Summer Workshop in Mathematics (26 - 31 July 2010) at IISER, Pune

IISER, Pune

Parthasarathi

How to reach IISER

Aim :
The aim of the Summer workshop is to motivate students to take up Mathematics for research. We have invited eminent mathematicians of our country to speak in this workshop. We also want to create awareness about Mathematics education, in general. Thus, keeping this in mind we have requested each mathematician to be available in the afternoon to interact with audience. This workshop is continuation of the similar one held last year.

Organisation :

• Executive Organising Committee :

  1. Prof. K. N. Ganesh (Director IISER, Pune)

  2. Prof. L. Shashidhara (IISER, Pune)

• Local Organising Committee :

  1. Dr. R. Parthasarathi (IISER, Pune)

  2. Dr. Anupam Kumar Singh (IISER, Pune)

  3. Dr. Ayan Mahalanobis (IISER, Pune)

Invited Speakers(Confirmed) :

Prof. V. BALAJI	Dr. T.E. VENKATA BALAJI
Prof. BASUDEB DATTA	Prof. J.K.VERMA
Prof. BALMOHAN LIMAYE	Prof. SHOBHA MADAN
Prof. JAIKUMAR RADHAKRISHNAN	Prof. R. RAMANUJAM
Prof. KAVITHA TELIKEPALLI	Prof.N.M.Singhi
Prof. SOMESH BAGCHI	Prof. D.S.NAGARAJ

Schedule :
There will be usually two lectures (one hour each) in the morning and discussion sessions in the afternoon at 2:30 PM . Note that some of the lectures could be reshuffled according to availability of speakers.

Abstracts :

Title: Triangulations of Surfaces. 
Speaker: Basudeb Datta
 
Abstract: This is an introduction to triangulations of closed surfaces. 
Let $gT$ denote the connected sum of $g$ copies of the torus. 
We prove the following: 
(i) There exists a triangulation of $gT$ in $R^3$. 
(ii) If $K$ is any triangulation of $gT$ then 
(the number of vertices in $K$) - (the number of edges in $K$) + (the number of faces in $K$) $ = 2 - 2g$. 
(iii) If $gT$ is homeomorphic to $hT$ then $g = h$. 

Title: Tree of life
Speaker: Prof. N.M. Singhi

Mathematical tools used in two problems occurring daily life will be discussed
1. A phylogenetic tree or tree of life is a branching diagram or "tree" showing the inferred evolutionary relationships among various biological species or other entities based upon similarities and differences in their physical and/or genetic characteristics. Thus each living entity is joined to its ancestor by a 'branch' in this tree. Studying this tree is one of the active areas of Biology today. Mathematical tools to study this tree, provided by discrete mathematics and algebraic geometry, will be discussed .
2. Compression techniques used in propagation of information (for example TV Signals) are generally based on mathematical tools developed by using topology, discrete mathematics, geometry etc. Fractals and their use in compression techniques will be discussed.

Title:Arithmetic Progressions in subsets of Integers
Speaker:Prof. Madan

In the study of additive patterns in 'large' subsets of integers, an important problem is to look for arithmetic progressions. The subject begins with van der Waerden's theorem (on monochromatic colourings of integers...). Erdos and Turan conjectured a stronger form of this, whose solution is now Szemeredi's Theorem: Any subset of positive density in the set of integers contains arbitrarly long arithmetic progressions. We will give a proof of this theorem for the existence of APs of length three due to Klaus Ross.

Titles of Talk: Moduli Theory - I and II
Speaker: Prof. T.E. Venkata Balaji

Moduli theory has been one of the most fascinating areas of Mathematics from classical to modern times. This has been so because it integrates several areas of Mathematics like Algebra, Topology, Analysis and Number Theory which it uses to uncover the amazing God-given geometry hidden in problems of classification of geometric objects.

Prerequisite :
We have requested all our speakers to keep the lectures elementary and target interdisciplinary audience. Hence, as such, there is no prerequisite for this workshop except enthusiasm and readiness.

Participation :
This workshop is mainly for the students of IISER, Pune. We can accommodate about 20-25 students/teachers from Pune as well. Interested people (including IISER students) who want to attend this workshop please send an email to Dr. R. Parthasarathi (email: parthaATiiserpune.ac.in) expressing their interest. No help, such as, TA/DA, transport, accommodation etc. is provided for the participation.