Previous Conferences & Workshops

Abstract: For surfaces immersed into a compact Riemannian manifold, we consider the curvature functional given by the $L^2$ integral of the second fundamental form. We discuss an an area bound in terms of that functional, with application to the...

Abstract: We present new-curvature one-cycle sweepout estimates in Riemannian geometry, both on surfaces and in higher dimension. More precisely, we derive upper bounds on the length of one-parameter families of one-cycles sweeping out essential...

Abstract : It is a joint work with G. Courtois, S. Gallot and A.Sambusetti. We prove a compactness theorem for metric spaces with anupper bound on the entropy and other conditions that will be discussed.Several finiteness results will be drawn. It...

The study of the planar-circular-restricted 3-body problem led to Poincaré's "last geometric theorem", nowadays known as the Poincaré-Birkhoff theorem. It is a fixed point theorem for certain area-preserving annulus homeomorphisms. Birkhoff's proof...

Abstract: For a given finite subset S of a compact Riemannian manifold (M; g) whose Schouten curvature tensor belongs to a given cone, we establish a necessary and
sufficient condition for the existence and uniqueness of a conformal metric on $M...

Abstract: It is a basic open question in geometric measure theory to understand regularity of a stationary integral varifold. Even a.e. regularity remains an open question. The central issue is analyzing the varifold near a point Z with a tangent...

The (stochastic) gradient descent and the multiplicative update method are probably the most popular algorithms in machine learning. We introduce and study a new regularization which provides a unification of the additive and multiplicative updates...