Manchester Geometry Seminar - Andrey Jivkov
| Dates: | 16 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: Andrey Jivkov (Manchester)
Title: What becomes of Geometry when the Manifold is gone?
Abstract: Classical differential geometry describes physical systems as smooth fields evolving on manifolds. However, many systems of interest evolve through discrete structural changes, for which smooth geometry provides at best an effective approximation.
In this talk, I will present a combinatorial geometric framework in which systems are described as cell complexes and physical quantities are represented by cochains. I will introduce combinatorial differential forms and show how transport and conservation of scalar quantities arise algebraically from incidence relations. I will then discuss ongoing work on vector-valued forms, including Lie-like algebraic structures, discrete connections, and the interpretation of curvature and torsion as obstructions to transport consistency.
The framework should be viewed as a developing alternative to continuum-based geometric descriptions, rather than as a discretisation of them. The talk aims to highlight geometric structures, conceptual parallels with classical differential geometry, and open mathematical questions.
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Frank Adams Room 1
Alan Turing Building
Manchester
