I will discuss a mean field game model on the synchronization of coupled oscillators, initially proposed by Yin, Mehta, Meyn, and Shanbhag, and recently examined by Carmona, Cormier, and Soner. This m...
I will discuss the rigorous derivation of hydrodynamic limits of the Boltzmann multi-species equation, for Mach and Knudsen numbers vanishing at the same rate. Solutions to the kinetic system are cons...
Building on previous work by Davis and Lück, and recent constructions of bivariant K-theory as a stable \(\infty\)-category, I will sketch the construction of a Chern character running from groupoid-e...
For a quasilinear equation involving the n−Laplacian and an exponential nonlinearity, I will discuss quantization issues for blow-up masses in the non-compact situation, where the exponential nonlinea...
Nash systems are strongly coupled systems of semilinar parabolic equations that describe closed-loop Nash equilibria in stochastic differential games. Despite existence, uniqueness and regularity for ...
The Flux Problem is a famous problem in condensed matter physics, solved by Lieb. It states that the magnetic flux through each plaquette of a square lattice in 2d (with either OBC/PBC or PBC/PBC) th...
The moduli space of cubic surfaces marked by their \(27\) lines admits multiple compactifications arising from different perspectives. By work of Gallardo-Kerr-Schaffler, it is known that Naruki’s cro...
Schrödinger-type equations model a lot of natural phenomena and their solutions have interesting and important properties. This gives rise to the search for normalised solutions, i.e., when the mass i...
