# TIMC-Vista Foundation Regional Programme

Date:

Sat, 21st Oct 2017

Venue:

**Dr. H. Narasimhaiah Auditorium,**

National College, Basavanagudi, Bangalore

**Coordinator: **Sanjeevakumar Deshpande email: ss_desh25 *at* rediffmail *dot* com>

**10:00 - 11:00 – H. A. Gururaja, IISER, Tirupati.****Title:**On some global theorems in surface theory**Abstract:***After a brief introduction to the notion of curvature of surfaces in R*^{ 3}, I will discuss a few global theorems in surface theory.**11:00 - 11:30 – Coffee/Tea break****11:30 - 12:30 – P. S. Datti, former faculty,****TIFR CAM**, Bengaluru.**Title:**Two Dimensional Systems and Stability Analysis**Abstract:***After a brief introduction to general autonomous systems and their basic properties, we will concentrate on 2D systems. Several examples from mechanical systems, population dynamics, etc will be discussed. (If time permits) Phase plane analysis of some systems will be carried out in detail.***12:30 - 14:30 – Lunch Break****14:30 - 15:30 – R. Sivaguru, TIFR CAM, Bengaluru.****Title:**Complex Analysis in One and More Variables**Abstract:***Real analysis in several variables is largely similar in spirit to the theory in one variable. In contrast, Complex analysis in several variables is strikingly different from the one variable theory. We will explore one such phenomenon discovered by Hartogs. It roughly translates as: in several variables, holomorphic functions defined on a ”thin” set naturally extend to a ”fat” set. This does not happen in one variable. We will develop most of the tools that we need and will only assume familiarity with undergraduate complex analysis.***15:30 - 16:00 – Coffee/Tea break****16:00 - 17:00 – Ramesh Sreekantan, isi, bengaluru.****Title:**An Introduction to Leavitt Path Algebras**Abstract:***One of the first invariants one encounters in Algebra is that of dimension of a vector space. One learns, for instances, that if V and W are two vector spaces of different dimensions, then they cannot be isomorphic. This is known to fail over arbitrary rings in general. Rings which have this property as said to have the Invariant Basis Number property. Leavitt provided quite general examples of rings where this fails. Recently, these rings have reappeared as special cases of certain path algebras associated to graphs - now called Leavitt Path Algebras. We will introduce them and give a few examples and applications.*