ATMW Preliminary workshop on Symplectic Geometry and Contact Topology (2014)

Brief write up about the workshop

The field of symplectic and contact geometry and topology is currently a very active area of mathematical research. It is intertwined with many other areas of mathematics and even mathematical physics, such as Hamiltonian Dynamics and Geometric Optics, low-dimensional topology, Algebraic Geometry, the theory of integrable systems, and the mathematical theory of Mirror Symmetry to name a few. In the last three decades, since the area emerged as a separate subject, there were found many new powerful methods, such as the introduced by M.Gromov theory of holomorphic curves led to creation of Gromov-Witten theory and the Floer homology theory in its different flavors. As a result, several outstanding problems in Hamiltonian Dynamics, e.g. Arnold’s and Weinstein’s conjectures were solved, and a link to the Mirror Symmetry theory was found.

A detailed proposal about how the the discussion meeting will take place and emphasizing the national need for having such a discussion meeting

While there are many young Indian mathematicians and graduate students who are interested in learning this subject, this area, unfortunately, is not very popular in India. The proposed Advanced School and Discussion meeting is designed to change the sutuation and facilitate the research in this area in India. The main part of the program will take place in TIFR, Mumbai from December 15 to December 22. During this period there will be given several intensive lecture courses oriented to graduate students, postdocs and other mathematicians interested in learning this important area. The lectures will be given by leading specialists in symplectic topology and related areas of mathematics, such as Dusa McDuff (Columbia), Kenji Fukaya (SCGP), Ko Honda (UCLA), and three Stanford mathematicians: Soren Galatius, Sheel Ganatra and Yakov Eliashberg. A preparatory meeting for the workshop will be organized at HRI, Allahabad, during the period December 1–13, 2014. Symplectic geometry has always been a very important topic in mathematics. Traditionally very large part of the interactions between mathematics and theoretical physics has been via symplectic geometry. The topic of symplectic geometry, and its role as a platform for interactions between mathematics and theoretical physics,were elevated by a level after the appearance in 1986 of the seminal paper of Gromov on symplectic geometry.
The subjects Quantum cohomology and Gromov-Witten theory were born.Since early nineties, symplectic geometry is witnessed a very high level of activity, which continues unabated till the present day. Yakov Elaishberg, who is one of the leaders in symplectic geometry, came up, during his recent visit to India, with a proposal to organize a workshop in TIFR on symplectic geometry. he has now completed the initial important work of getting consents form some world experts to lecture in the workshop.

Indranil Biswas (T.I.F.R.), Mahan Mj (Ramakrishna Mission Vivekananda University at Belur Math), Yakov Elaishberg (Stanford University, U.S.A.) are the organizer. Local organizer at H.R.I. will be Rukmini Dey,Thangadurai.

Prior to the workshop we are planning to hold a preparatory meeting in HRI during 1–13 December, 2014.The sole purpose of this meeting is to prepare the Indian audience so that they can benefit extensively from the workshop. This will have the format of an AIS activity.

List of topics to be lectured on in the preparatory meeting along with the speaker’s names:

The Preparatory School

The lectures will be held from 1-12 evening. participants will leave on 13th morning.

• MD : Mahuya Datta : Introduction to Symplectic Geometry (4.5 hrs)
• RD : Rukimini Dey : Quantization of symplectic manifolds (1.5 hrs)
• SB1 : Somnath Basu : Introduction to Floer Theory (3 hrs)
• SV : Sushmita Venugopalan : Introduction to Gromov-Witten Theory (4.5 hrs)
• SB2 : Samik Basu : Introduction to Madsen-Weiss Theore (3 hrs)
• DP : Dishant Pancholi : Introduction to Contact Topology (4.5 hrs)
• HS : Dheeraj Kulkarni : Gromov Compactness (4.5 hrs)
• DK/FP : and Fran Presas : Lefschetz fibrations on symplectic/contact manifolds (4.5 hrs)
• RG : Rajesh Gopakumar : A Physics perspective on Mirror Symmetry and/or Gromov-Witten Invariants (3 hrs)
• DF : David Farris : Introduction to Lagrangian Floer Homology (1.5 hrs)

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1.By train

Allahabad is well connected by train from various parts of the country. The most convenient trains from New Delhi to Allahabad are 12418 Prayagraj Express, and 12276 Duronto Express. Trains passing through Allahabad include 12311 Howrah–Kalka Mail, 12322 Mumbai–Howrah Mail, and 12669 Chennai–Chhapra Ganga Kaveri Express. For detailed information on these and other trains to Allahabad, please see the Indian Railways Web sites.

2.By air

There is a single daily flight, AI 9811 of Air India, from Delhi to Allahabad on all days of the week except Sunday. For details, please see the Air India Web site.

3.By road

Allahabad is 238 km. from Lucknow, and 125 km. from Varanasi. There are frequent bus services between these cities and Allahabad, typically once every half hour. Private taxis also operate on these routes.

The road journey from Lucknow to Allahabad takes about 5 hours. Buses leave Lucknow from the Charbagh Bus Depot, and terminate at the Civil Lines Bus Depot in Allahabad.

The road journey from Varanasi to Allahabad takes about 3 hours. Most vehicles enter Allahabad along the Shastri Bridge over the river Ganga. In that case, one reaches Chak, a place near the Institute (see below), before Allahabad city.

4.From Allahabad city to HRI

The HRI campus is at Jhusi, about 13 km. from Allahabad city towards Varanasi. The Institute operates a regular bus service from the HRI City Guest House, to the campus. Please see http://www.hri.res.in/contact.html for the address and phone number of the City Guest House, and http://www.hri.res.in/∼yashpal/busschedule.pdf for the timetable of bus services between the City Guest House and the campus.

If you are coming to Allahabad by train, then come out through the Civil Lines Exit of the station, and take a rickshaw or a tempo from the station to the HRI City Guest House. The distance from the station to the City Guest House is about 4 km.

If you are coming from the city to HRI by a vehicle other than an HRI bus, the following information may be useful. To reach the campus from the city, one goes along the Shastri bridge over the river Ganga. Three km. beyond the end of the bridge, along the Grand Trunk Road (G. T. Road), there is an HRI sign, where one should turn right, off the highway and into Chhatnag Road. This point on the G. T. Road is called Chak. The HRI campus is a further 3 km. from Chak, along Chhatnag Road. The entrance to the campus is about 100 m. before the Birla Guest House, an establishment owned by a private industrial company.