11:30 a.m.
Dr. John Treuer
Title: Compactness of the dbar-Neumann operator and Property (P)
Abstract: We give a brief introduction to an important problem in several complex variables, the dbar-Neumann problem, and state current problems about compactness of the dbar-Neumann operator via Property (P).
12:05 p.m.
Dr. Youngho Yoo
Title: Combinatorial optimization and graph theory
Abstract: Many combinatorial optimization problems can be formulated as an integer linear program. While linear programs (optimizing linear functions over polyhedra) enjoy a strong duality and are efficiently solvable, integrality constraints are more difficult to enforce and studying the gap between fractional and integral solutions can lead to interesting combinatorial structure. In this talk I will discuss some examples of such problems related to structural graph theory.
12:25 p.m.
Dr. Yuliia Yershova
Title: Zero-range models with internal structure in the analysis of strongly inhomogeneous media
Abstract: In this talk, I will consider a prototype large-coupling transmission problem, posed on a bounded domain, containing a low-index inclusion located at a positive distance to the boundary. Mathematically, this is modelled by a weighted Laplacian, where the weight on the containing domain is 1 and the weight on the inclusion is assumed to be large (high contrast). This is supplemented by the Neumann boundary condition on the outer boundary and natural continuity conditions on the interface (i.e., the inclusion boundary). A formal asymptotic argument suggests that eigenvalues of this operator should converge to those of the so-called electrostatic problem (although the existing results do not quite yield spectral convergence). Our operator-theoretic approach based on the analysis of critical-contrast periodic composites, allows one to improve these results in two respects: (a) our estimates are of the operator-norm resolvent type, implying, in particular, the uniform convergence of the associated spectra in any compact set; (b) our estimates are uniform with respect to the contrast parameter and are order-sharp, i.e. the rate of convergence in terms of the contrast cannot be improved further. Based on joint work with Cherednichenko, Kiselev and Silva.
12:45 p.m. Dr. Bo Zhu Title: Geometry of positive scalar curvature on complete manifolds Abstract: In this talk, we will introduce the Gromov's conjecture on the volume growth of geodesic ball on complete manifold. In particular, we will talk about its relation with the related topics in geometric analysis.