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Autumn Semester 2024

Date / Time Speaker Title Location
7 October 2024
13:30-14:30 		Prof. Dr. Anton Khoroshkin
University of Haifa
Details

Talks in Mathematical Physics

Title On Generating Series of Cohomology of Generalized Configuration Spaces
Speaker, Affiliation Prof. Dr. Anton Khoroshkin, University of Haifa
Date, Time 7 October 2024, 13:30-14:30
Location Y27 H 25
Abstract A generalized configuration space on $X$ consists of a collection of points on $X$ with specific rules governing which points cannot coincide. In this work, I will introduce a new algebraic structure, called a "contractad," on the union of these spaces for $X = \mathbb{R}^n$, which extends the concept of the little discs operad. I will demonstrate how this algebraic framework can be used to extract information regarding the Hilbert series of cohomology rings. Surprisingly, the same approach can be applied to generate series for various combinatorial data associated with graphs, such as the number of Hamiltonian paths, Hamiltonian cycles, acyclic orientations, and chromatic polynomials. Additionally, natural compactifications of these configuration spaces for $X = \mathbb{C}$ generalize the Deligne-Mumford compactification of moduli spaces of rational curves with marked points. If time allows, we will also discuss the generating series for their cohomology. The talk is based on the joint work with D.Lyskov: https://arxiv.org/abs/2406.05909
On Generating Series of Cohomology of Generalized Configuration Spacesread_more
Y27 H 25
21 October 2024
13:30-14:30 		Iakovos Androulidakis
National and Kapodistrian University of Athens
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Talks in Mathematical Physics

Title On a conjecture by A. Weinstein
Speaker, Affiliation Iakovos Androulidakis, National and Kapodistrian University of Athens
Date, Time 21 October 2024, 13:30-14:30
Location Y27 H 25
Abstract Geometric (pre)quantization can be performed only for integral symplectic manifolds. In 1989 Alan Weinstein conjectured that using the notion of Diffeology, as well as Noncommutative Geometry methods, one might obtain the representations required to “quantise the unquantisable” from a torus bundle rather than a line bundle. In joint work with P. Antonini, we showed that the obstruction to integrality can be lifted by adding extra dimensions and passing to the diffeological category. In fact, the added dimensions force the C*-algebra associated with this construction to be nothing else than the crossed product algebra associated with a torus action.
On a conjecture by A. Weinsteinread_more
Y27 H 25
28 October 2024
13:30-14:30 		Piero Grassi
Università del Piemonte Orientale
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Talks in Mathematical Physics

Title Quantum Field Theories on Supermanifolds
Speaker, Affiliation Piero Grassi, Università del Piemonte Orientale
Date, Time 28 October 2024, 13:30-14:30
Location Y27 H 25
Abstract We illustrate the construction of quantum field theories on supermanifolds and we provide a complete Cartan-calculus to deal with superdiffeomorphisms in curved space. We will briefly review the geometry of supermanifolds and we discuss the challenges related to quantum field theory applications.
Quantum Field Theories on Supermanifoldsread_more
Y27 H 25
2 December 2024
13:30-14:30 		Ezra Getzler
Northwestern University
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Talks in Mathematical Physics

Title Title T.B.A.
Speaker, Affiliation Ezra Getzler, Northwestern University
Date, Time 2 December 2024, 13:30-14:30
Location Y27 H 25
Abstract tba
Title T.B.A.read_more (CANCELLED)
Y27 H 25
16 December 2024
13:30-14:30 		Konstantin Wernli
Centre for Quantum Mathematics, University of Southern Denmark
Details

Talks in Mathematical Physics

Title Gluing formulas for heat kernels
Speaker, Affiliation Konstantin Wernli, Centre for Quantum Mathematics, University of Southern Denmark
Date, Time 16 December 2024, 13:30-14:30
Location Y27 H 25
Abstract Abstract: Motivated by heat kernel renormalization of perturbative quantum field theory, we study the cutting and gluing behaviour of the heat kernel on a Riemannian manifold $M$ which is cut along a compact hypersurface $\gamma$ into two Riemannian manifolds $M_1$, $M_2$. Under a certain assumption on $(M,\gamma)$ (which we conjecture to be true for all Riemannian manifolds), we prove a gluing formula for the heat kernel which involves only the heat kernels on $M_1, M_2$ and $\gamma$. This is a joint work with Pavel Mnev, arxiv:2404.00156.
Gluing formulas for heat kernelsread_more
Y27 H 25

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