya Datta (ISI Kolkata)
Sushil Gorai (IISER Kolkata)
Ritwik Mukherjee (NISER Bhubaneswar)
Sivaguru Ravisankar (TIFR Mumbai)
Rukmini Dey (ICTS)
List of Participants
Aakriti Garg, NISER
Abhishek Das, NISER
Abhrojyoti Sen, NISER
Aleksander Milivojevic, Stony Brook
Amit Tripathy, NISER
Anantadulal Paul, NISER
Anindya Chanda, ISI Kolkata
Anish Anand, NISER
Anuj Verma, NISER
Aparajita Karmakar, (to join) IISER P
Arijit Dey, IIT Madras
Chandrahas Piduri, IISER K
Chethan Gowdigere, NISER
Chitrabhanu Chaudhuri, IISER Pune
Divakaran Divakaran, IMSc
Gargi Ghosh, IISER Kolkata
Gaurav Swansi, NISER
Gobinda Sau, RKMVU
Haresh Kumar Chaudhry, NISER
Harshit Yadav, IIT Kanpur
Jay Mandal, IIT Mumbai
Jithin Paul, IISER Mohali
Kartik Sahoo, NISER
Kaushik Mohanta, IIT Kanpur
Mahuya Datta, ISI Kolkata
Moumita Patra, NISER
Nihar Gargava, IIT Kanpur
Palash Dubey, NISER
Pratyush K. Mishra, IISER Mohali
Rahul Kumar, HRI
Ripan Saha, Raiganj University
Ritwik Mukherjee, NISER
Ronnie Sebastian, IIT Mumbai
Rukmini Dey, ICTS
Sachchidanand Prasad, NIT Rourkela
Samik Basu, RKMVU
Shreyas Gupta, IISc
Shubham Girdhar, NISER
Sivaguru Ravisankar, TIFR Mumbai
Somnath Basu, IISER Kolkata
Subhajit Mishra, IISER K
Subhojit Mandal, Univ. of Hyd.
Sudip Naskar, IIT Indore
Sujit Kumar Panigrahi, NISER
Surojit Ghosh, RKMVU
Sushil Gorai, IISER Kolkata
Sutanu Roy, NISER
Swagata Sarkar, CEBS Mumbai
Utsav Chaudhury, IISER Kolkata
Yathukishore GV, NISER
Schedule of Lectures

Time table from 10th to 22nd July, 2017

Day 1 (10th July)
Lecture 1Overview talkRitwik Mukherjee
Lecture 2Review of Differential Geometry-ISamik Basu
Lecture 3Review of Complex Geometry-ISushil Gorai
Lecture 4 Review of (Co)homology-ISomnath Basu
Potential Evening discussionReview of complex analysis of several variables
Day 2 (11th July)
Lecture 1Review of Differential Geometry-IISamik Basu
Lecture 2Review of Differential TopologyRitwik Mukherjee
Lecture 3Review of Complex Geometry-IISushil Gorai
Lecture 4Introduction to Symplectic GeometryMahuya Datta
Potential Evening discussionHow do symplectic manifolds arise from physics?
Day 3 (12th July)
Lecture 1Review of Complex Geometry-IIISushil Gorai
Lecture 2Several Complex Variables & J-holomorphic curves-ISivaguru Ravisankar
Lecture 3Review of (Co)homology-IISomnath Basu
Lecture 4TutorialSivaguru Ravisankar
Potential Evening discussionClassifying Spaces
Day 4 (13th July)
Lecture 1Analytic foundations for Moduli Space of maps-IMahuya Datta
Lecture 2Several Complex Variables & J-holomorphic curves-IISivaguru Ravisankar
Lecture 3Introduction to Stable Maps and Gromov ConvergenceRitwik Mukherjee
Lecture 4Tutorial Mahuya Dattar
Potential Evening discussionTBD
Day 5 (14th July)
Lecture 1Homology classes and PseudocyclesSomnath Basu
Lecture 2Introduction to Gromov-Witten InvariantsRitwik Mukherjee
Lecture 3Analytic foundations for Moduli Space of maps-IIMahuya Datta
Potential Evening discussionGromov Compactness Theorem
Day 6 (15th July)
Lecture 1Analytical foundations for Moduli Spaces of maps-IIIMahuya Datta
Lecture 2Introduction to Moduli Space of curves-IChitrabhanu Chaudhuri
Lecture 3Introduction to Loop SpacesSamik Basu
Potential Evening discussionOrbifolds & Mapping Class Groups
Day 7 (17th July)
Lecture 1Introduction to Mirror Symmetry-IUtsav Choudhury
Lecture 2Rational Homotopy Theory of loop spaces-IAleksander Milivojevic
Lecture 3Introduction to Moduli Space of curves-IIChitrabhanu Chaudhuri
Potential Evening discussionIntroduction to Morse Theory
Day 8 (18th July)
Lecture 1Introduction to Witten Conjecture-IChitrabhanu Chaudhuri
Lecture 2Introduction to Quantum CohomologyRitwik Mukherjee
Lecture 3Atiyah-Bott Localization TheoremUtsav Choudhury
Lecture 4Introduction to Floer TheorySomnath Basu
Potential Evening discussionTBD
Day 9 (19th July)
Lecture 1Rational Homotopy Theory of loop spaces-IIAleksander Milivojevic
Lecture 2Introduction to Teichmuller spacesDivakaran Divakaran
Lecture 3Introduction to Mirror Symmetry-IIUtsav Choudhury
Lecture 4Introduction to Geometric Quantization-IRukmini Dey
Potential Evening discussionTBD
Day 10 (20th July)
Lecture 1Introduction to Geometric Quantization-IIRukmini Dey
Lecture 2Topology of Moduli space of curves-ISamik Basu
Lecture 3Introduction to Witten Conjecture-IIChitrabhanu Chaudhuri
Lecture 4Tutorial Utsav Choudhury
Potential Evening discussionGromov-Witten Invariants and TQFT
Day 11 (21st July)
Lecture 1The Physics of Mirror Symmetry-IChethan Gowdigere
Lecture 2Gromov Compactness TheoremDivakaran Divakaran
Lecture 3Topology of Moduli space of curves-IISamik Basu
Lecture 4Introduction to Geometric Quantization-IIIRukmini Dey
Potential Evening discussionFloer Theory & String Topology
Day 12 (22nd July)
Lecture 1The Physics of Mirror Symmetry-II Chethan Gowdigere
Lecture 2Advanced Topics in Complex AnalysisSivaguru Ravisankar
Lecture 3Advanced Topics in Complex GeometrySushil Gorai
Informal discussionSummary of what we covered
Registration

Any questions should be sent to the following email address
j.holomorphic.curves@gmail.com