The aim of this course is to present some recent advances in the theory of stable sheaves on higher dimensional hyper-Kähler manifolds. In the first part we will review Mukai's theory on K3 surfaces. ...
In 1998, Thomas Schick discovered a purely homological obstruction to the existence of positive scalar curvature metrics on oriented closed smooth manifolds in terms of torality properties of their fu...
The tautological ring is a certain subring of the Chow ring of the moduli space of curves. It is generated by the algebraic cycles that arise from the modular nature of the moduli space, and is one of...
The Torelli locus - the image of the moduli space of curves (M_g) in the moduli space of abelian varieties (A_g) - is much-studied but still mysterious. In characteristic p, A_g has a beautiful strati...
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 talk is to show the connections between Liouville type equations and the conformal geometry of Riemann surfaces. In particular, we will focus on an isoperimetric inequality, the socall...
In this talk we consider inverse problems for the partial differential equations describing the behavior of certain fluids. Our focus will be on the fluid-structure interaction problem and the object...
In this talk we will discuss the (de-)linearization of modules over smooth varieties, introduced by A. Grothendieck, and we will introduce the classic Berstein-Gelfand-Gelfand (BGG) theory. The two ar...
Even before the introduction of Conformal Field Theory by Belavin, Polyakov and Zamolodchikov, it appeared indirectly in the work of den Nijs and Nienhuis using Coulomb gas techniques. The latter post...
Effective feedback control is essential for optimizing dynamical systems by minimizing a predefined cost function, thereby stabilizing the system toward a desired state. Despite its proven effectivene...
