Abstract: (See the attached PDF file) Note: Prof. Srivastava has indicated that this seminar would be accessible to M.Sc. students and that it will highlight some nice aspects of set theory.

Abstract : We begin with a review of moonshine for sporadic groups indicating the current status of this active new area of research which intersects several fields in mathematics and theoretical physics. We then discuuss the relation of black hole quantum gravity and mock modular forms originally introduced as mock theta functions by Ramanujan.

Abstract: In general, inverse problems are those where one needs to recover the unknown parameter of a system from the knowledge of the external observation. In this talk, I will mainly give an overview of Calder\'on’s inverse problems arising in several linear and nonlinear partial differential equations. I will discuss two different kinds of inverse problems for the Maxwell system and p-Laplace equation. One is the parameter identification problems and another one is the shape reconstruction issues. In particular, I will concentrate on the problem of determining the conductivity of a medium and the shape of an inclusion from the knowledge of boundary voltage or current measurements.

Abstract: We shall present the solution by David Rees and RY Sharp of Teissier's conjectures about Hilbert-Samuel multiplicity and mixed multiplicities of ideals. We will first review preliminaries about the Northcott-Rees theory of reductions and Hilbert functions of a set of ideals. Date & Time: Tuesday 16 Jan 2018, 11:30-1pm Venue: Room 115

Abstract: Erd\H{o}s and R\’{e}nyi introduced in 1960 the study of sums of $s$-th powers by probability methods. Their model has been largely developed since then. The talk will give a survey of this probabilistic approach, up to the most recent contributions obtained jointly with Javier Cilleruelo.

Abstract: In this talk we present two new formulations for elasticity and poromechanics that include rotations and total fluid-solid pressure as additional unknowns. We address the unique solvability of each problem and construct finite-element and finite-volume-element schemes for their numerical approximation. The stability and convergence of the methods are rigorously derived, and these results are of particular interest in the incompressible limit. We finally discuss how the formulations are modified when solving an interface problem defined by the coupling of an elastic and a poroelastic medium.