## Index Theory and Flexibility in Positive Scalar Curve Geometry

Bernhard Hanke

Augsburg University

October 18, 2018

Lan Hsuan Haung

IAS

October 17, 2018

Thomas Rudelius

October 17, 2018

Jeroen Zuiddam

Member, School of Mathematics

October 16, 2018

These two talks will introduce the asymptotic rank and asymptotic subrank of tensors and graphs - notions that are key to understanding basic questions in several fields including algebraic complexity theory, information theory and combinatorics.

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.

Mikhail Gromov

IHES

October 16, 2018

Todd Thompson

Ohio State University & Institute for Advanced Study

October 16, 2018

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

Vinod Vaikuntanathan

MIT

October 15, 2018

We will describe a recently discovered connection between private information retrieval and secret sharing, and a new secret-sharing scheme for general access structures that breaks a long-conjectured exponential barrier.

Based on joint work with Tianren Liu and Hoeteck Wee.

Camillo De Lellis

Professor, School of Mathematics

October 15, 2018

Christina Sormani

IAS

October 15, 2018

James Pascaleff

University of Illinois, Urbana-Champaign

October 15, 2018

A symplectic Lie groupoid is a Lie groupoid with a

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.

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.