Based on joint work with Tianren Liu and Hoeteck Wee.
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.
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.
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