The study of hyperkaehler manifolds of lowest dimension (and of
gauge theory on them) leads to a chain of generalizations of the
notion of a quiver: quivers, bows, slings, and monowalls. This talk
focuses on bows, their representations, and...
We consider a system of NN particles evolving
according to the gradient flow of their Coulomb or Riesz
interaction, or a similar conservative flow, and possible added
random diffusion. By Riesz interaction, we mean inverse
power ss of the distance...
In 2017 Lucio Galeati understood that a suitable scaling limit
of certain hyperbolic PDEs with noise may lead to deterministic
parabolic equations. Since then, in collaboration with Lucio and
Dejun Luo, we have understood the phenomenon from several...
We consider a class of interacting particle systems with two
types, A and B which perform independent random walks at different
speeds. Type A particles turn into type B when they meet another
type B particle. This class of systems includes models...
Our study is motivated by earlier results about nodal count of
Laplacian eigenfunctions on manifolds and graphs that share the
same flavor: a normalized nodal count is equal to the Morse index
of a certain energy functional at the critical point...
We consider systems of NN particles interacting
through a repulsive potential in the Gross-Pitaevskii regime. We
prove complete Bose-Einstein condensation and we determine the form
of the low-energy spectrum, in the limit of large NN. Our