Seminars, for informal dissemination of research results, exploratory work by research teams, outreach activities, etc., constitute the simplest form of meetings at a Mathematics research centre.
CAMGSD has recorded the calendar of its seminars for a long time, this page serving both as a means of public announcement of forthcoming activities but also as a historic record.
An important geometric invariant of a hypersurface singularity is its Fukaya–Seidel category. In this talk, I will motivate and describe the study of two special families of isolated singularities. Time permitting, I will introduce “type A symplectic Auslander correspondence”, a purely geometrical construction which realises a notable result in representation theory.
I will discuss geometric, algebraic, and combinatorial constructions related to loop spaces in topology. The talk will revolve around a functorial construction that models the passage from a topological space X to its free loop space LX. The input is a coalgebra equipped with additional structure and the output is a chain complex with a compatible “rotation” operator. The construction is dual in an appropriate sense to the Hochschild complex of a dg algebra/category. When applied to the coalgebra of chains on X, suitably interpreted, it produces a chain complex that is naturally quasi-isomorphic to the chains on LX with rotation operator corresponding to the circle action. This statement does not require any hypotheses on X (such as simple connectivity, nilpotence, finite type, etc…) or on the underlying ring of coefficients. The model turns out to be useful when studying and computing explicitly the structure of the free loop space of a manifold.
Mirror Symmetry predicts a correspondence between the complex geometry (the B-side) and the symplectic geometry (the A-side) of suitable pairs of objects. In this talk I will consider certain orbifold del Pezzo surfaces falling outside of the standard mirror symmetry constructions. I will describe the derived category of coherent sheaves of the surfaces (their B-side), and discuss early results on the A-side. This is joint work with Franco Rota.
