Course overview -- Sommersemester 2021

Monday,
2021-04-26
16:15
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.

Monday,
2021-05-03
16:15
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.

Monday,
2021-05-10
16:15
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.

Monday,
2021-05-17
16:15-17:45
Anderssen (BBB)
Vincent Müller (Freiburg): t.b.a
Monday,
2021-05-31
10:15
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)

Monday,
2021-06-07
00:00
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.

Monday,
2021-06-14
16:15-17:45
Anderssen (BBB)
Marc-Antoine Fiset (ETH Zürich): Deformed G_2 Shatashvili-Vafa algebra for superstrings on AdS_3 × M^7
Monday,
2021-06-21
16:15
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).

Monday,
2021-06-28
16:15
Euwe (SR 226)
Jin Li: On the geometry of resolutions of G2-conifolds
Notice the unusual room.

Given a compact G_2 manifold with isolated conical singularities, the process of resolutions of these singularities gives us a one-parameter family of G_2 structures, which can be viewed as a curve in some moduli space. This talk reports the progress in estimating the length of the curve under some Riemannian metric on the moduli space.

Monday,
2021-07-05
16:15
Anderssen (BBB)
Zhengfang Wang: Singularity categories and singular Hochschild cohomology

The singularity category was introduced by Buchweitz and then rediscovered by Orlov motivated by the homological mirror symmetry conjecture. Following Buchweitz, in analogy with Hochschild cohomology, one defines the singular Hochschild cohomology of an algebra as the Yoneda algebra of the diagonal bimodule in the singularity category of bimodules.

The first half of the talk is an introduction to singularity categories and Hochschild cohomology. The second half will show that singular Hochschild cohomology is endowed with the same rich algebraic structure as classical Hochschild cohomology, namely a Gerstenhaber bracket in cohomology and a B-infinity structure at the cochain complex level. We will also talk about its relationship with the deformation theory of singularities.

Monday,
2021-07-12
16:15
bbb Raum Anderssen
Elias Hofmann (Freiburg): Relativistische Modelle des Universums um einen zentralen Stern

Wir betrachten in diesem Vortrag eine zentrale Masse, die wir als statisch und kugelsymmetrisch annehmen. Ziel wird es sein, die diese Masse umgebende Raumzeit differentialgeometrisch zu beschreiben. Wir werden hierzu zwei Modelle entwickeln und untersuchen: Die intuitivere Schwarzschild-Raumzeit, sowie die Kruskal-Raumzeit. Dabei werden wir ein besonderes Augenmerk auf die auftretenden Singularitäten legen, wobei wir zwischen Koordinatensingularitäten und physikalischen Singularitäten unterscheiden.

Monday,
2021-07-19
16:15
Anderssen (BBB)
Ryszard Nest: Determinants, group cocycles and multiplicative Chern character

The well known central extension of loop groups is an example of a group two-cocycle naturally constructed from action of the restricted linear group on a certain non-linear category of idempotents in a polarised Hilbert space. We will explain the concepts involved in this construction, its generalisation to a construction of higher cocycles and give some examples of non-trivial three-cocycles for the double loop group, both formal and smooth. On the other hand, these group cocycles lead to functionals on algebraic K-theory, the so called regulators. We will sketch this relation and, in particular, the relation to the Tate tame symbol in algebraic geometry and multiplicative Chern of Connes and Karoubi associated to universal finitely summable Fredholm modules.


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