## Explicit formulae for Stark Units and Hilbert's 12th problem

## Uncovering 80 Years of Research into the Near and Middle East at IAS

## 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

## Structures in the Floer theory of Symplectic Lie Groupoids

multiplicative symplectic form. We take the perspective that such an object is symplectic manifold with an extra categorical structure. Applying the machinery of Floer theory, the extra structure is expected to yield a monoidal structure on the Fukaya category, and new operations on the closed string invariants. I will take an examples-based approach to working out what these structures are, focusing on cases where the

Floer theory is tractable, such as the cotangent bundle of a compact manifold.

## 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