Information about the Øresund Seminar in Lund 16/9, 2022
After a break during covid, the Øresund Seminar will start again in the autumn of 2022. It will take place in Lund, at the Centre for Mathematical Sciences. The lectures will be in the lecture room Hörmander, just to your right when you enter the mathematics department. You can follow this link to find your way to the mathematics department, the entrance is on the east side towards sjön Sjön.
Below is a schedule for the day. After the talks, we go for dinner at Grand Hotel.
We needed to know before 2/9 if you want to join for dinner. Please contact Magnus Goffeng if you want to join last minute.
13.15-14.00: Pengfei Guan (McGill University)
Title: Gauss curvature type flow and associated entropies
Abstract:
Gauss curvature flow was introduced by Firey to model the evolving shape of tumbling stone in 1970s. It is a parabolic type Monge-Ampére type equation. Of interest is the fate of "worn stone": the convergence of the normalized flow. In this respect, the entropy functional is crucial. In the talk, we discuss recent developments on non-homogeneous Gauss curvature type flows and the Gauss curvature flow in space forms. The entropy argument is re-tooled to obtain non-callapsing estimates and convergence for new these flows. The key is the almost monotonicity of the entropy along the flows. We will also discuss some related open problems.
14.15-15.00: Ayman Kachmar (Lebanese University, KAW-professor at Lund University)
Title: Quantum tunneling in deep potential wells and strong magnetic field revisited
Abstract:
This talk is on a joint work with B. Helffer. Inspired by a recent paper* by C. Fefferman, J. Shapiro and M. Weinstein, we investigate quantum tunneling for a Hamiltonian with a symmetric double well and a uniform magnetic field. In the simultaneous limit of strong magnetic field and deep potential wells with disjoint supports, tunneling occurs and we derive accurate estimates of its magnitude.
*) Lower bound on quantum tunneling for strong magnetic fields. SIAM J. Math. Anal. 54(1), 1105-1130 (2022).
15.00-15.30 Coffee break
15.30-16.15: Mads Kyed (Hochschule Flensburg)
Title: On Lp estimates for time-periodic solutions to parabolic boundary value problems of Agmon-Douglis-Nirenberg type
Abstract:
A celebrated result of Agmon, Douglis and Nirenberg states that if an elliptic operator A satisfies the so-called complementing condition with respect to a number of boundary operators, then a solution to the corresponding boundary value problem satisfies an a priori Lp estimate. A similar result holds for the initial-value problem associated to the parabolic operator $\partial_t-A$. In my talk, I will consider the time-periodic boundary value problem related to the operator $\partial_t-A$ and show a time-periodic version of the Agmon-Douglis-Nirenberg Theorem. I will utilize an idea of Arkeryd and present a simple proof based on Fourier multipliers and a Paley-Wiener theorem. The original elliptic case version of the theorem will follow as a special case. Moreover, I will show that the estimate for the parabolic initial-value problem follows from the time-periodic version of the theorem, and thus argue that there is simple a one-fits-all approach to all three cases. Finally I will demonstrate the new technique on a time-periodic Navier-Stokes problem.
16.30-17.15: Benjamin Eichinger (TU Wien, Austria)
Title: An approach to universality using Weyl m-functions
Abstract:
We describe an approach to universality limits for orthogonal polynomials on the real line which is completely local and uses only the boundary behavior of the Weyl m-function at the point. We show that bulk universality of the Christoffel-Darboux kernel holds for any point where the imaginary part of the m-function has a positive finite nontangential limit. This approach is based on studying this problem in the setting of canonical systems and the realization that bulk universality for an associated matrix reproducing kernel at a point is equivalent to the fact that the corresponding m-function has normal limits at the same point.
Our approach automatically applies to other self-adjoint systems with 2×2 transfer matrices such as continuum Schrödinger and Dirac operators. We also obtain analogous results for orthogonal polynomials on the unit circle.
The talk is based on a joint work with Milivoje Lukic and Brian Simanek.