Manchester Geometry Seminar - Adam Maskalaniec
| Dates: | 23 March 2026 |
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| Times: | 15:00 - 16:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Current University students |
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Speaker: Adam Maskalaniec (Warsaw)
Title: k-contact geometry in relativistic hydrodynamics
Abstract: We develop a rigorous geometric framework for the study of relativistic spin hydrodynamics, described by generalized thermodynamic relations. Our approach extends the classical contact geometric description of equilibrium thermodynamics by introducing k-contact geometry, a generalisation of contact geometry to field theories, providing a natural mathematical language to capture multi-parameter thermodynamic structures that appear in relativistic systems with spin degrees of freedom.
The dynamical evolution of such systems is described by k-contact Hamiltonian systems, where the dynamics is constrained to preserve Legendrian submanifolds of the k-contact manifold. Within this setting, we provide a geometric interpretation of pseudo-gauge transformations, a feature in dissipative field theories that leads to non-uniqueness in definitions of energy-momentum tensors. However, such generalisation carries a fundamental limitation of existing contact-geometric formulations of thermodynamics, which are typically tied to extensive variables.
Motivated by the scale invariance of relativistic hydrodynamical systems, we extend this framework to intensive physical systems—those invariant under scaling symmetries—by investigating the conformal symmetries of k-contact systems and associated reduction procedures. We show that these symmetries modify the k-contact form while preserving the underlying k-contact distribution. We develop a novel distributional approach to the reduction of k-contact dynamics, providing a rigorous geometric basis for the transition from extensive to intensive variables.
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Frank Adams Room 1
Alan Turing Building
Manchester
