Summer Workshop in Mathematics (26  31 July 2010) at IISER, Pune
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 :
Prof. K. N. Ganesh (Director IISER, Pune)
Prof. L. Shashidhara (IISER, Pune)
Local Organising Committee :
Dr. Anupam Kumar Singh (IISER, Pune)
Dr. Ayan Mahalanobis (IISER, Pune)
Invited
Speakers(Confirmed) :
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.
Prof. Basudeb Datta 
26^{th} July,2010 
09:3010:30

Triangulations of surfaces 
Prof. N.M. Singhi 
26^{th} July,2010 
11:3012:30 
Tree of life 
Dr. T.E. Venkata Balaji 
27^{th} July,2010 
09:3010:30 
Moduli theory 
Prof. R. Ramanujam 
27^{th} July,2010 
11:3012:30 
Games and Computations 
Prof. V. Balaji 
28^{th} July,2010 
09:3010:30 
Finite Group theory and applications 
Prof. D.S.Nagaraj 
28^{th} July,2010 
11:3012:30 
Group actions 
Prof. Somesh Bagchi 
29^{th} July,2010 
09:3010:30 

Prof. Shobha Madan 
29^{th} July,2010 
11:3012:30 
Arithmetic Progressions in subsets of Integers 
Prof. Jaikumar Radhakrishnan 
30^{th} July,2010 
09:3010:30 
Shannon's entropy 
Prof. Kavitha Telikepalli 
30^{th} July,2010 
11:3012:30 
Efficient algorithms for some simple problems 
Prof. B. Limaye 
31^{st} July,2010 
09:3010:30 
The Fundamental Theorem of Calculus for the Rectangle 
Prof. J.K. Verma 
31^{st} July,2010 
11:3012:30 
Polytopes and polynomial equations 
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 Godgiven 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 2025 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.