Organized By: David Eisenbud, David Morrison, Irena Peeva A matrix factorization of an element w in a polynomial or power series ring (more generally, in a local or graded regular commutative ring) is a pair of square matrices (A, B) of the same size such that AB = BA = wE, where E is an … Read more

Organized by: Lukasz Fidkowski, Dan Freed, and Anton Kapustin Previously, phases of matter were mostly classified based on symmetry principles, or purely on the basis of topological properties. Recent developments however have highlighted the interplay of symmetry and topology as manifested by topological insulators and other symmetry protected topological (SPT) phases, and by symmetry enrichment … Read more

Organized By: Mohammed Abouzaid, Denis Auroux, Ron Donagi, Kenji Fukaya, Tony Pantev Mirror symmetry’s most spectacular predictions are those about enumerative invariants of Calabi-Yau threefolds, which exhibit intricate structures when studied for all degrees and genera. This workshop will focus on new developments whose goal is to provide a conceptual approach to the study of … Read more

Organized by Thomas Ryttov and Robert Shrock The evolution of an asymptotically free gauge theory from large Euclidean momentum in the ultraviolet (UV) to small momentum scales in the infrared (IR) is of fundamental field-theoretic importance. The evolution of the gauge coupling is described by the renormalization-group beta function. There is particular interest in the … Read more

Organized by: Dan Cristofaro-Gardiner, Richard Hind, Michael Hutchings. Despite the fundamental importance of symplectic geometry, many basic questions about it are not well understood. Quantitative symplectic geometry is concerned with closely related questions of size and time in symplectic geometry. Specifically, when can one symplectic manifold with boundary (such as a domain in ) be … Read more