Ari Laptev's 70th birthday conference

Virtual conference on the occasion of the 70th birthday of Ari Laptev - August 12 - 13, 2020

Registration:
A registration is required here. There is no registration fee.

Speakers:

R. Benguria (Santiago)
M. Esteban (Paris)
R. Frank (Caltech & LMU Munich)
E.H. Lieb (Princeton)
B. Simon (Caltech)
S. Smirnov (Geneva)
S.T. Yau (Harvard)

Date: August 12 - 13, 2020
The conference is transmitted via Zoom.

Zoom host of the conference:
NTNU Norwegian University of Science and Technology,
Trondheim, Norway

Pavel Exner (Czech Academy of Sciences, Czech Technical University, Prague)
Rupert Frank (Caltech, Pasadena, LMU, Munich)
Fritz Gesztesy (Baylor University, Waco)
Helge Holden (NTNU, Trondheim)
Timo Weidl (University of Stuttgart, Stuttgart)

Time Speaker and Title
9 a.m. ET
(3 p.m. CEST)
Opening, P. Exner (Prague)
9:10 a.m. ET
(3:10 p.m. CEST)
S.T. Yau (Harvard)
Stability and Partial Differential Equations in Mirror Symmetry
10 a.m. ET
(4 p.m. CEST)
L. Carleson (Stockholm)
10:10 a.m. ET
(4:10 p.m. CEST)
R. Benguria (Santiago)
A variational formulation for Dirac Operators in bounded domains and applications to spectral geometric inequalities
11:00 - 11:10 a.m. ET
(5:00 - 5:10p.m. CEST)
Break
11:10 a.m. ET
(5:10 p.m. CEST)
S. Smirnov (Geneva)
12 noon ET
(6 p.m. CEST)
T. Ekholm (Mittag-Leffler)
12:10 p.m. ET
(6:10 p.m. CEST)
R. Frank (Caltech/LMU Munich)
Time Speaker and Title
9 a.m. ET
(3 p.m. CEST):
G. Hansson (Stockholm)
9:10 a.m. ET
(3:10 p.m. CEST):
E.H. Lieb (Princeton)
Sharpened $L^p$ Triangle Inequalities 
10a.m. ET
(4 p.m. CEST):
A. Lindquist (Stockholm, Shanghai)
10:10 a.m. ET
(4:10 p.m. CEST)
M. Esteban (Paris)
Magnetic Interpolation Inequalities in Dimensions 2 and 3
11:00 - 11:10 a.m. ET
(5:00 - 5:10 p.m. CEST)
Break
11:10  a.m. ET
(5:10 p.m. CEST)
V. Mehrmann (Berlin)
11:20 a.m. ET
(5:20 p.m. CEST)
B. Simon (Caltech)
The Tale of a Wrong Conjecture: Borg’s Theorem for Periodic Jacobi Matrices on Trees
12:10 p.m. ET
(6:10 p.m. CEST
Closing (P. Exner, R. Frank, F. Gesztesy, H. Holden, T. Weidl)
M. Esteban (Paris)
Magnetic Interpolation Inequalities in Dimensions 2 and 3.

Abstract: In this talk I will present various results concerning interpolation inequalities, best constants and information about the extremal functions involving Schrödinger magnetic operators in dimensions 2 and 3. The particular, and physical interesting, cases of constant and of Aharonov-Bohm magnetic fields will be discussed in detail.

These works have been made in collaboration with D. Bonheure, J. Dolbeault, A. Laptev, and M. Loss.
R. Benguria (Santiago)
A variational formulation for Dirac Operators in bounded domains and applications to spectral geometric inequalities

Abstract: In this talk I will present spectral features of the Dirac operator with infi nite mass boundary conditions in a smooth bounded domain of $\mathbb{R}^2$. A non-linear variational formulation to characterize its principal eigenvalue will be presented. This characterization allows for a simple proof of a Szeg \H{o} type inequality as well as a new formulation of a Faber-Krahn type inequality for this operator.
Moreover, strong numerical evidence supporting the existence of a Faber-Krahn type inequality, will be given.

This talk is based on joint work with Pedro Antunes, Vladimir Lotoreichik, and Thomas Ourmières-Bonafos.
E.H. Lieb (Princeton)
Sharpened $L^p$ Triangle Inequalities 

Abstract: Consider the Lp  triangle inequality for the norms of two functions, |f+g| \leq |f|+|g|, which is saturated when f=g, but which is poor when f and g have disjoint support.  In 2009 Carbery proposed a slightly more complicated inequality for p\geq 2 to take into account the possible orthogonality, or lack of it, of f and g. With Eric Carlen, Rupert Frank and Paata Ivanisvili it has now been proved. In fact, a much stronger version has been proved -- and, moreover, for all -\infty < p < \infty.

In a recent, subsequent paper with Carlen and Frank an extension to more than two functions was given. 
B. Simon (Caltech)
The Tale of a Wrong Conjecture: Borg’s Theorem for Periodic Jacobi Matrices on Trees

Abstract: I will begin by reviewing work on removal of eigenvalue degeneracy and its relevance to gap splitting. I’ll next discuss Borg’s theorem. I’ll then describe a framework for discussing periodic Jacobi matrices on trees and possible versions of Borg’s theorem and a recent note that there are counterexamples. Finally, I’ll discuss possible modified conjectures. This includes joint work with Nir Avni and Jonathan Breuer.
S.T. Yau (Harvard)
Stability and Partial Differential Equations in Mirror Symmetry

Abstract: This is joint work with Tristan Collins where we studied the concept of Deformed Hermitian Yang Mills equations. It also contains some work that we did with Jacob Adams. The equations arise in the study of mirror symmetry through the SYZ program. The solutions of such equations lead to the concept of stability in algebraic geometry, which seems to be very much related to the concept of Bridgeland stability and the Chern number inequality.

Contact:

 

Mail-Adress of the conference

Timo Weidl
Prof. TeknD

Timo Weidl

Professor - Chair for Analysis and Mathematical Physics

[Photo: Robin Lang, 2018]

Elke Peter
 

Elke Peter

Administration Office - Chair for Analysis and Mathematical Physics

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