In this talk I will try to indicate the nature of stacks and gerbes,
to discuss Grothendieck's dream of higher Galois theory, and some of
the progress and problems this raises.

The well known work of Kleiman, shows that several properties of invertible sheaves on schemes, such as ampleness or nefness, are nicely described by their numerical data using the language of cones. In this talk we will focus on the different types of cones of divisors arising in the context of...

Lusternik-Schnirelmann category was introduced in the context of the calculus of variations as a lower bound for the number of critical points of any function. In this talk we shall review the classical notion of LS category, its main properties and its generalization to foliated manifolds.

Unprojection theory, initiated by Miles Reid, aims to
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Hovey, Palmieri and Strickland have defined the concept of stable homotopy
...

A theorem of Gromov states that any contact manifold of
...

In the gauge theoretic approach, the geometric Langlands correspondence is understood as a mirror symmetry.
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This is an introductory lecture to the index of differential operators. We´ll discuss the analytic and topological information it carries and the theorem of Atiyah and Singer, explaining how it subsumes previous geometric results, such as the Gauss-Bonnet theorem. We´ll also describe the topics...

This is joint with Megumi Harada of McMaster University.
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We will discuss the Poisson geometry of the moduli space of (non-strongly) parabolic Higgs bundles over a Riemann surface with marked points in terms of Lie algebroids and Lie groupoids.