## dS/dS and T\bar T

Eva Silverstein

September 24, 2018

Eva Silverstein

September 24, 2018

Andrea Malchiodi

SISSA

October 2, 2018

We consider the classical problem of prescribing the scalar curvature of a manifold via conformal deformation of the metric, dating back to works by Kazdan and Warner. This problem is mainly understood in low dimensions, where blow-ups of solutions are proven to be "isolated simple". We find natural conditions to guarantee this also in arbitrary dimensions, when the prescribed curvatures are Morse functions. As a consequence, we improve some pinching conditions in the literature and derive existence

results of new type. This is joint work with M. Mayer.

Avi Wigderson

Herbert H. Maass Professor, School of Mathematics

October 2, 2018

Tensors occur throughout mathematics. Their rank, defined in analogy with matrix rank, is however much more poorly understood, both from a structural and algorithmic viewpoints.

Robin Neumayer

Northwestern University; Member, School of Mathematics

October 1, 2018

Viswambhara Makam

University of Michigan; Member, School of Mathematics

October 1, 2018

Guy Moshkovitz

Member, School of Mathematics

October 1, 2018

Dor Minzer

Tel Aviv University; Member, School of Mathematics

October 1, 2018

Marco Méndez Guaraco

University of Chicago; Member, School of Mathematics

October 1, 2018

Jacob Matherne

Member, School of Mathematics

October 1, 2018

Ángel Martínez Martínez

Universidad Autónoma de Madrid; Member, School of Mathematics

October 1, 2018