W-algebras are certain vertex algebras associated with nilpotent elements of a simple Lie algebra. The apparence of the AGT conjecture in physics led many researchers toward to these algebraic structu...
The aim of this course is to present some recent advances in the theory of stable sheaves on higher dimensional varieties, in particular Fano and hyper-Kähler manifolds. We will start by reviewing the...
It is well known that the space of modular forms is not stable under differentiation. This is why quasi-modular forms have been introduced. Also Drinfeld modular forms, that are the positive character...
Knots form an infinite and complex data set, with topological invariants that are often intertwined in ways not yet fully understood. Many foundational challenges in knot theory and low-dimensional to...
Affine W-algebras form a family of vertex algebras indexed by the nilpotent orbits of a simple finite dimensional complex Lie algebra. Each of them is built as a noncommutative Hamiltonian reduction o...
I will present a study on the asymptotic behavior of the volume preserving mean curvature and the Mullins-Sekerka flat flows in three dimensional space, for which we need to establish a sharp quantitat...
In this seminar we will illustrate a work in collaboration with Ariela Briani and Hitoshi Ishii that extents the well known result on thin domains of Hale and Raugel. The test function approach of C. ...
Let us consider a complex abelian scheme endowed with a non-torsion section. On some suitable open subsets of the base it is possible to define the period map, i.e. a holomorphic map which marks a bas...
The Zilber-Pink conjecture is a very general statement that implies many well-known results in diophantine geometry, e.g., Manin-Mumford, Mordell-Lang, André-Oort and Falting's Theorem. After a genera...
We consider a large class of spatially-embedded random graphs that includes among others long-range percolation, continuum scale-free percolation and the age-dependent random connection model. We assu...
