Sala Seminari (Dip. Matematica)
I will discuss the "hows and whys" of the following recent results (joint
with J.Lotay, UCL):
1) in a negative Kaehler–Einstein manifold M, compact minimal Lagrangian
submanifolds L are locally unique;
2) for any small Kaehler–Einstein perturbation of M there corresponds a
deformation of L which is minimal Lagrangian with respect to the new
These results are also available on arXiv:1704.08226
Let $\varphi : M^m \to N^n$ be an immersed minimal submanifold in
Euclidean or hyperbolic space. In this talk, I survey on some recent
results obtained in collaboration with various colleagues from Brazil, to
ensure that the Laplace-Beltrami operator of $M$ has purely discrete
(respectively, purely essential) spectrum. In the last case, we also give
an explicit description of the spectrum. Our criteria apply to many
examples of minimal submanifolds constructed in the literature, and answer
In this talk, we will present a probabilistic representation
formula for the Navier-Stokes equations on compact Riemannian manifolds.
Such a formula has been provided by Constantin and Iyer in the flat
case. On a Riemannian manifold, there are several different choices of
Laplacian operators acting on vector fields. We shall use the de
Rham-Hodge Laplacian operator which seems more relevant to the
probabilistic setting, and adopt Elworthy-Le Jan-Li's idea to decompose
it as a sum of the square of Lie derivatives. This is a joint work with
Le congetture di Kazhdan-Lusztig forniscono una formula esplicita per
calcolare il carattere delle rappresentazioni con peso più alto di
un'algebra di Lie semisemplice complessa.
La dimostrazione originale di queste congetture si basa su risultati
geometrici molto profondi, fra tutti il teorema di decomposizione e la
teoria di Hodge.
In his PhD thesis, Paul Seidel found examples of symplectomorphisms which are smoothly isotopic to the identity, but not isotopic to the identity within the symplectomorphism group.
Abstract: New developments concerning the relationships between species trees, representing the branching histories of populations of organisms, and gene trees, which represent the histories of individual genomic regions, have generated new combinatorial structures. These include “coalescent histories” and “ancestral configurations”, structures that for a given gene tree topology and species tree topology encode the different evolutionary configurations of the gene tree in the branches of the species trees.