Previous Special Year Seminar

I will discuss how some questions in conformal geometry can be answered using twistor theory. One such application is to the classification of locally conformally flat Hermitian surfaces. Another application is to determining the conformal...

We consider the problem of finding complete conformal metrics determined by a symmetric function of Ricci tensor in a negative convex cone on compact manifolds. A consequence of our main results is that any smooth bounded domain in Euclidean space...

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...

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...