## Index Theory and Flexibility in Positive Scalar Curve Geometry

## Stability of the Positive Mass Thm

## How to Test String Theory

## Asymptotic spectra and their applications II

Matrix rank is well-known to be multiplicative under the Kronecker product, additive under the direct sum, normalized on identity matrices and non-increasing under multiplying from the left and from the right by any matrices. In fact, matrix rank is the only real matrix parameter with these four properties.

## Notions of Scalar Curvature

## Proto-Neutron Star Winds: Supernova Diversity, Magnetars, and Heavy Element Nucleosynthesis

The mechanism of the explosion of massive stars remains uncertain. I will

discuss aspects of the critical condition for explosion, the observed

supernova diversity, and the connection to gamma-ray bursts and

super-luminous supernovae. I will focus on the first few seconds after

explosion, during the "proto-neutron star" cooling epoch, when a wind

driven by neutrino heating emerges from the cooling neutron star into the

overlying massive stellar progenitor, powering the explosion. I will

## Breaking the Circuit-Size Barrier in Secret Sharing

Based on joint work with Tianren Liu and Hoeteck Wee.

## Critical Hoelder exponents

## Introduction to Scalar Curvature and Convergence