Homogenization of second order level set PDE in periodic media
Dienstag, 1.6.21, 14:15-15:15, Hörsaal II (virtuell: Lasker)
I will discuss the homogenization of a class of interface motions "in nondivergence form" with periodically varying coefficients. Compared to uniformly elliptic second order PDE, the difficulty here is the equation only induces averaging in d - 1 dimensions. This leads to strong anisotropic effects: in particular, typically the homogenized coefficients are discontinuous. I will describe the behavior of the homogenized coefficients at discontinuities and also explain how to prove a comparison principle for the effective motion.
On a stochastic version of transfer operators
Montag, 7.6.21, 00:00-01:00, Anderssen (BBB)
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. \n\nIn 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.
A surface and a threefold with equivalent singularity categories
Freitag, 11.6.21, 10:30-11:30, virtueller Raum Lasker
Freitag, 11.6.21, 13:00-14:00, online: Zoom
Deformed G2 Shatashvili-Vafa algebra for superstrings on AdS3 × M^7
Montag, 14.6.21, 16:15-17:15, Anderssen (BBB)
Homogenization in a class of non-periodically perforated domains
Dienstag, 15.6.21, 14:15-15:15, Hörsaal II (virtuell: Lasker)
We consider the deterministic homogenization of the Poisson problem and the Stokes system in a class of non-periodically perforated domains. The size of the perforations is comparable to the distance between two neighbouring holes. The boundary conditions for both problems are of homogeneous Dirichlet type along the holes and the macroscopic boundary. The homogenization of these PDEs when the holes are periodically distributed in space is well-known. We aim at extending these results to local perturbations of the periodic case, that is when the geometry is not periodic but tends to be periodic far from the origin. This setting takes into account local defects that could appear in a pure periodic microstructure. In this talk, we first introduce the conditions imposed on the non-periodic porous medium. We then construct classical objects of the homogenization such as correctors and we obtain convergence rates of the solution to its two scale expansion for both Poisson problem and Stokes system. We finally comment on the optimality of these convergence rates.\n
Verallgemeinerte metrische Räume mit einfacher Automorphismengruppe
Dienstag, 15.6.21, 14:30-15:30, Philidor
Über eine gemeinsame Arbeit mit Evans, Hubicke, Konecny und Li.\nIm Beweis der Einfachheit der Isometriegruppe der Urysohnkugel (Tent-Z,2013) wurde wesentlich verwendet, dass die Urysohnkugel eine SIR, eine Stationary Independence Relation trägt.\nWir zeigen hier, dass abzählbare Strukturen mit einer SIR, die ein paar Extraaxiome erfüllt, einfache Automorphismengruppen haben. Das ist anwendbar auf einige Graphen in Cherlins Liste aller abzählbaren, metrisch homogenen Graphen.\n\n
Neue Ideen zum Einsatz von DGS-Software und Tabellenkalkulationen im Geometrieunterricht der Sekundarstufe I
Dienstag, 15.6.21, 19:30-20:30, https://uni-freiburg.zoom.us/j/3852066250?pwd=Rk5IYklvdWt5OFVDWExUMWJhazd2dz09 Kenncode: NZUWh12NY
Seit mehr als 30 Jahren werden Vorschläge entwickelt, wie man dynamische Geometriesysteme (DGS) und andere Computerprogramme gewinnbringend im Geometrieunterricht der Sekundarstufe I einsetzen kann. Die Fülle des Materials wird inzwischen unüberschaubar. Dieser Vortrag versucht trotzdem, einige neue Ideen zu diesem Thema vorzustellen, die im Rahmen der Lehrbuchreihe "Mathe 21" entstanden sind. \n\nOrt: https://uni-freiburg.zoom.us/j/3852066250?pwd=Rk5IYklvdWt5OFVDWExUMWJhazd2dz09\n\nKenncode: NZUWh12NY\n
Liquid Tensor Experiment -- a Progress Report
Donnerstag, 17.6.21, 14:15-15:15, online: vGK1821
In December 2020, Peter Scholze posed a challenge to formally verify\nthe main theorem on liquid R-vector spaces,\nwhich is part of his joint work with Dustin Clausen on condensed\nmathematics.\nI took up this challenge with a team of mathematicians\nto verify the theorem in the Lean proof assistant.\nHalf a year later, we have finished the main technical ingredient of\nthis challenge. In this talk I will report on the progress we've made\nand what remains to be done and discuss our experience formalizing\ncutting edge research. No prior knowledge of Lean or liquid mathematics\nis assumed.
Freitag, 18.6.21, 13:00-14:00, online: Zoom
Classification of ground states for critical Dirac equations
Montag, 21.6.21, 16:15-17:15, BBB Anderssen
In this talk I will present a classification result for nonlinear Dirac equations with critical nonlinearities on the Euclidean space.\nThey appear naturally in conformal spin geometry and in variational problems related to critical Dirac equations on spin manifolds.\nMoreover, two-dimensional critical Dirac equations recently attracted a considerable attention as effective equations for wave propagation in honeycomb structures.\nExploiting the conformal invariance of the problem ground state solutions can be classified, in analogy with the well-known result for the Yamabe equation.\n\nThis is a joint work with Andrea Malchiodi (SNS, Pisa) and Ruijun Wu (SISSA, Trieste).
On the Boucksom-Zariski decomposition for irreducible symplectic varieties and bounded negativity
Freitag, 25.6.21, 11:00-12:00, virtueller Raum Lasker
Process-guided neural networks: a case on domain adaptation
Freitag, 25.6.21, 13:00-14:00, online: Zoom
On the geometry of resolutions of G2-conifolds
Montag, 28.6.21, 16:15-17:15, Euwe (SR 226)
Given a compact G2 manifold with isolated conical singularities, the process of resolutions of these singularities gives us a one-parameter family of G2 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.
Digitales Lernmaterial zur Netflix Challenge (Sek. II)
Dienstag, 29.6.21, 19:30-20:30, Ort: https://uni-freiburg.zoom.us/j/3852066250?pwd=Rk5IYklvdWt5OFVDWExUMWJhazd2dz09 Kenncode: NZUWh12NY
Wie kann Netflix Nutzer/innen passende Filmempfehlungen aussprechen? So lautete die Aufgabe der Netflix Challenge, die der Streamingdienst 2006 ausschrieb. Wir haben zu eben dieser Challenge und dem veröffentlichten Datensatz digitales Lernmaterial entwickelt und in mathematischen Modellierungsprojekten mit Schüler/innen erprobt. Auf digitalen Arbeitsblättern erkunden die Lernenden zuerst den Datensatz und erarbeiten anschließend ein mathematisches Modell eines Empfehlungssystems. Durch das Lernmaterial erhalten sie einen Einblick in wesentliche Strategien der mathematischen Modellierung und des Maschinellen Lernens. Das Material zeigt exemplarisch wie datenlastige Problemstellungen aufbereitet und im Distanzlernen / in Präsenz durchgeführt werden können. Der Vortrag bietet einen Einblick in die Problemstellung, das mathematische Modell und die digitale Umsetzung des online verfügbaren Lernmaterials.\n\nOrt: https://uni-freiburg.zoom.us/j/3852066250?pwd=Rk5IYklvdWt5OFVDWExUMWJhazd2dz09\n\nKenncode: NZUWh12NY