# Veranstaltungsübersicht -- Sommersemester 2021

 Montag, 2021-04-26 16:15 Uhr Anderssen (BBB) Severin Barmeier: From scattering amplitudes to quiver representations and back Scattering amplitudes are basic observables in physics. In this talk I will explain how scattering amplitudes for massless particles can be obtained from the representation theory of quivers. This talk is based on arXiv:2101.02884 joint with Koushik Ray. Montag, 2021-05-03 16:15 Uhr Anderssen (BBB) Moritz Doll: Refined Weyl Law for the Perturbed Harmonic Oscillator We consider the quantum harmonic oscillator $H_0=(1/2)(-\Delta+|x|^2)$. The underlying classical flow is periodic with period $2\pi$. By an explicit calculation one can see that the solution operator to the dynamical Schrödinger equation of $H_0$ is the identity (modulo a sign) at $2\pi\mathbb{Z}$ and locally smoothing otherwise. This periodicity is related to a sharp remainder estimate for the counting function of the eigenvalues of $H_0$. If we perturb the operator by a pseudodifferential operator of lower order, then we break the symmetry and could hope for an improved remainder estimate. We will present results on recurrence of singularities for these operators as well as an improved remainder estimate. This is based on joint work with Oran Gannot, Jared Wunsch, and Steve Zelditch. Montag, 2021-05-10 16:15 Uhr Anderssen (BBB) Jonas Schnitzer: Maurer-Cartan elements, twisting and homotopy The globalisation of Kontsevich's formality to smooth manifolds depends on choices, namely of a torsion-free covariant derivative and some section of a pro-finite dimensional vector bundle. In my talk, I explain that even if the globalised formality changes with different choices, its homotopy class does not. The idea of the proof relies on some basic knowledge of strong homotopy Lie algebras, their morphisms, Maurer-Cartan elements and the so-called twisting procedure, which I recall in an introductory part. This talk is based on arXiv:2102.10645 joint with Andreas Kraft. Montag, 2021-05-17 16:15-17:45 Uhr Anderssen (BBB) Vincent Müller (Freiburg): t.b.a Montag, 2021-05-31 10:15 Uhr ZOOM (link in the email) Medet Nursultanov: Narrow escape problem on Riemannian manifolds We use geometric microlocal methods to compute an asymptotic expansion of the mean first arrival time for Brownian particles on Riemannian manifolds. This approach provides a robust way to treat this problem, which has thus far been limited to very special geometries. (Joint work with Justin Tzou and Leo Tzou) Montag, 2021-06-07 00:00 Uhr Anderssen (BBB) Ksenia Fedosova: On a stochastic version of transfer operators About thirty years ago, the classical statistical mechanics inspired a method that allows to obtain some information on the automorphic forms. The method, called the transfer operator approach, involves a construction of a so-called transfer operator from a certain discretisation of the geodesic flow on the manifold. For a modular surface, this transfer operator is ultimately connected to a Gauss map. One can show that the 1-eigenfunctions of this operator correspond via a certain integral transform to the eigenfunctions of the Laplace operator. In this talk, we try to construct an analogue of the transfer operator, using the Brownian paths on the manifold instead of the geodesics. We obtain an operator, whose 1-eigenfunctions turn out to be the boundary forms of eigenfunctions of the Laplace operator. We investigate some of its properties and hopefully show the connection with quantum modular forms. Montag, 2021-06-14 16:15-17:45 Uhr Anderssen (BBB) Marc-Antoine Fiset (ETH Zürich): Deformed G_2 Shatashvili-Vafa algebra for superstrings on AdS_3 × M^7 Montag, 2021-06-21 16:15 Uhr BBB Anderssen William Borrelli: Classification of ground states for critical Dirac equations In this talk I will present a classification result for nonlinear Dirac equations with critical nonlinearities on the Euclidean space. They appear naturally in conformal spin geometry and in variational problems related to critical Dirac equations on spin manifolds. Moreover, two-dimensional critical Dirac equations recently attracted a considerable attention as effective equations for wave propagation in honeycomb structures. Exploiting the conformal invariance of the problem ground state solutions can be classified, in analogy with the well-known result for the Yamabe equation. This is a joint work with Andrea Malchiodi (SNS, Pisa) and Ruijun Wu (SISSA, Trieste). Montag, 2021-07-05 16:15 Uhr Anderssen (BBB) Zhengfang Wang: Singularity categories and singular Hochschild cohomology TBA Montag, 2021-07-12 16:15 Uhr bbb Raum Anderssen Elias Hofmann (Freiburg): TBA

## Abonnieren

Die Einträge dieser Veranstaltung können im iCalender Format abonniert werden. die URL dazu lautet:
http://wochenprogramm.mathematik.uni-freiburg.de/ical/SS2021/Oberseminar%3A%20Differentialgeometrie.ics