PDE and mathematical physics

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Referent:in

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3. Oktober 2024
16:15-18:00

Prof. Dr. Gunther Uhlmann

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Titel	Calderon's Inverse Problem
Referent:in, Affiliation	Prof. Dr. Gunther Uhlmann,
Datum, Zeit	3. Oktober 2024, 16:15-18:00
Ort	HG F 26.1
Abstract	Calderon's inverse problem asks whether one can determine the conductivity of a medium by making voltage and current measurements at the boundary. This question arises in several areas of applications including medical imaging and geophysics. I will report on some of the progress that has been made on this problem since Calderon proposed it in 1980, including recent developments on similar problems for nonlinear equations and nonlocal operators. We will also discuss several open problems.

Calderon's Inverse Problemread_more

31. Oktober 2024
16:15-18:00

Joscha Henheik
IST Austria

Details

Titel	Universalities in BCS theory
Referent:in, Affiliation	Joscha Henheik, IST Austria
Datum, Zeit	31. Oktober 2024, 16:15-18:00
Ort	HG F 26.1
Abstract	In nature one finds superconductors of varying critical temperatures and energy gaps. For weak superconductors, where the critical temperature is small, a universal phenomenon occurs: The ratio of the energy gap and critical temperature is a universal value, independent of the specific superconductor. I will present recent work on such universal phenomena in the BCS theory of superconductivity. Based on joint works with A. B. Lauritsen and B. Roos.

Universalities in BCS theoryread_more

21. November 2024
16:15-18:00

Prof. Dr. Gigliola Staffilani
Department of Mathematics, MIT

Details

Titel	The Schrödinger equation as inspiration of beautiful mathematics
Referent:in, Affiliation	Prof. Dr. Gigliola Staffilani, Department of Mathematics, MIT
Datum, Zeit	21. November 2024, 16:15-18:00
Ort	HG D 7.1
Abstract	In the last two decades great progress has been made in the study of dispersive and wave equations. Over the years the toolbox used in order to attack highly nontrivial problems related to these equations has developed to include a collection of techniques: Fourier and harmonic analysis, analytic number theory, math physics, dynamical systems, probability and symplectic geometry. In this talk I will introduce a variety of results using as model problem mainly the periodic 2D cubic nonlinear Schrödinger equation. I will start by giving a physical derivation of the equation from a quantum many-particles system, I will introduce periodic Strichartz estimates along with some remarkable connections to analytic number theory, I will move on the concept of energy transfer and its connection to dynamical systems, and I will end with some results on the derivation of wave kinetic equations.

The Schrödinger equation as inspiration of beautiful mathematicsread_more

28. November 2024
16:15-18:00

Prof. Dr. Xuwen Chen
Department of Mathematics, University of Rochester

Details

Titel	Global Derivation of the 1D Vlasov-Poisson Equation from Quantum Many-body Dynamics
Referent:in, Affiliation	Prof. Dr. Xuwen Chen, Department of Mathematics, University of Rochester
Datum, Zeit	28. November 2024, 16:15-18:00
Ort	HG F 26.1
Abstract	We study the 1D quantum many-body dynamics with a screened Coulomb potential in the mean-field setting. Combining the quantum mean-field, semiclassical, and Debye length limits, we prove the global derivation of the 1D Vlasov-Poisson equation. We tackle the difficulties brought by the pure state data, whose Wigner transforms converge to Wigner measures. We find new weighted uniform estimates around which we build the proof. As a result, we obtain, globally, stronger limits, and hence the global existence of solutions to the 1D Vlasov-Poisson equation subject to such Wigner measure data, which satisfy conservation laws of mass, momentum, and energy, despite being measure solutions. This happens to solve, even with general data, the 1D measure solution case of an open problem regarding the conservation law of the Vlasov-Poisson equation raised by Diperna and Lions.

Global Derivation of the 1D Vlasov-Poisson Equation from Quantum Many-body Dynamicsread_more

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