Abstract The quadratic reciprocity law of Fermat, Euler, Legendra and Gauss and its generalizations has been one of the central pursuits of number theory. The developments range from class field theory giving the reciprocity law for abelian extensions of number Read More …

# Category: Seminars

## Seminar: Some Recent Progress in Quasilinear Hyperbolic Systems: New Local Solvability Methods and Stochastic Analysis

Abstract Quasilinear symmetric and symmetrizable hyperbolic system has a wide range of applications in engineering and physics including unsteady Euler and potential equations of gas dynamics, inviscid magnetohydrodynamic (MHD) equations, shallow water equations, non-Newtonian fluid dynamics, and Einstein field equations Read More …

## Seminar: Stability of Quiver representations

Abstract A notion of stability arose in Algebraic Geometry in the work of Mumford. It was further studied and developed by Seshadri, Narasimhan, Ramanan and others. A. King adopted these notions in geometric study of representation of quivers. This gives Read More …

## Seminar: Strong, Weak Convergence and Beyond

Abstract It is well known that in infinite dimensional spaces the weak and strong convergence are two different concepts. In general, the weak convergence does not imply the strong convergence. But unfortunately, in practical applications, one can only expect to Read More …

## Seminar: Secure and Fault-tolerant Computing

Abstract As fabrication technology scales, chips are becoming less reliable, thereby increasing the power and performance costs for fault-tolerance. To make matters worse, power-density is becoming a significant limiting factor for performance and System-on-Chip (SoC) design in general. In the Read More …

## Seminar: Relation between orbits of unimodular elements and its application

Abstract This is a topic in classical algebraic K-Theory. I will recall definitions of elementary linear group, elementary symplectic group, linear transvection group, symplectic transvection group and symplectic group w.r.t. any alternating form. These groups have natural action on the Read More …

## Seminar: Real elements in groups of type $F_4$

Abstract Let $G$ be a group (resp. an algebraic group defined over a field $k$). For the latter case, let $G(k)$ denote the group $k$-rational points of $G$. An element $g \in G$ (resp. $G(k)$) is called real (resp. $k$-real) Read More …

## Seminar: On Stiefel-Whitney Classes of vector bundles over real Stiefel Manifolds

Abstract In this talk, we will first define characteristic rank of a connected closed smooth manifold and upper characteristic rank of a finite connected CW complex. Then we will give the full description of upper characteristic ranks of Stiefel manifolds. Read More …

## Seminar: On the Fourier coefficients of a Cohen-Eisenstein series

Abstract In the first part of this talk, we present a formula for the coefficients of a weight 3/2 Cohen-Eisenstein series of squarefree level N. This formula generalizes a result of Gross and it proves in particular a conjecture of Read More …

## Seminar: Hitchin pairs on a singular curve

Abstract In this talk, we present the moduli problem of rank 2 torsion free Hitchin pairs of fixed Euler characteristic ? on a reducible nodal curve. We describe the moduli space of the Hitchin pairs. We define the analogue of Read More …