We will discuss a classification of four-dimensional Riemannian manifolds \( (M^4,g)\) admitting two or more complex structures which are \(g\)-orthogonal, inducing the same orientation....
The gluing maps on the moduli space of curves are integral to much of the enumerative geometry of curves. For example, Gromov-Witten invariants satisfy recursive relations with respect to the gluing m...
I will present some rigidity theorems about cocompact CAT(0)-spaces. For instance, I will show that if a cocompact CAT(0) space is close enough to a Euclidean space, then it is isometric to it. In the...
Vertex algebras of chiral differential operators on a complex reductive group G are "Kac-Moody" versions of the usual algebra of differential operators on G. Their categories of modules are especially...
We present some recent results concerning elliptic and evolution problems driven by mixed operators, which are the sum of local and nonlocal ones under a peridynamical approach, as introduced by Silli...
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...
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...
The Thesis revolves around the interaction between projective 2-representations of 2-categories and 2-dimensional topological quantum field theories with defects. On the one hand, the language of proj...
We discuss a nonlocal fractional problem that serves as a nonlocal counterpart of the classical problem of functions of least gradient. We show how we obtain the existence of minimizers by using thei...
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...
