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Autumn Semester 2022

Date / Time Speaker Title Location
20 October 2022
16:00-18:00 		Dr. Christiane Klein
Universität Leipzig
Event Details

PDE and Mathematical Physics

Title Construction of the Unruh state on Kerr-de Sitter
Speaker, Affiliation Dr. Christiane Klein, Universität Leipzig
Date, Time 20 October 2022, 16:00-18:00
Location KOL G209
Abstract In order to study physical effects of quantum fields on curved spacetimes, one needs appropriate Hadamard states to describe the fields. In this talk, we present a rigorous construction, including the proof of the Hadamard property, of the Unruh state for the free scalar field on slowly rotating Kerr-de Sitter spacetimes.
Construction of the Unruh state on Kerr-de Sitterread_more
KOL G209
27 October 2022
16:00-18:00 		Dr. Megan Griffin-Pickering
Durham University
Event Details

PDE and Mathematical Physics

Title Recent results on the quasi-neutral limit for the ionic Vlasov-Poisson system
Speaker, Affiliation Dr. Megan Griffin-Pickering, Durham University
Date, Time 27 October 2022, 16:00-18:00
Location KOL G209
Abstract Vlasov-Poisson type systems are well known as kinetic models for plasma. The precise structure of the model differs according to which species of particle it describes, with the `classical' version of the system describing the electrons in a plasma. The model for ions, however, includes an additional exponential nonlinearity in the equation for the electrostatic potential, which creates several mathematical difficulties. For this reason, the theory of the ionic system has so far not been as fully explored as the theory for the electron equation. A plasma has a characteristic scale, the Debye length, which describes the scale of electrostatic interaction within the plasma. In real plasmas this length is typically very small, and in physics applications frequently assumed to be very close to zero. This motivates the study of the limiting behaviour of Vlasov-Poisson type systems as the Debye length tends to zero relative to the observation scale--known as the 'quasi-neutral' limit. In the case of the ionic model, the formal limit is the kinetic isothermal Euler system; however, this limit is highly non-trivial to justify rigorously and known to be false in general without very strong regularity conditions and/or structural conditions. I will present a recent work, carried out in collaboration with Mikaela Iacobelli, in which we prove the quasi-neutral limit for the ionic Vlasov-Poisson system for a class of rough (L^\infty) data: that is, data that may be expressed as perturbations of an analytic function, small in the sense of Monge-Kantorovich distances. The smallness of the perturbation that we require is much less restrictive than in the previously known results.
Recent results on the quasi-neutral limit for the ionic Vlasov-Poisson systemread_more
KOL G209
27 October 2022
16:00-18:00 		Prof. Dr. Gabriel Paternain
University of Cambridge
Event Details

PDE and Mathematical Physics

Title Resonant forms at zero for dissipative Anosov flow
Speaker, Affiliation Prof. Dr. Gabriel Paternain, University of Cambridge
Date, Time 27 October 2022, 16:00-18:00
Location KOL G209
Abstract The Ruelle zeta function is a natural function associated with the periods of closed orbits of an Anosov flow, and it is known to have a meromorphic extension to the whole complex plane. The order of vanishing of the Ruelle zeta function at zero is expected to carry interesting topological and dynamical information and can be computed in terms of certain resonant spaces of differential forms for the action of the Lie derivative on suitable spaces with anisotropic regularity. In this talk I will explain how to compute these resonant spaces for any transitive Anosov flow in 3D, with particular emphasis in the dissipative case, that is, when the flow does not preserve any absolutely continuous measure. A prototype example is given by the geodesic flow of an affine connection with torsion and we shall see that for such a flow the order of vanishing drops by 1 in relation to the usual geodesic flow due to the Sinai-Ruelle-Bowen measure having non-zero winding cycle. This is joint work with Mihajlo Cekic.
Resonant forms at zero for dissipative Anosov flowread_more
KOL G209
3 November 2022
16:00-18:00 		Dr. Léo Bigorgne
Université de Rennes 1
Event Details

PDE and Mathematical Physics

Title Modified scattering for small data solutions to the Vlasov-Maxwell system
Speaker, Affiliation Dr. Léo Bigorgne, Université de Rennes 1
Date, Time 3 November 2022, 16:00-18:00
Location KOL G209
Abstract Abstract: We will capture the asymptotic behavior of the solutions to the Vlasov-Maxwell system arising from sufficiently small and regular data. Our analysis is based on vector fields methods, allowing us to exploit the null structure of the equations, and the Glassey-Strauss decomposition of the electromagnetic field. In particular, we will see that the electromagnetic field approaches, for large time, a solution to the vacuum Maxwell equations. Due to the long-range effects of the Lorentz force, the Vlasov field converges along logarithmic corrections of the linear characteristics.
Modified scattering for small data solutions to the Vlasov-Maxwell systemread_more
KOL G209
17 November 2022
16:15-17:00 		Dr. Morris Brooks
Universität Zürich
Event Details

