It is known that contractive homomorphisms of the disc and the bi-disc algebra to the space of bounded linear operators on a Hilbert space are completely contractive, thanks to the dilation theorems of B. Sz.-Nagy and Ando respectively. Examples of contractive homomorphisms of the (Euclidean) ball algebra which are not completely contractive was given by G. Misra. From the work of V. Paulsen and E. Ricard, it follows that if m >= 3 and B is any ball in C^m with respect to some norm, then there exists a contractive linear map which is not complete contractive. The characterization of those balls in C^2 for which contractive linear maps are always completely contractive remained open. In this talk, we intend to answer this question for balls in C^2 which are of the form {z= (z1, z2) :||zA||=||z1A1+z2A2||op<=1} for some choice of an 2-tuple of 2x2 linearly independent matrices A = ( A1, A2)

Mumford forms are sections of a certain line bundle defined over the moduli space of smooth algebraic curves of genus g>0. In this talk we discuss the relationship of Mumford forms with a certain Bosonic measure coming from String theory, and their estimates.

We consider a finite volume element method for approximating the solution of a time fractional diffusion problem involving a Riemann-Liouville time fractional derivative of order alpha between 0 and 1. For the spatially semidiscrete problem, we establish optimal with respect to the data regularity L2(X)-norm error estimates, for the cases of smooth and middly smooth initial data, i.e., v in H2(X) intersection H^1_0(X) and v in H10(X). For non-smooth data v in L2(X), the optimal L2(X)-norm estimate is shown to hold only under an additional assumption on the triangulation, which is known to be satisfied for symmetric triangulations. Superconvergence result is also proved and as a con- sequence a quasi-optimal error estimate is established in the L^infty(X)-norm. Further, two fully discrete schemes based on convolution quadrature in time generated by the backward Euler and the second-order backward difference methods are developed, and error estimates are derived for both smooth and nonsmooth initial data. Finally, some numerical results are presented to illustrate the theoretical results.

I will talk about formal group laws and their relation to complex oriented cohomology theories. In the end I will state Landweber exact functor theorem.

In this talk I will explain some results on the extensions of mod-p characters of affine pro-p Iwahori–Hecke algebras. As a preliminary application we compute the degree one extensions of smooth representations of SL(2,Q_p). These calculations also reveal interesting phenomenon on Iwahori subgroup cohomology of smooth representations. If time permits I will explain how these extensions can be related to local Galois representations.

We will discuss results given by Csikvari who proved that certain graph parameters have their extreme points at the star and at the path among the trees on a fixed number of vertices. He gave many applications of the so-called generalized tree shift which induces a partially ordered set on trees having fixed number of vertices. He proved that certain graph parameters (Wiener-index, Estada index, the number of closed walks of a fixed length, largest eigenvalue of the adjacency matrix A and Laplacian matrix L, coefficients of independence polynomial, coefficients of the edge cover polynomial, coefficients of the characteristic polynomials of A and L in absolute value) increase or decrease along this poset of trees

We observe periodic phenomena everyday in our lives. The daily temperature of Delhi or the number of tourists visiting the famous Taj Mahal or the ECG data of a normal human being, clearly follow periodic nature. Sometimes, the observations may not be exactly periodic due to different reasons, but they may be nearly periodic. The received data is usually disturbed by various factors. Due to random nature of the data, statistical techniques play important roles in analyzing the data. Statistics is also used in the formulation of appropriate models to describe the behavior of the system, development of an appropriate technique for estimation of model parameters, and the assessment of model performances. In this talk we will discuss different techniques which we have developed for the last twenty five years for analyzing periodic data, other than the standard Fourier analysis.

We will discuss results given by Csikvari who proved that certain graph parameters have their extreme points at the star and at the path among the trees on a fixed number of vertices. He gave many applications of the so-called generalized tree shift which induces a partially ordered set on trees having fixed number of vertices. He proved that certain graph parameters (Wiener-index, Estada index, the number of closed walks of a fixed length, largest eigenvalue of the adjacency matrix A and Laplacian matrix L, coefficients of independence polynomial, coefficients of the edge cover polynomial, coefficients of the characteristic polynomials of A and L in absolute value) increase or decrease along this poset of trees