Past Events
The solutions of certain 1-parametric symplectic embedding problems - like finding for each a>0 the smallest 4-ball B^4(c(a)) into which the ellipsoid E(1,a) symplectically embeds - have revealed that symplectic rigidity has an intricate fine structure. The first proofs of these results…
We consider eigenvector statistics of large random matrices. When the matrix entries are sampled from independent Gaussian random variables, eigenvectors are uniformly distributed on the sphere and numerous properties can be computed exactly. In particular, it can be shown that extremal…
Suppose you take an insulated piece of metal, and allow the temperature to equilibrate. What's the behaviour of the hottest spot? Surprisingly, in many cases, it travels to the boundary! I'll discuss some cases in which this does and does not happen, and show that it occurs in obtuse triangles…
We introduce a notion of stability for varieties fibered over curves, motivated by Kollár's stability for homogeneous polynomials with integer coefficients. We analyze geometric implications of stability for fibrations whose fibers are complete intersections in weighted…
A general polarized hyperelliptic K3 surfaces of degree 4 is a double cover of P^1 x P^1 branched along a bidegree (4,4) curve. Classically there are two compactifications of their moduli spaces: one is the GIT quotient of (4,4) curves, the other is the Baily-Borel…
The recent development of Almgren-Pitts min-max theory has presented the abundance of minimal hypersurfaces. In particular, in a bumpy closed Riemannian manifold $(M^{n+1}, g)$ $(3\leq n+1\leq 7)$, X. Zhou’s multiplicity one theorem and Marques-Neves Morse index theorem lead to the fact that for…
When considering pseudoholomorphic curves, we often assume things about an almost complex structure to guarantee that some moduli space is nice. If we need to deal with moduli spaces which are not nice, we can sometimes reduce the problem to the study of sections of an obstruction…
I report here on joint work with Jean-Michel Roquejoffre and Luca Rossi.
Epidemics of the past have been known to follow communication lines. Some recent observations report similar patterns for the Covid-19 propagation in Italy. In this talk, I will present a reaction-diffusion…