Previous Special Year Seminar

We discuss Einstein-scalar field Lichnerowicz equations on compact Riemannian manifolds from the viewpoint of existence results and stability issues. We prove that the Einstein-scalar field Lichnerowicz equation is stable when $n \le 5$, and...

After recalling the definition of $Q$-curvature and some applications, we will address the question of prescribing it through a conformal deformation of the metric. We will address some compactness issues, treated via blow-up analysis, and then...

The goal of this course to provide an introduction to Monge-Ampere-type equations in conformal geometry and their applications. The plan of the course is the following: After providing some background material in conformal geometry, I will describe...

We will discuss the introduction of the scattering operators associated with a conformal manifold by Graham and Zworski. Then we will discuss some uses of such family of operators in describing conformally invariant global quantities for conformal...

The goal of this course to provide an introduction to Monge-Ampere-type equations in conformal geometry and their applications. The plan of the course is the following: After providing some background material in conformal geometry, I will describe...

In this talk I will discuss the construction of blowing up solutions to the Yamabe Problem in high dimensions. I will show how one can use the methods of S. Brendle to produce smooth counterexamples to the Weyl Vanishing Conjecture also.

I will report on a work in progress joint with Andrei Okounkov. We extend the methods developed in an earlier work with Mirkovic and Rumynin on modular representations of semi-simple Lie algebras to representation of symplectic reflection algebras...

This talk is concerned with categorification of quantum Kac-Moody algebras and their integrable representations. First, I show how to fulfill the task by using sheaf theory. Then I will argue that the constructions could be well understood and...

It is long expected that to study the representation theory of the double loop group and the corresponding Lie algebra, the third cohomology group should play an important role. The idea is that the third cohomology classes are naturally realized...