TENTANG EPISODE INI
In this talk I plan to discuss some joint work with Sheila Miller related to knots. Quandles are algebraic structures that can be associated to (tame) knots, and they in fact constitute one of the few complete invariants we have for knots. However, there is some dissatisfaction with quandles as invariants, as it heuristically seems difficult to determine whether two quandles are isomorphic. Our result supports this impression: we show that the isomorphism relation of quandles is as complex as it possibly could be in Borel reducibility terms, being Borel complete. On the other hand, equivalence of tame knots is trivial from a Borel reducibility perspective, raising the prospect that more manageable complete invariants might exist.
Inggris
Britania Raya
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CARI EPISODE TERDAHULU
Cari episode sebelumnya dari Mathematical, Foundational and Computational Aspects of the Higher Infinite.
EPISODE LAIN DALAM PODCAST INI
For various questions in Infinite Graph Theory, matroids have turned out to be the right tool to tackle them. This introduction to infinite matroids will be self-contained; in particular I will explain what a matroid is.
Miller, B (Universität Wien)
Friday 18th December 2015 - 10:00 to 11:00
Co-author: Philipp Schlicht (Universität Bonn)
Transfinite machine models of computation provide an approach to an `effective mathematics of the uncountable'. However, their set-theoretical interest seems to be limited by the fact that even the strongest such model, Koepke's Ordinal Turing Machine…
We discuss several results related to the question of when a Borel graph has a Borel matching. Here, the analogue of Hall's matching theorem fails, but there are positive results giving Borel matchings in several contexts if we are willing to discard null or meager sets. We also discuss some applic…
The limit of this kind of computability is the least ordinal which is \Pi_1 gap-reflecting on admissibles. If you would like to know what any of this means, come to the talk!
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