Previous Conferences & Workshops

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...

The dichotomy conjecture asks if every Constraint Satisfaction Problem is either in P or NP-complete. We will study the basic algorithms and reductions for such problems. We will see many (equivalent) stronger versions of this conjecture actually...

In this lecture, we will try to explain the essential ingredients in the construction of toroidal and minimal compactifications of smooth integral models of (general) PEL-type Shimura varieties, following the approaches of Faltings and Chai. Since...

Motivated by some recent progress in the study of concentration phenomena for singularly perturbed elliptic nonlinear equations and the analogies with some problems in geometric analysis, we prove existence of new entire solutions of the focusing...

We show a connection between the semidefinite relaxation of unique games and their behavior under parallel repetition. Denoting by val(G) the value of a two-prover unique game G, and by sdp(G) the value of a natural semidefinite program to...

In this lecture, we will try to explain the essential ingredients in the construction of toroidal and minimal compactifications of smooth integral models of (general) PEL-type Shimura varieties, following the approaches of Faltings and Chai. Since...

We report a recent result, due to Clozel-Harris-Labesse, Morel and the speaker, on the previous work of Clozel, Kottwitz, Harris-Taylor and Taylor-Yoshida. There are two main features in our work. One feature, which is also crucial in the other...

Let p be a prime. Let F be an algebraic closure of the finite field F_p with p elements. An integral canonical model N of a Shimura variety Sh(G,X) of Hodge type is a regular, closed subscheme of a suitable pull back of the Mumford moduli tower M...

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...