List of talks Summer Semester 2024

June 14th 2024 - Leonid Ryvkin (University of Lyon), "Title: TBA".

Abstract: TBA.

May 28th 2024 - Rosa Marchesini (University of Göttingen), "Title: TBA".

Abstract: TBA.

May 24th 2024 - Stefano Ronchi (University of Göttingen), "Cotangent spaces for higher Lie groupoids and applications".

Abstract: In the same way Lie groupoids can encode local symmetries of a manifold, Lie 2-groupoids are a way to encode higher symmetries. After a short crash course on this topic, we present the construction of a cotangent space for Lie 2-groupoids analogous to the well known one for Lie groupoids. This turns out to have a canonical shifted symplectic structure (that is, symplectic up to homotopy) in the same way the cotangent groupoid is canonically a symplectic groupoid, and the tangent bundle of a manifold is canonically symplectic. This makes our cotangent space a good global model for a class of symplectic Q-manifolds that appear in some TQFTs. We will then discuss various applications, including a definition of hamiltonian actions of Lie 2-groupoids. This talk is based on joint work in progress with Miquel Cueca and Chenchang Zhu.

May 17th 2024 - Fabrizio Zanello (University of Potsdam), "A leisurely stroll through the multisymplectic approach to Lagrangian field theories".

Abstract: The mathematical toolbox of multysimplectic geometry was introduced in order to generalize the symplectic formulation of classical mechanics to Lagrangian field theories. After a substantial body of foundational works for first order field theories, though, the program came to a standstill due to technical difficulties. In this talk we give an overview of the motivations, techniques and limitations of the traditional results and present some of the core ideas of a new approach, recently proposed by Blohmann, to overcome those technical difficulties. The talk is based on an ongoing joint project with Antonio Miti.

May 10th 2024 - Luisa Herrmann (University of Potsdam), "On a problem of optimal transport under marginal martingale constraints".

Abstract: Based on an article by Mathias Beigelböck and Nicolas Juillet, I will first describe the martingale version of the optimal transport problem after which I will define the convex order and give some examples. I will then discuss the central question as to whether the set of all martingale transport plans is nonempty and present a  constructive proof of the existence under certain assumptions.

May 3rd 2024 - Alejandro Peñuela Diaz (University of Potsdam), "Construction of marginally outer trapped surfaces".

Abstract: In physics, marginally outer trapped surfaces (MOTS) can be understood as quasi-local versions of black hole boundaries. Therefore, these surfaces are crucial to understand black holes and are widely used in black hole simulations. From a mathematical point of view, MOTS are prescribed mean curvature surfaces, that is a generalization of a minimal surface. I will talk about marginally outer trapped surfaces, introduce some of their properties, and explain the challenges when trying to construct them analytically.

April 26th 2024 - Alberto Bonicelli (University of Pavia), "Convergence results in the stochastic sine-Gordon model: an algebraic viewpoint".

Abstract: The importance of the sine-Gordon model in 1+1 spacetime dimensions resides in the integrability of the field theory that it describes. A recent result showed how, within the setting of algebraic quantum field theory, this property translates into a convergence result for both the formal series associated to the S-matrix and to the interacting field of the quantum field theory. After introducing an algebraic approach to the perturbative study of singular stochastic PDEs, I will show how an adaptation of the aforementioned convergence results yields convergence of the momenta of the solution to a stochastic version of the sine-Gordon equation. Interestingly enough, our two-step procedure passes through the quantum theory and recollects the stochastic information via the classical limit.

April 19th 2024 - Leonard Schmitz (MPI Leipzig), "Free generators and Hoffman's isomorphism for the two-parameter shuffle algebra".

Abstract: Signature transforms have recently been extended to data indexed by two and more parameters. With free Lyndon generators, ideas from B∞-algebras and a novel two-parameter Hoffman exponential, we provide three classes of isomorphisms between the underlying two-parameter shuffle and quasi-shuffle algebras. In particular, we provide a Hopf algebraic connection to the (classical, one-parameter) shuffle algebra over the extended alphabet of connected matrix compositions. This is joint work with Nikolas Tapia.

April 12th 2024 - Alexander Schmeding (NTNU, Trondheim), "On manifolds of Lie group valued continuous BV-functions".

Abstract: Functions of bounded variation (BV) with values in a Banach space are a classical topic of analysis with specific applications for example in rough path theory. In the theory of rough paths one considers routinely even BV-functions with values in non-linear spaces such as manifolds and (finite and infinite-dimensional) Lie groups. In this talk we will explain how the well known construction of manifolds of mappings carries over to the world of BV-functions. As a consequence we are able to generalise the construction of current groups to the BV-setting. This also strengthens known regularity properties a la Milnor for Banach Lie groups. Joint work with H. Glöckner and A. Suri (Paderborn).