PDE and Mathematical Physics

Title The Fröhlich Polaron at strong coupling
Speaker, Affiliation Dr. Morris Brooks, Universität Zürich
Date, Time 17 November 2022, 16:15-17:00
Location KOL G209
Abstract In this talk we will discuss recent results of Robert Seiringer and myself, concerning the ground state energy and the energy-momentum relation of the Fröhlich polaron, which is a model describing the interactions between a charged particle and a polarized medium. We especially verify a conjecture by Landau and Pekar from 1948, claiming that the energy-momentum relation asymptotically coincides with the one of a free particle having an increased mass M=alpha^4 m, where m is an explicit constant, in the regime of large couplings alpha between the particle and the medium, and suitably small momenta.
The Fröhlich Polaron at strong couplingread_more
KOL G209
17 November 2022
17:15-18:00 		Izak Oltman
UC Berkeley
Event Details

PDE and Mathematical Physics

Title A probabilistic Weyl-law for randomly perturbed Berezin-Toeplitz operators
Speaker, Affiliation Izak Oltman, UC Berkeley
Date, Time 17 November 2022, 17:15-18:00
Location KOL G209
Abstract I will discuss a recent result about describing the spectrum of randomly perturbed Berezin-Toeplitz operators, which generalizes a result of Martin Vogel from 2020 about quantizations of the torus. I will briefly discuss similar spectral results regarding randomly perturbed non-self-adjoint operators. Then I will explain how to construct Berezin-Toeplitz operators (which are quantizations of smooth functions on compact Kähler manifolds). Finally, I will discuss the main idea of proving a Weyl-law, which requires constructing an exotic calculus of Berezin-Toeplitz operators.
A probabilistic Weyl-law for randomly perturbed Berezin-Toeplitz operatorsread_more
KOL G209
1 December 2022
16:00-18:00 		Prof. Dr. Bruno Nachtergaele
UC Davis
Event Details

PDE and Mathematical Physics

Title Spectral gaps and spectral gap stability for quantum lattice systems
Speaker, Affiliation Prof. Dr. Bruno Nachtergaele, UC Davis
Date, Time 1 December 2022, 16:00-18:00
Location KOL G209
Abstract A salient feature of topological insulators and symmetry protected topological phases of quantum lattice systems is the spectral gap above the ground state. I will review recent results of two types. The first are proofs of lower bounds for the spectral gap for a variety of specific models. The second type of results is concerned with the stability of the spectral gap and other fundamental characteristics of the system under uniformly small perturbations of the interactions in the model Hamiltonian. I will discuss the basic strategies used to approach both types of problems.
Spectral gaps and spectral gap stability for quantum lattice systemsread_more
KOL G209
8 December 2022
16:00-18:00 		Ryan Unger
Event Details

PDE and Mathematical Physics

Title Retiring the third law of black hole thermodynamics
Speaker, Affiliation Ryan Unger,
Date, Time 8 December 2022, 16:00-18:00
Location KOL G209
Abstract In this talk I will present a rigorous construction of examples of black hole formation which are exactly isometric to extremal Reissner--Nordström after finite time. In particular, our result can be viewed as a definitive disproof of the ``third law of black hole thermodynamics.''
Retiring the third law of black hole thermodynamicsread_more
KOL G209
15 December 2022
13:30-14:30 		Dr. Alessandro Pizzo
Universita' Roma 2
Event Details

PDE and Mathematical Physics

Title Stability of gapped quantum systems under small perturbations
Speaker, Affiliation Dr. Alessandro Pizzo, Universita' Roma 2
Date, Time 15 December 2022, 13:30-14:30
Location Y13 K 05
Abstract I will consider families of quantum lattice systems that have attracted much interest amongst people studying topological phases of matter. Their Hamiltonians are perturbations, by interactions of short range, of a Hamiltonian consisting of strictly local terms and with a (strictly positive) energy gap above its ground-state energy. I will review the main ideas of a novel method based on local Lie-Schwinger conjugations of the Hamiltonians associated with connected subsets of the lattice. By this method fermions and bosons are treated on the same footing, and our technique does not face a large field problem, even though bosons are involved.
Stability of gapped quantum systems under small perturbationsread_more
Y13 K 05

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