Past Algebraic and Symplectic Geometry Seminar

24 February 2015
15:45
Daniel Grieser
Abstract
We study isolated singularities of a space embedded in a smooth Riemannian manifold from a differential geometric point of view. While there is a considerable literature on bi-lipschitz invariants of singularities, we obtain a more precise (complete asymptotic) understanding of the metric properties of certain types of singularities. This involves the study of the family of geodesics emanating from the singular point. While for conical singularities this family of geodesics, and the exponential map defined by them, behaves much like in the smooth case, the situation is very different in the case of cuspidal singularities, where the exponential map may fail to be locally injective. We also study a mixed conical-cuspidal case. Our methods involve the description of the geodesic flow as a Hamiltonian system and its resolution by blow-ups in phase space. 
 
This is joint work with Vincent Grandjean.
  • Algebraic and Symplectic Geometry Seminar
3 February 2015
15:45
Richard Thomas
Abstract
I will describe a little of Kuznetsov's wonderful theory of Homological projective duality, a generalisation of classical projective duality that relates derived categories of coherent sheaves on different algebraic varieties. I will explain an approach that seems simpler than the original, and some applications that occur in joint work with Addington, Calabrese and Segal.
  • Algebraic and Symplectic Geometry Seminar

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