Current contact: Gerardo Mendoza
The seminar takes place Mondays 2:40 - 3:30 pm in Wachman 617. Click on title for abstract.
Nestor Guillen, University of Massachusetts at Amherst
Andy Raich, University of Arkansas
José González Llorente, Universidad Autónoma de Barcelona
The Mean Value Property for harmonic functions is at the crossroad of Potential Theory, Geometric Function Theory and Probability. In the last years substantial efforts have been made to build up stochastic models for certain nonlinear PDE's like the $p$-laplacian or the infinity-laplacian and the key is to figure out which are the corresponding (nonlinear) mean value properties. After introducing a "natural" nonlinear mean value property related to the $p4-laplacian we will focus on functions satisfying the so called one-radius mean value property. We will review some classical results in the linear case ($p=2$) and then recent nonlinear versions in the more general context of metric measure spaces.
Nordine Mir, Texas A&M-Qatar (note special day and time)
I will discuss recent joint results with B. Lamel regarding the convergence and divergence of formal holomorphic maps between real-analytic CR submanifolds in complex spaces of possibly different dimension. Our results resolve in particular a long standing open question in the subject and recover all known previous existing ones. We will also discuss the new approach developed in order to understand the convergence/divergence properties of such maps.
Luis Ragognette, Federal University of São Carlos, Brazil
The theory of hyperfunctions deals with generalized functions that are even more general than distributions. Our goal in this talk is to discuss techniques that allowed us to study microlocal regularity of a hyperfunction with respect to different subspaces of the space of hyperfunctions. In other to do that we used a subclass of the FBI transforms introduced by S. Berhanu and J. Hounie. This is a joint work with Gustavo Hoepfner.
Gerardo Mendoza, Temple University
Fuchs-type operators and certain generalizations arise on manifolds with conical or more general stratifications. While the elliptic theory of such operators is by now fairly well understood, important aspects of the corresponding theory for complexes are still being developed. In this talk I will describe recent progress (joint work with T. Krainer) in the case of conical singularities on the elucidation of the boundary conditions that can be specified in order to obtain a complex in the Hilbert space category.
Renan Medrado, Universidade Federal do Ceará, Brazil
The aim of this talk is to present a characterization of Denjoy-Carleman (local and micro-local) regularity using a general class of FBI transform introduced by S.~Berhanu and J.~Hounie in 2012. As an application we exhibit a microlocal Denjoy-Carleman propagation of regularity theorem, that do not seem possible to prove using the classical FBI transform. This is a joint work with Gustavo Hoepfner.
Ryan Hynd, University of Pennsylvania
We will consider the dynamics of a finite number of particles that interact pairwise and undergo perfectly inelastic collisions. Such physical systems conserve mass and momentum and satisfy the Euler-Poisson equations. In one spatial dimension, we will show how to derive an extra entropy estimate which allows us to characterize the limit as the number of particles tends to infinity.
Irina Mitrea, Temple University
One of the classical methods for solving elliptic boundary value problems in a domain $\Omega$ is the method of layer potentials, whose essence resides in reducing the entire problem to solving an integral equation on $\partial\Omega$. In this talk I will discuss spectral properties of the intervening singular integral operators and show how the two-dimensional setting plays a special role in this analysis.