October 17th 2025 - Rosa Preiß (Technische Universität Berlin), "New directions for signature varieties".
Abstract: Varieties of signature tensors were introduced by Améndola-Friz-Sturmfels in 2019. In this informal talk, I will give an overview of the works that followed this groundbreaking article, introduce the halfshuffle map M_p adjoint to a polynomial map p and hint current WIP.
Based on joint work with Annika Burmester, Steven Charlton, Laura Colmenarejo, Abhiram Kidambi, Felix Lotter. Special thanks to Francesco Galuppi.
October 22nd 2025 (at 9:00 am) - Jean Thibaut (CPT Marseille), "Generalized gauge theories on Lie algebroids".
Abstract: In this presentation we first introduce the formalism of Cartan geometry and present specific applications to describe gravitational theories by building action functionals from Characteristic classes and invariant polynomials.
In the second part we introduce the notion of generalized connections on Lie algebroids. We show they can be used to describe ordinary gauge theories (Ehresmann connections for particle physics and Cartan connections for gravitational theories) with a Higgs sector and the BRST formalism (used as a renormalization tool for the gauge theories) from a single unified mathematical structure corresponding to the Atiyah Lie algebroid of a principal bundle.
October 24th 2025 - Martin Geller (University of Oxford), "The Geometry of Rough Space".
Abstract: How can we differentiate functionals on rough path space? In this talk, I’ll be discussing how we can approach this question, as well as some of my results.
October 29th 2025 (at 11:30 am) - Debjit Pal (Leibniz Universität Hannover), "Strong generalized holomorphic principal bundles".
Abstract: We explore a classical problem within the framework of generalized complex (GC) geometry, a structure introduced by Hitchin and further developed by Gualtieri and Cavalcanti - namely, the development of an appropriate bundle theory in this setting. In this talk, we present the theory of strong generalized holomorphic (SGH) principal bundles, along with their connections and curvatures. These bundles interpolate between holomorphic and flat symplectic bundles. This is a joint work with Mainak Poddar.
November 7th 2025 - Ko Sanders (Leibniz Universität Hannover), "Distributions of positive type and entanglement quantum field theory".
Abstract: Distributions of positive type arise naturally in quantum field theory as two-point distributions. Motivated by this application, one would like to perform various constructions with such distributions, but a key obstruction is that cut-off functions f(x,y) that equal 1 in a neighbourhood of the diagonal x=y cannot be of positive type. After reviewing basic definitions and results on distributions of positive type, I will show how this obstruction can be overcome in Euclidean space by using test-functions of positive type and finding lower bounds on their Fourier transforms. If time permits I will show how this workaround allows us to construct quantum states with interesting entanglement properties.
November 14th 2025 - Bin Zhang (Sichuan University), "Absolutely convergent cyclotomic conical zeta values".
Abstract: Zeta values which are discrete sums on the one dimensional cone $]0, +\infty[$ generalise to multizeta values which are discrete sums on $k$-dimensional Chen cones $0<x_k<\cdots<x_1$ with $k$ in $\N$. Going from Chen cones to general convex polyhedral cones leads to conical zeta values which in turn generalise to cyclotomic conical zeta functions when inserting a $U(1)$-valued character in the sum. In this talk, we show that absolutely convergent cyclotomic conical zeta values span the same space as absolutely convergent cyclotomic multiple zeta values.
For this purpose, we regularise cyclotomic conical zeta functions by means of regularised conical zeta values. We then implement subdivisions of cones combined with a rescaling resulting from symmetry properties of the roots of the unity, to reduce them to regularised cyclotomic multiple zeta values. To do so, we first reinterpret regularised conical zeta values as regularised cyclotomic matrix zeta values built from matrices. This way, we can describe transformations on the matrices involved in the cyclotomic matrix zeta values induced by subdivisions of cones applied to regularised conical zeta values. These are some of the operations on matrices we use to write regularised cyclotomic multiple zeta values as rational linear combinations of regularised cyclotomic multiple zeta values. We give a necessary and sufficient criterion for the absolute convergence of cyclotomic matrix zeta values and view absolute convergent cyclotomic multiple zeta values as limits of regularised cyclotomic matrix zeta values. In the limit we obtain that absolutely convergent cyclotomic conical zeta values can be written as rational linear combinations of regularized cyclotomic multiple zeta values.
This is joint work with Li Guo, Sylvie Paycha and Zhiyao Zhang.
