All talks are in Lecture Hall 6, on Mondays, during 15:30-16:30. Mon 2015-02-16 Anbu Arjunan. Title: Stone-von Neumann Theorem. Abstract: We initially state two theorem's, namely Stone's theorem on k-parameter unitary group and Hahn-Hellinger theorem . Then, we will use above result to prove so called " Stone-von Neumann theorem", which states that any two strongly continuous k-parameter groups of unitary operators in a Hilbert space satisfying the Weyl commutation relations are unitarily equivalent. Mon 2015-03-02 Debayudh Das Title: Morse theory and a characterization of high-dimensional spheres. Abstract: Morse theory is an important tool in Mathematics. Among other things it describes how one can decompose a given smooth manifold as a cell complex. In this talk I shall give a brief introduction to basics of Morse theory with the help of examples. As an application I will sketch the proof of a theorem due to Smale that says that a homotopy sphere is homeomorphic to the unit sphere in dimensions greater than 5. Mon 2015-03-09 Rajib Sarkar Title: On the number of defining equations for algebraic sets. Abstract: Given an algebraic set X (i.e., solution to some collection of polynomials in n variables) in k^n, we are interested in finding the least number of polynomials whose set of common solutions is exactly X. Kronecker[1882] proved that this least number is at most n+1. We shall see that this least number is at most n, as done in the paper of Eisenbud and Evans[1973] and will illustrate this using examples for the case n=1 and 2. Mon 2015-03-16 Abhishek T Bharadwaj Title: On periods of Weierstrass's \wp function with algebraic invariants. Abstract: The Weierstrass's \wp function associated with a period lattice L satisfies the equation \wp'(z)^{2}$ =4\wp^{3}(z) -g_{2}\wp(z)-g_{3} where g_{2} and g_{3} are the invariants. If g_{2} and g_{3} are algebraic then with the help of Schneider-Lang Theorem, we will prove that the non zero periods in L are transcendental. Thu 2015-03-26, 15:30-16:45 Room: Lecture Hall 2 (Unusual date and room) Naveen Kumar Title: Existence of Meromorphic Function on Compact Riemann Surface. Abstract: A connected compact complex manifold X of complex dimension 1 is called a compact Riemann surface. X may be considered as purely algebraic object also. More precisely, compact Riemann surfaces are the same objects as smooth, connected, projective curves over the complex number field. To establish the algebraicity of X, one needs to know the existence of meromorphic function f on X. A priori it is not clear that why such f should exist. We shall address this existence problem and try to see the positive answer to this along with some examples in this talk. Tue 2015-03-31, 15:30-16:45 Room: Lecture Hall 3 (Unusual date and room) S P Murugan Title: Creating More Convergent Series Abstract: The problem is the following: Does there exist permutations sigma of the set of positive integers N with the following two properties: 1) sigma sends convergent series to convergent series; 2) there exist divergent series whose image under sigma is convergent. We also discuss the following questions: a) How difficult is it to construct such a sigma (or is its existence established purely abstractly)? b) Is sigma unique, or are there many such permutations of N? In the latter event, how many are there? c) Can the set of all such sigma be easily characterized? 2015-04-09, 15:30-16:45 Room: Lecture Hall 2 (Unusual date and room) Praveen Kumar Roy Title: Global stability theorem. Abstract: we start with the definition of Foliation and then will see some examples of it. after this we will try to approach towards the proof of the theorem which says that if F is c^r (r>1) co-dimension one foliation of compact connected n-dimension c^s (r=