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Universität Augsburg
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Universität Augsburg
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Jun.-Prof. Dr. Ángel González Prieto
Universidad Complutense de Madrid
spricht am
Montag, 20. Januar 2025
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16 Uhr s.t.
im
Raum 2004 (L1)
über das Thema:
| Abstract: |
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The relationship between computational models and dynamics has captivated mathematicians and computer scientists since the earliest conceptualizations of computation. Recently, this connection has gained renewed attention, fueled by T. Tao's program aiming to discover blowing-up solutions of the Navier-Stokes equations using an embedded computational model, and by the intriguing links between static solutions and contact structures. In this vibrant context, a series of groundbreaking works have shown that Turing machines can be simulated through the flow lines of certain remarkable dynamical systems.
In this talk, we will introduce a novel perspective on computability in dynamical systems, drawing inspiration from Topological Quantum Field Theory. We will demonstrate that any computable function can be realized through the flow of a volume-preserving vector field on a smooth bordism. This result not only provides a new computational model but also unveils compelling insights into the interplay between the topological characteristics of the flow, the existence of compatible contact-like geometric structures on the bordism, and the computational complexity of the function. Joint work with E. Miranda and D. Peralta-Salas |
| Hierzu ergeht herzliche Einladung. |
| Prof. Dr. Kai Cieliebak |
Kaffee, Tee und Gebäck eine halbe Stunde vor Vortragsbeginn im Raum 2006 (L1).