I am going to present the dichotomy conjecture for CSPs of certain infinite templates, motivate this conjecture, and provide a rough overview of what we know about it.
We discuss mild solutions to the Navier-Stokes equation on the n-dimensional hyperbolic space . Substantial results have been already obtained by Pierfelice. In this talk, we show how to extend the rest of the Fujita-Kato theory of mild solutions from to . This includes well-posedness results for and initial data for , global in time results for small initial data, and decay results for both u and . As part of this, we discuss extending to the hyperbolic space known facts in Euclidean space concerning the strong continuity and contractivity of the semigroup generated by the Laplacian. This work, together with Pierfelice’s, contributes to providing a full theory for mild solutions on . This a thesis defense.
Well-Posedness and Global in Time Behavior for Mild Solutions to the Navier-Stokes Equation on the Hyperbolic Space with Initial Data in
Mar. 18, 2021 11am (Zoom)
Noncomm Geometry
Stefano D'Alesio (ETH Zurich)
X
In this talk, using Van den Bergh' double Poisson structures, I will propose a procedure for noncommutative Poisson reduction, starting from noncommutative Hamiltonian spaces and applying a derived version of `classical' noncommutative Poisson reduction. Working out an example of V. Ginzburg, instead of considering quotients by two-sided ideals generated by noncommutative gauge elements, we lift these to elements in higher homological degrees and introduce a differential to form an analogue of the Koszul complex, and then introduce noncommutative analogues of the BRST generators. I will explain how this is the noncommutative counterpart of the classical BRST complex for representation schemes. The main examples are moduli spaces of representation of quivers, such as Nakajima quiver varieties. Further research possible is to elaborate a noncommutative derived version of quasi-Poisson reduction, with applications to the moduli spaces of flat connections on Riemann surfaces.