November 21st 2025 - Gihyun Lee (University of Potsdam), "Vector-valued oscillatory integrals and $(\rho,\delta)$-type pseudodifferential calculus".
Abstract: I shall report on ongoing joint work with Vishvesh Kumar (Ghent University, Belgium), in which we construct a general pseudodifferential calculus of type $(\rho,\delta)$ associated with symbols taking values in a locally convex space. Our framework covers the classical Kohn-Nirenberg and Weyl calculi, while our main motivation is to generalize Connes’ pseudodifferential calculus on noncommutative tori to the general $(\rho,\delta)$-type. I will introduce the vector-valued oscillatory integral underlying our construction and discuss the technical difficulties that do not appear in the scalar- or Banach space-valued $(\rho,\delta)$-type calculi in the literature.
November 28th 2025 - Jan Mandrysch (IQOQI Wien), "How to measure quantum fields? Implementing a causal measurement scheme".
Abstract: While measurement processes in standard quantum mechanics are well understood, the extension of these ideas to quantum field theory (QFT) remains a key challenge. In particular, ensuring that measurements respect fundamental principles such as relativistic causality is crucial. A persistent issue concerning measurements in QFT is, though, that the usual axioms for QFT alone are insufficient to prevent superluminal signaling. In this talk, I will discuss a recent proposal by Fewster and Verch for a local, covariant and causal measurement framework in algebraic QFT. In particular, I will discuss completeness of the framework and motivate its underlying assumptions focussing on the concrete setting of a free scalar field and Gaussian measurements. We conclude that the Fewster-Verch approach is suitable to model typical measurements in QFT.
The talk is based on joint work with Miguel Navascués (Lett Math Phys 115, 115 (2025), https://doi.org/10.1007/s11005-025-02001-3).
December 5th 2025 - Chuangzhong Li (Shandong University of Science and Technology), "TBA".
Abstract: TBA.
December 12th 2025 - Yannic Vargas (CUNEF University Madrid), "A Pre-tty Pre-amble to Pre-Lie Algebras from Combinatorial Species".
Abstract: We present an introduction to pre-Lie algebras, an algebraic structure closely related to Lie algebras. From a combinatorial perspective, pre-Lie algebras are connected to the notion of insertion of objects of a given nature into one another. In recent years, pre-Lie algebras have found numerous applications in algebra, combinatorics, quantum field theory, and numerical analysis.
To better understand the nature of pre-Lie algebras, we employ the framework of species, a categorification of the concept of generating functions. This perspective allows us to describe, in a combinatorial way, several algebraic properties of pre-Lie algebras. In particular, we present a “pre-Lie-like” notion of symmetric operads, called Nested Pre-Lie operads (NPL for short). After giving several examples of NPL operads, we explain how to construct NPL-algebras, in the same way algebraic structures emerge from operads by considering algebras over operads.
To do so, we use a new variant of species based on polynomial functions. This is joint work with Dominique Manchon, Hedi Regeiba, and Imen Rjaiba.
January 16th 2026 - Daan Janssen (University of York), "TBA".
Abstract: TBA.
January 23th 2026 - Janina Bernardy (MPI Bonn), "TBA".
Abstract: TBA.
January 23th 2026 - Malte Leimbach (MPI Bonn), "TBA".
Abstract: TBA.
January 29th 2026 (Joint session with the Geometry Seminar, at 16:15) - Claudio Dappiaggi (University of Pavia), "Equivalence between local and global Hadamard States with Robin boundary conditions on half-Minkowski spacetime".
Abstract: We construct the fundamental solutions and Hadamard states for a Klein-Gordon field in half-Minkowski spacetime with Robin boundary conditions in arbitrary dimensions using a generalisation of the Robin-to-Dirichlet map. On the one hand this allows us to prove the uniqueness and support properties of the Green operators. On the other hand, we obtain a local representation for the Hadamard parametrix that provides the correct local definition of Hadamard states, capturing `reflected' singularities from the spacetime timelike boundary. This allows us to prove the equivalence of our local Hadamard condition and the global Hadamard condition with a wave-front set described in terms of generalized broken bicharacteristics, obtaining a Radzikowski-like theorem in half-Minkowski spacetime.
Joint work with B. Costeri, R. D. Singh and B. Juárez-Aubry -- ArXiv: 2509.26035 [math-ph]
January 30th 2026 - Beatrice Costeri (University of Pavia), "TBA".
Abstract: TBA.
