Speaker: Jonny Evans (University College London)

Title: Unlinking and unknottedness of monotone Lagrangian submanifolds

Abstract: I will explain some recent joint work with Georgios Dimitroglou Rizell in which we use moduli spaces of holomorphic discs with boundary on a monotone Lagrangian torus in C^n to prove that all such tori are smoothly isotopic when n is odd and at least 5.

Speaker: Igor Khavkine (Utrecht University)

Title: Topology, rigid cosymmetries and linearization instability in higher gauge theories.

Abstract: We consider a class of non-linear PDE systems, whose equations possess Noether identities (the equations are redundant), including non-variational systems (not coming from Lagrangian field theories), where Noether identities and infinitesimal gauge transformations need not be in bijection. We also include theories with higher stage Noether identities, known as higher gauge theories (if they are variational). Some of these systems are known to exhibit linearization instabilities: there exist exact background solutions about which a linearized solution is extendable to a family of exact solutions only if some non-linear obstruction functionals vanish. We give a general, geometric classification of a class of these linearization obstructions, which includes as special cases all known ones for relativistic field theories (vacuum Einstein, Yang-Mills, classical N=1 supergravity, etc.). Our classification shows that obstructions arise due to the simultaneous presence of rigid cosymmetries (generalized Killing condition) and non-trivial de Rham cohomology classes (spacetime topology). The classification relies on a careful analysis of the cohomologies of the on-shell Noether complex (consistent deformations), adjoint Noether complex (rigid cosymmetries) and variational bicomplex (conserved currents). An intermediate result also gives a criterion for identifying non-linearities that do not lead to linearization instabilities.

Speaker: James Tener (UC Berkeley)

Title: Segal CFT and vertex operator algebras via bounded operators.

Abstract: I will introduce several notions of conformal field theory and discuss the relationships between them. While there are not many general theorems allowing one to move between different definitions, it is possible to do so in specific examples. I will focus on the construction of examples of CFTs in Segal's geometric picture. These CFTs will be "manifestly unitary," which will allow us to more easily make rigorous their relationship with the corresponding theories in other frameworks.

Quarterly Seminar


Topology and Geometry