# Analysis Seminar

Current contact: Gerardo Mendoza

The seminar takes place Mondays 2:40 - 3:30 pm in Wachman 617. Click on title for abstract.

• Monday April 16, 2018 at 14:40, Wachman 617
TBA

Nestor Guillen, University of Massachusetts at Amherst

TBA

• Monday March 26, 2018 at 14:40, Wachman 617
TBA

Terrence Napier, Lehigh University

TBA

• Monday March 19, 2018 at 14:40, Wachman 617

Andy Raich, University of Arkansas

The main goal of this talk is to show that geometric information captured by certain invariant CR tensors provides sufficient information to establish the closed range property for $\bar\partial$ on a domain in $\mathbb{C}^n$. A secondary goal of the talk is to provide a general construction method for establishing when a domain (or its boundary) satisfies weak $Z(q)$.

• Monday March 12, 2018 at 14:40, Wachman 617

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 $p$-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.

• Monday March 5, 2018 at 14:30, Wachman 617
No meeting

• Wednesday February 28, 2018 at 17:00, Wachman 617

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.

• Monday February 19, 2018 at 14:40, Wachman 617

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.

• Monday February 12, 2018 at 14:40, Wachman 617

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.

• Monday February 5, 2018 at 14:40, Wachman 617

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.

• Monday January 29, 2018 at 14:40, Wachman 617

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.

• Monday January 22, 2018 at 14:40, Wachman 617

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.