On a stochastic version of transfer operators
Monday, 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.
Deformed G2 Shatashvili-Vafa algebra for superstrings on AdS3 × M^7
Monday, 14.6.21, 16:15-17:15, Anderssen (BBB)
Classification of ground states for critical Dirac equations
Monday, 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 geometry of resolutions of G2-conifolds
Monday, 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.