Antrittsvorlesung von Jun.-Prof. Dr. Janina Letz und Prof. Dr. Stephan Stadler
20.04., 16:15 Uhr
Antrittsvorlesung von Prof. Dr. Stephan Stadler
Titel: Not a Knot
Abstract:
A mathematical knot is a loop in space — like a piece of string with its ends joined — studied up to continuous deformations such as stretching, bending, and twisting, but without cutting or passing through itself.
Among all knots, special importance is given to the unknot, which is simply a round circle, even if it may appear tangled at first glance. This leads to a natural question: how can we tell whether a given knot is actually the unknot in disguise?
A beautiful answer comes from differential geometry. The Fáry–Milnor theorem shows that if a knot is not sufficiently ''curved'', then it can be untangled into a circle. In this talk, I will explain this idea and explore how it extends to knots in curved spaces, as well as its surprising connections to the modern geometry of singular spaces.
Antrittsvorlesung von Jun.-Prof. Dr. Janina Lenz
Title: What is the size of a derived category?
Abstract: One studies commutative rings through their action. The objects a commutative rings acts on are modules and complexes. The derived category of a commutative ring is the collection of all complexes with certain maps. I will explain how one can measure the size of the derived category and the information it recovers about the ring.
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