Yoshihiro Tonegawa - Analysis on the mean curvature flow and the reaction-diffusion approximation (Part 5)

In this talk I will present a survey of the connections between canonical metrics and random point processes on a complex algebraic variety X. When the variety X has positive Kodaira dimension,

I will first discuss some earlier work on the curvature of direct images of adjoint line bundles under a smooth proper fibration, or more generally a surjective map and (maybe) some of its

(joint work with Assaf Naor) The Heisenberg group $\mathbb{H}$ is a sub-Riemannian manifold that is unusually difficult to embed in $\mathbb{R}^n$. Cheeger and Kleiner introduced a new notion of

Percolation of random nodal lines

On closed surfaces there are three basic ways to evolve a metric, by conformal change, by pull-back with diffeomorphisms and by horizontal curves, moving orthogonally to the first two types of

I will discuss a Kuranishi-type theorem for deformations of complex structure on ALE Kahler surfaces, which will be used to prove that for any scalar-flat Kahler ALE surface, all small deformations of

We show that n-manifolds with a lower volume bound v and upper diameter bound D whose curvature operator is bounded below by $-\varepsilon(n,v,D)$ also admit metrics with nonnegative curvature

Anti-de Sitter geometry is a Lorentzian analog of hyperbolic geometry. In the last 25 years a number of connections have emerged between 3-dimensional anti-de Sitter geometry and the geometry of

Sweep-out techniques in geometry and topology have recently received a great deal of attention, leading to major breakthroughs. In this talk, we will present several width estimates relying on min-max

I will discuss whether the Minkowski sum of two compact convex bodies can be made smoother by a generic rotation of one of them.  Here "generic" is understood in the sense of Baire category. The main

Our recent joint work with D. Gu established a discrete version of the uniformization theorem for compact polyhedral surfaces.   In this talk, we prove that discrete uniformizaton maps converge to

Schlenker and Krasnov have established a remarkable Schlaffli-type formula for the (renormalized) volume of a quasi-Fuchsian manifold. Using this, some classical results in complex analysis and Gromov