Workshop for young researchers in analysis and mathematical physics

9 oct. 2023, 09:00 → 11 oct. 2023, 15:30 Europe/Paris

B101 (LMU Munich)

Charlotte Dietze (LMU Munich), Florent Noisette (IMB), Jonas Peteranderl (LMU)

The goal of this workshop is to allow PhD and post-doctoral students from the Institut Mathematique de Bordeaux (IMB) and Ludwig-Maximilians-Universität (LMU) to present their work at an international conference, learn about the work of others and build a network of young researchers.

The workshop will take place in room B101, Theresienstr. 39.

List of speakers:

• Lea Boßmann
• Florian Haberberger
• Vincent Laheurte
• Phan Thành Nam
• Larry Read 
• Marwa Shahine
• Adrien Tendani-Soler
• Leonard Wetzel
• Mahdi Zreik

 

List of speakers for the discussion session:

• Max Duell
• Emanuela Giacomelli

 

List of speakers for the poster session:

• Janik Kruse
• Sascha Lill
• Davide Lonigro
• Umberto Morellini
• Siegfried Spruck

 

Scientific committee:
• Sylvain Ervedoza
• Christèle Etchegaray
• Prof. Dr. Simone Rademacher
• Prof. Dr. Arnaud Triay

Organizing committee:
• Charlotte Dietze, LMU Munich, dietze@math.lmu.de
• Florent Noisette, IMB, florent.noisette@math.u-bordeaux.fr
• Jonas Peteranderl, LMU Munich, peterand@math.lmu.de

 

Please register until September 7 if you would like to attend.

 

 

 

lundi 9 octobre

09:00 → 09:15 Registration

09:15 → 09:30 Registration: Welcome

09:30 → 10:30 Isoperimetric inequalities and the critical mass in nuclear fission

I will discuss the connection from the classical isoperimetric inequality to the critical mass in nuclear fission reactions predicted by the liquid drop model. In particular, I will address several open questions and some recent results on the existence and nonexistence of minimizers. The talk is based on joint work with Rupert Frank.

Orateur: Prof. Phan Thanh Nam (LMU)

10:30 → 11:00 Coffee Break

11:00 → 12:00 Fredholm Property of the Linearized Boltzmann Operator for a Mixture of Polyatomic Gases

In this talk, we consider the Boltzmann equation that models a mixture of polyatomic
gases assuming the internal energy to be continuous. Under some convenient assumptions on
the collision cross-section, we prove that the linearized Boltzmann operator L is a Fredholm
operator. For this, we write L as a perturbation of the collision frequency multiplication
operator. We prove that the collision frequency is coercive and that the perturbation operator
is Hilbert-Schmidt integral operator.

Orateur: Dr Marwa Shahine (IMB)

12:00 → 13:45 Lunch

13:45 → 14:45 Sub-Riemannian fluids

In this presentation, I will introduce the Euler and Navier-Stokes systems with anisotropic velocity fields, where this anisotropy is defined by a geometric structure. Additionally, I will discuss the issues of well-posedness and regularity for the subRiemannian Navier-Stokes system. The analysis is based on the propagation of carefully selected families of vector fields through the energy and relies on hypoellipticity, geometry and analysis on stratified Lie groups.

Orateur: Adrien Tendani Soler (Université de Bordeaux)

14:45 → 15:15 Coffee Break

15:15 → 16:30 Discussions: Poster Session

16:30 → 17:30 Welcome drinks

mardi 10 octobre

09:00 → 10:00 Effective descriptions of interacting Bose gases

Since the first realization of a Bose-Einstein condensate in a laboratory in 1995, low-temperature Bose gases have been studied from many different perspectives. In this talk, I will give a basic introduction into the mathematical description of an interacting Bose gas and explain the concept of effective evolution equations.

Orateur: Lea Boßmann (LMU Munich)

10:00 → 10:30 Coffee Break

10:30 → 11:30 Bose Gases — Results and Methods

I will begin by discussing the significant results concerning Bose Gases, tracing their origins back to Albert Einstein's groundbreaking work on ideal gases in 1924. Our exploration will also emphasize the theoretical underpinnings and methodologies involved, such as the introduction of the one-particle density matrix by Roger Penrose and Lars Onsager in 1956, along with the utilization of the Fock space formalism. Finally, I will provide an overview of ongoing research and the unresolved questions in this field.

Orateur: Florian Haberberger (LMU)

11:30 → 13:15 Lunch

13:15 → 14:15 High frequency controllability cost of linear hyperbolic systems, with a long gaze at localized data.

We revisit the classical issue of the controllability/observability cost of linear first order evolution systems, starting with ODEs, before turning to some linear first order evolution PDEs in several space dimensions, including hyperbolic systems and pseudo-differential systems obtained by linearization in fluid mechanics. In particular we investigate the cost of localized initial data, and in the dispersive case, of initial data which are semi-classically microlocalized.

