The upcoming talk
At the next session of the TCS,
on the 17th of December 2025,
at 2:15 – 4:15 p.m. CET / 3:15 – 5:15 p.m. EET
Rafał R. Suszek
(KMMF WFUW)
shall talk about
“Stacky Dynamics
in the Shadows of Principaloid Bundles“.
Abstract
A novel definition shall be presented of a gauge(d) field theory with the configuration bundle given by the Godement quotient F (aka the shadow) of a principaloid bundle with connection (P,Θ), introduced by Strobl and the speaker earlier this year, with respect to the defining action of its structure Lie groupoid G⇒M. The field theory shall be descended from a two-dimensional Polyakov-Alvarez-Gawędzki σ-model with target M, the latter being endowed with a metric gM and a bundle gerbe 𝒢 with connective structure of curvature H∊ Z3(M), which codetermines the σ-model through the corresponding degree-3 Cheeger-Simons differential character (aka the surface holonomy). It is to be viewed as an effective formulation of charged-loop dynamics on the characteristic foliation M⫽G, consistent with the principle of homogeneity of internal structures (configurational degrees of freedom, gauges etc.) over the spacetime of the field theory.
The crucial rôle of a prequantisable multiplicative Bott-Shulman-Stasheff extension (H,ρ) of the gerbe’s curvature H (turning G⇒M into a Laurent-Gengoux-Xu prequantisable pre-quasi-symplectic groupoid), and that of a combined gM-isometric and ρ-holonomic reduction of the structure group Bisec(G⇒M) of P shall be emphasised in a coherent descent of the σ-model to F from its local trivialisation. The latter employs the structure of a smooth 2-stack on bundle gerbes with connective structure (which shall be explained), alongside an augmentation of 𝒢 that hinges on a canonical coupling between the comomentum component of the Spencer operator of ρ, as defined by Crainic et al., and the connection Θ. Time permitting, the abstract mechanism shall be illustrated with the example of the physically and mathematically important and much-studied Alekseev-Malkin-Meinrenken quasi-symplectic groupoid.
(All seminar talks are given on the online zoom platform. Unless requested otherwise by the speaker or required by the circumstances, and then specifically indicated in the announcement, the talks consist of two halves, 45 minutes each, separated by a 15-minute break. The web link for every session is circulated via the TCS mailing list. In order to be enlisted, please contact the Organisers.)
Calendar 2025/2026
| Date | Speaker (affiliation) | Title (with a link to the slides, whenever available) |
| October 15th, 2025 | Athanasios Chatzistavrakidis (Ruđer Bošković Institute, Zagreb) | Basic curvature tensors in geometry and physics |
| October 29th, 2025 | Martha Valentina Guarín Escudero (Charles University, Faculty of Mathematics and Physics, Prague) | Fedosov connections and L∞-algebras associated to dg-manifolds |
| November 12th, 2025 | Marcin Piątek (Instytut Fizyki, Uniwersytet Szczeciński) | Geometric Foundations of Celestial Amplitudes |
| December 3rd, 2025 | Jakub R. Filipek (WFUW, Warszawa) | Twisted Abelian Differential Cohomology and Weakly Abelian Lie Groups |
| December 17th, 2025 | Rafał R. Suszek (KMMF, WFUW) | Stacky Dynamics in the Shadows of Principaloid Bundles |
| January 14th, 2026 | Richard J. Szabo (School of Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh) | TBA |
| January 28th, 2026 | Cristian Ortiz (IME-USP, São Paulo) | TBA |
| February 25th, 2026 | Mikołaj Korzyński (CFT PAN) | TBA |
| March 11th, 2026 | ||
| March 25th, 2026 | ||
| April 8th, 2026 | ||
| April 22nd, 2026 | ||
| May 6th, 2026 | ||
| May 20th, 2026 | ||
| June 3rd, 2026 | ||