October 18th 2024 - Elke Rosenberg (University of Potsdam), "Weyl asymptotics for discrete pseudo-differential operators".
Abstract: For a class of elliptic self-adjoint pseudo-differential operators in a discrete semi-classical setting we give asymptotic estimates for the number of eigenvalues in a fixed interval. Here we assume the related symbols to be periodic with respect to momentum. The associated operator acts on functions on a lattice scaled by a semi-classical parameter. Under the assumption that the boundaries of the spectral Interval are non-critical values of the principal symbol, we show that the exact leading order term for the number of eigenvalues is given by the phase space volume of the pre-image of the interval under the principil symbol.
October 25th 2024 (11 AM) - Luisa Herrmann (University of Potsdam), "Euler's polyhedron formula applied to Kepler-Poinsot-polyhedra".
Abstract: If one interprets the Kepler-Poinsot-polyhedra as the union of several objects and applies Euler's polyhedron formula on their number of vertices, edges and faces, than the result is two. This is also the case for normal connected polyhedra without holes. In my presentation I will explain how to interpret the Kepler-Poinsot-polyhedra as the union of several objects and how to count them. For that purpose, it is helpful to understand what a polygon, whose number of vertices is rational but not an integer could be. This makes it possible to apply Euler's polyhedron formula on the star polyhedra. Even though single polygons, whose number of vertices is not an integer, are not definable, one can count them as faces on two of the four star polyhedra. Therewith one gets the value two by applying Euler's polyhedron formula.
October 25th 2024 (2 PM) - Johannes Blümlein (DESY), "Analytic Integration Methods in Quantum Field Theory".
Abstract: A survey is given on the present status of analytic calculation methods and the mathematical structures of zero- and single scale Feynman amplitudes which emerge in higher order perturbative calculations in the Standard Model of elementary particles, its extensions and associated model field theories, including effective field theories of different kind. The methods include symbolic summation methods, symbolic solutions of differential equations, different classes of higher transcendental functions and special numbers. A main characteristics of the objects studied is their representation as iterative integrals, including higher transcendental letters in the associated alphabets.
October 30th 2024 - Emiel Claasen (MPI, Potsdam), "From modular graph forms to iterated integrals (Part 1)".
Abstract: Modular Graph Forms (MGFs) are a class of modular forms represented by lattice sums associated to directed simple graphs. They originated from the calculation of graviton amplitudes in type II string theory. MGFs have remarkable mathematical properties such as an intricate network of algebraic and differential relations or the appearance of (conjecturally single-valued) multiple zeta values in their Fourier expansion. In particular, they are conjectured to arise as expansion coefficients of certain generating series dubbed equivariant iterated Eisenstein integrals. In this first of two talks, I will introduce the MGFs, talk about their appearance in string theory, and set the stage for their systematic conversion into their iterated integral representations.
November 8th 2024 - Lucas Broux (MPIMS, Leipzig), "Malliavin calculus in regularity structures" (online).
Abstract: TBA.
November 8th 2024 (2 PM) - Sumati Surya (Raman Research Institute, Bengalore), "TBA".
Abstract: TBA.
November 15th 2024 - Martin Peev (Imperial College), "TBA" (online).
Abstract: TBA.
November 22nd 2024 - Yunnan Li (Guangzhou University), "TBA" (online).
Abstract: TBA.
December 6th 2024 - Chenchang Zhu (Georg-August-Universität Göttingen), "TBA".
Abstract: TBA.
January 10th 2025 - Christiane Klein, "TBA".
Abstract: TBA.
January 17th 2025 - Lena Janshen (Georg-August-Universität Göttingen), "TBA".
Abstract: TBA.
January 31st 2025 - Tobias Diez (Shanghai Jiao Tong University), "TBA".
Abstract: TBA.
