We show that two basic properties of Galilei symmetries can be extended, against common belief, to Carroll symmetries when properly interpreted. The first property is the fact that one can take critical Galilei limits using the fact that the Galilei algebra can be centrally extended to a Bargmann algebra. We demonstrate that, although the Carroll algebra does not allow such a central extension, one can nevertheless formulate a critical Carroll limit provided one allows for Euclidean or spacelike branes. The second property of Galilei symmetries is the fact that one can obtain systems with Bargmann symmetry by performing a null reduction over a spatial dimension. We show that similarly critical Carroll systems can be obtained by performing a Carrollian version of the null reduction over a time direction. In the supersymmetric case the resulting theories can be identified with critical Carroll limits of the star supergravities introduced by Hull.

We will provide an overview of the Atiyah class, starting from its original appearance in 1957, up to recent developments. In concrete examples, such as complex manifolds and Lie algebras, we will understand it as the class measuring the obstruction to the existence of some feature, e.g global holomorphic connections. After packaging everything in the language of Lie algebroids, we will present a generalization for representations up to homotopy and an (incomplete) attempt for Manin pairs. Parts of this talk refer to joint work with Sylvain Lavau, Fani Petalidou and Yannick Voglaire.

It is well-known, but remains underappreciated, that higher gauge theories require flux quantization laws for their global completion. A famous proposal for type IIA 10D supergravity is flux quantization in twisted K-theory, whose lift to 11D, however, is problematic. Here we proceed the other way around: After recalling the recently established S^4 flux quantizable superspace formulation of full 11D supergravity, including the coframe and gravitino dynamics, we explain how the (appropriately defined) dimensional reduction of its S^1-symmetric backgrounds yields a manifestly cyc(S^4) flux quantizable superspace formulation of IIA supergravity. We note that the latter choice of flux quantization law is close, but not quite the famously hypothesized twisted K-theory. Based on joint work with Hisham Sati and Urs Schreiber.

Categorifications of the notion of Hilbert space play an important role in string theory, quantum information theory, and unitary quantum field theory, especially in the study of topological phases of matter. As is often the case in categorification, there is not a unique higher-categorical generalization, but rather a variety of different notions. In this talk, I will describe the origins of my interest in the subject, beginning with work carried out during my PhD under the supervision of Richard Szabo on higher geometric quantization and higher geometry. I will then discuss a systematic framework for organizing and comparing notions of higher Hilbert spaces in the finite-dimensional setting. The talk is based on earlier work with Severin Bunk and Richard Szabo, as well as upcoming work with Gio Ferrer, Dave Penneys, and Luuk Stehouwer.

I review briefly elements in the above topics, which lead to a very enjoyable collaboration with Richard for several years: specifically I will sketch how recoil of a D-brane can be supersymmetrized on the world sheet, leading to a logarithmic N=1 superconformal algebra, how this is related to a consistent quantization of the non-commutative target space of recoiling matrix D-branes, and finally how a non-linear Schroedinger equation characterises the quantum evolution of point-like branes (D-particles). In the latter case, we use Galilean invariance of the system to show that there are three possible solutions of the associated non-linear Schroedinger equation, depending on the strength of the open string interactions among the D-particles. Happy Birthday, Richard, and many many happy returns!

We present the Bianchi identities for torsion and curvature in NC differential geometry and in NC Riemannian geometry. These follow from the Cartan Calculus and allow to test and compare the different notions of curvature discussed in the literature: via exterior forms, vector fields, principal bundles. The global and the local description –e.g. widely used in the literature on gauge theories– are considered and the NC notion of (twisted) commutator of covariant derivatives revisited. This presentation is supported by COST Action Calista CA21109.

We study the $\phi^3$, scalar and spinor electrodynamics in the braided $L_\infty$ formalism . The quantization of these theories is performed in algebraic Batalin-Vilkovisky framework. We prove that UV/IR mixing is absent at one loop order.

T-duality is more than a mere redundancy of string theory; it is a powerful predictive tool for constraining the effective action. However, constructing higher-derivative corrections, especially for non-chiral theories, such as the bosonic string, typically involves an order-by-order procedure that becomes computationally prohibitive beyond the leading orders. In this talk, we address this issue by introducing an alternative approach to the current standard method, the generalized Bergshoeff-de Roo identification. Thereby, we bypass the existing bottlenecks to reveal a much simpler way to obtain higher derivative corrections in string theory.