2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019
Current contact: Gerardo Mendoza
The seminar takes place Mondays 2:40 - 3:30 pm in Wachman 617. Click on title for abstract.
Gerardo Mendoza, Temple University
Gerardo Mendoza, Temple University
Gerardo Mendoza, Temple University
No meeting
Sylvain Arguillère, Johns Hopkins University
Serena Federico, University of Bologna
Hussein Awala, Temple University
Marius Mitrea, University of Missouri
Yury Grabovsky, Temple University
Dorina Mitrea, University of Missouri
Peter S. Riseborough, Temple University
Cristian Gutiérrez, Temple University.
Camil Muscalu, Cornell University
The plan is to describe a new method of proving (multiple) vector valued inequalities in harmonic analysis.It is extremely robust, yet conceptually simple, and allowed us to give positive answers to a number of open questions that have been circulating for some time. Joint work with Cristina Benea.
Irina Mitrea, Temple University
In this talk I will discuss an optimal higher-order integration by parts formula with non-tangential traces in non-smooth domains and sketch its proof. This is joint work with Gustavo Hoepfner, Paulo Liboni, Dorina Mitrea, and Marius Mitrea.
Ovidiu Savin, Columbia University
I will discuss about the optimal regularity in a two-phase free boundary problem involving different elliptic operators and its connection with the Bellman equation. The proofs are based on some old ideas of Bernstein concerning elliptic equations in two dimensions. This is a joint work with L. Caffarelli and D. De Silva.
Eric Stachura
Density Functional Theory (DFT) is one of the most widely used methods for electronic structure calculations in materials science. It was realized that for N ≥ 103 electrons, it is impractical to find the N particle wave function for this system. One of the gems of DFT is the Hohenberg-Kohn Theorem, which says that the ground state electron density alone provides all properties of a given static system. When the system is allowed to evolve in time, the corresponding time dependent theory (TDDFT) was initiated by E. Runge and E. K. U Gross in the early 1980’s, and is one of the most popular theories for computing electronic excitation spectra. Runge and Gross proved a time dependent analog of the Hohenberg- Kohn Theorem, which is the starting point for our work. While attempting to develop a new proof of the Runge-Gross Theorem, there came a need to solve a Schr ̈odinger equation with time dependent Hamiltonian in R3N . By smoothing out the classical Coulomb potential, we show existence of unitary propagators for a general time dependent Schr ̈odinger equation where we allow the atomic nuclei to move along classical trajectories. By appealing to a classical 1973 result of Barry Simon, we can also understand the spectrum of the underlying time dependent Hamiltonian. This is joint work with Maxim Gilula (MSU) and is inspired by work of John Perdew (Temple). Preliminary report.
Hussein Awala, Temple University
In this talk I will discuss the boundary value problem with mixed Dirichlet and Neumann boundary conditions for the Laplacian and the Lame system in infinite sectors in two dimensions. Using a potential theory approach the problem is reduced to inverting a singular integral operator (SIO) naturally associated with the problem on appropriate function spaces. Mellin transform techniques are then employed in the study of the spectrum of the aforementioned SIO.