Here is the program for the research talks by the remaining shortlisted candidates for the positions in pure mathematics. All of the talks will be held in the Faculty of Science Seminar Room (Room 535a/b, opposite Nalini’s office). The unusual time for the third talk is to give us time to move to Carslaw LT 375 for a teaching seminar by Shusen Yan starting at 2.30. Titles and abstracts are below Wedesday, March 12: 11.00-12.00: Florica Cirstea 12.00- 1.00: Adam Sikora 1.20- 2.20: James Parkinson Thursday, March 13: 12.00-1.00: Shusen Yan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Florica Cirstea: Title: Singularities in nonlinear partial differential equations Abstract: Nonlinear elliptic equations with singularities arise in several areas of mathematics including geometry, mathematical physics, biology and applied probability. During the last decade an active investigation of singularities for semilinear elliptic equations has led to new and exciting discoveries by both analysts and probabilists. In this talk we discuss some recent progress concerning the study of singularities and the precise description of blow-up problems in nonlinear elliptic equations. ...................... Adam Sikora: Title: Boundary conditions for Degenerate elliptic operators" Abstract: Let S_t be a submarkovian semigroup on L^2(R^n) generated by a divergence form second order differential operator. We assume that the coefficients matrix C is positive almost everywhere but allow for the possibility that C is singular. Next, let \Omega be an open subset of R^n. We discuss when S leaves L^2(\Omega) invariant and the Dirichlet and Neumann boundary conditions for \Omega in this situation. The presentation is based on joint projects with Derek Robinson, Andrew Hassell, Thierry Coulhon, Tom ter Elst, and Yueping Zhu. ...................... James Parkinson: Title: Alcove walks in Lie theory Abstract: The combinatorial language of alcove walks is a common thread which ties together parts of building theory, symmetric function theory, geometry, and representation theory. We illustrate this point by writing down a combinatorial statement, along with theorems from each of these subjects that is equivalent to it. We then outline a simple proof of the combinatorial statement. ...................... Shusen Yan: Elliptic Problems of Ambrosetti-Prodi Type Abstract. In this talk, I will present some results on a conjecture raised by Lazer and McKenna in the early 1980s on the multiplicity of solutions for elliptic equations of Ambrosetti-Prodi type.