SOL is one of Thurston's eight classical homogeneous Riemannian geometries, possibly the most exotic one. To get some insight of this geometry, it might be helpful to visualize the shape of a large sp...
Fano varieties are projective varieties with “positive curvature”. Examples of Fano varieties are projective spaces, products of projective spaces, Grassmannians and hypersurfaces in projective spaces...
Non-commutative Iwasawa theory has emerged as a powerful framework for understanding deep arithmetic properties over number fields contained in a p-adic Lie extension and their precise relationship to...
In this talk I will report on a joint work in progress with E. Fatighenti, in which we study some special vector bundles on the Fano variety of lines of a cubic fourfold. We will see that these bundle...
Let G be a reductive connected group over an algebraically closed field of characteristic p . Of particular importance in the study of G is the set u(G) of unipotent conjugacy classes. It is known tha...
The Brauer group, classifying Azumaya algebras up to Morita equivalence, is a fundamental invariant in number theory and algebraic geometry. Given a moduli problem M (e.g. smooth curves of a given gen...
Cluster algebras are commutative algebras with a special combinatorial structure. A cluster algebra is a subalgebra of a field of rational functions in several variables that is generated by a disting...
Motivated by physics, in the late 1990s Sen discussed a construction of complete hyperkähler metrics in (real) dimension 4 and so-called ALF (asymptotically locally flat) asymptotics as a "superpositi...
I discuss how to practically put a log structure on a toroidal crossing space, and hopefully sketch applications to smoothing toric Fano varieties and log birational geometry. This is work in progress...
Positively multiplicative graphs are graphs whose adjacency matrix can be embedded in a matrix algebra admitting a distinguished basis labelled by its vertices with nonnegative structure constants. It...
