Speaker: Spiro Karigiannis (University of Waterloo) Title: Cohomologies on almost complex manifolds and their applications Abstract: We define three cohomologies on an almost complex manifold (M, J), defined using the Nijenhuis-Lie derivations induced from the almost complex structure J and its Nijenhuis tensor N, regarded as vector-valued forms on M. One of these can be applied to distinguish non-isomorphic non-integrable […]

Speaker: Hans Lindblad (Johns Hopkins University) Title:  Global Existence and Scattering for Einstein's equations and related equations satisfying the weak null condition Abstract: Einstein's equations in harmonic or wave coordinates are a system of nonlinear wave equations for a Lorentzian metric, that in addition satisfy the preserved wave coordinate condition. Christodoulou-Klainerman proved global existence for Einstein vacuum equations for […]

Speaker: Aram Harrow (MIT) Title: Monogamy of entanglement and convex geometry Abstract: The SoS (sum of squares) hierarchy is a flexible algorithm that can be used to optimize polynomials and to test whether a quantum state is entangled or separable.  (Remarkably, these two problems are nearly isomorphic.)  These questions lie at the boundary of P, NP and the unique games […]

Speaker: Nima Arkani-Hamed (IAS) Title: Spacetime, Quantum Mechanics and Positive Geometry at Infinity