Orateur: Vincent Laheurte (Institut de Mathématiques de Bordeaux)

14:15 → 14:45 Coffee Break

14:45 → 15:45 A Poincaré-Steklov map for the MIT bag model

In this talk, I will present some study of the Poincaré-Steklov (PS) operator associated with the MIT bag operator on a smooth domain $\Omega\subset \mathbb{R}^{3}$ with a compact boundary $\Sigma:=\partial\Omega$.
This operator can be seen as the analogue of the Dirichlet-to-Neumann mapping, where the free Dirac operator $D_m := -i\alpha\cdot\nabla +m\beta$ plays the role of the Laplace operator, and the Dirichlet and the Neumann traces are replaced by orthogonal projections of the Dirichlet traces along the boundary $\Sigma.$
More precisely, this operator is associated with the following boundary value problem
\begin{equation}
(D_m-z)v =0, \quad \text{ in } \Omega, \qquad
P_{\pm}t_{\Sigma}v = g\in H^{1/2}(\Sigma)^{4},
\end{equation}
where $P_{\pm}$ are the orthogonal projections along the boundary $\Sigma$ and $t_{\Sigma}$ is the classical trace operator.

In the first part of this talk, I will explain how the PS operator fits well into the framework of classical pseudodifferential operators and determine its principal symbol. In the second part, I will discuss the properties of the PS operator when the mass $m$ becomes large enough. Namely, I will show that it is a $1/m$-pseudodifferential operator and I will give its main properties, in particular its semiclassical principal symbol. Then, we apply these results to establish a Krein-type resolvent formula for the Dirac operator $D_M= D_m +M\beta 1_{\mathbb{R}^{3}\setminus\overline{\Omega}}$ in terms of the resolvent of the MIT bag operator when $M > 0$ is large enough. Finally, we show that the operator $D_M$ in the limit of the large coupling ($M\longrightarrow \infty$) converges to the MIT bag operator in terms of the norm-resolvent with a convergence rate of $\mathcal{O}(M^{-1}).$

Orateur: Mahdi Zreik

15:45 → 17:15 Discussions: Discussion session

Présidents de session: Emanuela Giacomelli (LMU Munich), Maximilian Duell (LMU)

18:30 → 20:00 Conference dinner

Standort: Hans im Glück am Königsplatz

https://www.google.com/maps/place/HANS+IM+GL%C3%9CCK+-+M%C3%9CNCHEN+K%C3%B6nigsplatz/@48.143869,11.5602831,17z/data=!3m1!4b1!4m6!3m5!1s0x47bf250a16f2e885:0x5748c7a526a38bc7!8m2!3d48.143869!4d11.562858!16s%2Fg%2F1q64hqs89?entry=ttu

Website: https://hansimglueck-burgergrill.ch/burger-restaurant/muenchen-koenigsplatz/

mercredi 11 octobre

09:00 → 10:00 Negative spectrum of Schrödinger operators with oscillating potentials

For a Schrödinger operator $-\Delta-\alpha V$, the decay of the potential $V$ towards infinity determines the finiteness of its negative spectrum. In the particular case where $V$ is asymptotically homogeneous of degree -2, the size of the coupling constant $\alpha$ distinguishes between the generation of finitely or infinitely many negative eigenvalues. In this talk we will show that a similar property holds when the potential has slower decay but oscillates at infinity.

Orateur: Larry Read (LMU)

10:00 → 10:30 Coffee Break

10:30 → 11:30 Szegő-type asymptotics for the half-filled lowest Landau level

Consider the Landau Hamiltonian $H=-\frac{\partial^2}{\partial x_1^2} + \left( - i \frac{\partial}{\partial x_2} - Bx_1 \right)^2$ in Landau gauge acting on $L^2(\mathbb R^2)$. Let $1_{\{B\}}(H)$ be the spectral projection onto the (infinitely degenerate) eigenspace corresponding to the eigenvalue $\lambda = B$. Leschke, Sobolev and Spitzer established an asymptotic expansion of the form [ \operatorname{tr}h(1_{[-l,l]^2} 1_{{B }}(H) 1_{[-l,l]^2}) = \alpha l^2 + \beta l + o(l) ] as $l\to \infty$, for fairly general functions $h$ with $h(0) = 0$. Our main result is a corresponding asymptotic expansion when replacing the projecton $1_{\{B\}}(H)$ by a subprojection $P$ onto a subspace incorporating only ``half'' the eigenfunctions (in a sense that will be made precise). We will see that in this case the subleading behavior of the asymptotic expansion features an additional logarithmic enhancement term $\log l$.

Orateur: M. Leonhard Wetzel (LMU)

11:30 → 12:00 Presentation: closing statements

12:00 → 13:00 Lunch