TEW Complex Analysis and Topology (2014)

Proposed Scientific Plan

In the proposed TEW, our theme would be Complex Analysis (from a topological viewpoint). This will be a follow up of the TEW on Complex Analysis that we organized at Burdwan last year. That was a tremendously successful program and we are proposing this second TEW at Burdwan because many participants have requested a follow up to fulfill their desire to build up a scholarship base.
We propose to have three mini-courses in this program consisting of around 4 lectures, each of 1.5 hrs duration. The rest of the time will be devoted to group discussions and tutorial. The aim of this course would be to depict a flow of ideas along with absolute mathematical precision wherever possible. We hope the courses will provide an intuitive, as well as concrete realization of foundational topics of algebraic topology and its application to complex analysis. The main aim is to discuss uniformization theorem of Riemann surfaces and its applications.
On the last day of the program, we plan to have 3-4 survey talks by experts that will connect the mini-courses to a current topic of present day research. This plan will be materialized only after the proposal is approved.

Proposed Syllabus
The syllabus of the workshop that we plan to follow is given below, along with the title of each course. The main aim of the course would be to convey the ideas and concepts through examples and then to state the main results in general setting.

1. Quotient Topological Spaces: Quotient spaces, connected sums, orientability, gluing constructions, Classification of compact surfaces, Euler characteristic.
2. Fundamental Groups: Homotopy, Fundamental groups, review of presentation of groups and free products, Van-Kampen theorem (statement only), notion of contractible and simply connected spaces, computation of fundamental groups of some basic topological spaces, eg. Circle, projective space, figure eight knot.
3. Covering of Topological Spaces: Covering spaces, covering map and fundamental group, path-lifting and homotopy, Deck transformation, Universal covering, Existence of universal cover, Classification of universal covering (statement and explanation). Proof of Picard's theorem.
4. Uniformization of Riemann Surfaces: Idea of Riemann surfaces, maps between Riemann surfaces, Riemann mapping theorem, Idea and statement of the uniformization theorem, Implication of uniformization for compact surfaces.

Proposed Speakers
We have communicated the following mathematicians who have kindly confirmed their participation.

1. Ravi S. Kulkarni, Bhaskaracharya Pratisthana, Pune.
2. Kingshook Biswas, RKMVU, Belur (will be available only during Dec 25—27).
3. Abhijit Pal, IIT Kanpur.
4. Kuntal Banerjee , Presidency University.

Topics to be covered by speakers
 

1.  Quotient Topological Spaces: Quotient spaces, connected sums, orientability, gluing constructions, Classification of compact surfaces, Euler characteristic.
2.  Fundamental Groups: Homotopy, Fundamental groups, review of presentation of groups and free products, Van-Kampen theorem (statement only), notion of contractible and simply connected spaces, computation of fundamental groups of some basic topological spaces, eg. Circle, projective space, figure eight knot.
3. Covering of Topological Spaces: Covering spaces, covering map and fundamental group, path-lifting and homotopy, Deck transformation, Universal covering, Existence of universal cover, Classification of universal covering (statement and explanation). Proof of Picard's theorem.
   By Ravi S. Kulkarni (RSK) and Abhijit Pal (AP)
4. Uniformization of Riemann Surfaces: Idea of Riemann surfaces, maps between Riemann surfaces, Riemann mapping theorem, Idea and statement of the uniformization theorem, Implication of uniformization for compact surfaces.
   By  Kingshook Biswas (KB)

Time Table

How To Reach

The venue is located at the city Burdwan in West Bengal which is around five minutes walking distance from the nearest Burdwan railway station  (also called Barddhaman Jn), Station Code: BWN.The nearest andmark to the venue is District Magistrate Banglow. Burdwan is well-connected by train to all major cities in north India.To reach the venue one may take a cycle rickshaw from the Barddhaman Jn railway station which would take 5 minutes. Within the town, cycle rickshaws are the most preferred mode of transport. Ask the rickshaw driver to drop you at the Barddhaman Bhavan (nearest landmark D.M. banglow).

The nearest airport to Burdwan is Kolkata. The town is very well-connected with Kolkata by suburban railway and road transport.There are many AC/ non-AC buses between Burdwan and Kolkata. It takes around two and half an hours for an one-sided travel between Burdwan and Kolkata.

Burdwan is a historical place which was a province of Mughal emperor.In each part of the city you must find a essence of ancient historical days.

  For more details about Burdwan, see

 http://en.wikipedia.org/wiki/Bardhaman