Where: MATH 2300

Speaker: Paolo Piccione (Sao Paolo) -

Abstract: The classical Allen-Cahn equation gives a bridge between the

theory of phase transition and the theory of minimal surfaces. In this talk

I will discuss the existence of multiple solutions for a suitable variant

of this equation, satisfying a volume constraint. This aims naturally at an

existence theory for constant mean curvature hypersurfaces. Joint work

with Vieri Benci (Pisa) and Stefano Nardulli (UFABC).

Where: Kirwan Hall 3206

Speaker: Norman Levenberg (Indiana University) -

Abstract: Given a convex body P one can associate a natural class of plurisubharmonic functions: those that grow like the logarithmic indicator function. These generalizations of Lelong classes in standard pluripotential theory arise in the theory of random sparse polynomials and in problems involving polynomial approximation. We give some examples of extremal plurisubharmonic functions in this setting and discuss other results in the general theory as well as connections with complex geometry.

Where: Math 2300

Speaker: Kuang-Ru Wu (Purdue) -

Abstract: Let Omega be a compact Riemann surface with boundary, and V a Hilbert space. We prove the existence of flat hermitian metrics on Omega x V with given boundary values. The result generalizes Lempert's theorem that had Omega be the unit disc. It also generalizes results of Donaldson and Coifman-Semmes to the case of infinite rank bundles but only on Riemann surfaces.

Where: Math 2300

Speaker: Mirna Pinsky (UMD) -

Where: MATH 2300

Speaker: Julius Ross (UIC (Chicago)) -

Abstract: I will describe a surprising duality between a case of the Dirichlet problem for the Complex Homogeneous Monge-Ampere Equation and a planar flow coming from fluid mechanics called the Hele-Shaw flow. Using this we are able to prove new things about both this PDE and renowned flow. I will present this in a way that suggests that it is a special case of something much more general, and end with a discussion as to what this may be. All of this is work with David Witt-Nystrom.

Where: Math 2300

Speaker: Mirna Pinsky (UMD) -

Where: 1308.0

Speaker: Homare Tadano (Tokyo University of Science) -

Where: Kirwan Hall 3206

Speaker: Tristan Collins (MIT) -

Abstract: A longstanding problem in mirror symmetry has been to understand the relationship between the existence of solutions to certain geometric nonlinear PDES (the special Lagrangian equation, and the deformed Hermitian-Yang-Mills equation) and algebraic notions of stability, mainly in the sense of Bridgeland. I will discuss progress in this direction through ideas originating in infinite dimensional GIT. This is joint work with S.-T. Yau.

Where: Math 2300

Speaker: Yanir Rubinstein (UMD) -

Abstract: In 1988 Richard Hamilton studied the Ricci flow on the 2-sphere and discovered the non-compact cigar soliton that Pereleman has called "an important example" in his celebrated work. In that same paper Hamilton also discovered compact singular solitons called teardrop solitons and these have been inspirational in their own right in the literature of conical Riemann surfaces. Together with K. Zhang we show that rather surprisingly the two constructions are related: the former is the blow-up limit of the latter in a sense.