Asymptotic spectra and their applications II

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.

Structures in the Floer theory of Symplectic Lie Groupoids

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.