Calendar
Tuesday, October 29, 2024
Time | Items |
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All day |
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3pm |
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4pm |
10/29/2024 - 4:00pm A global section to a flow on a 3-manifold is a closed cooriented embedded surface that is positively transverse to the flow lines. A Birkhoff section is a generalization where one allows the surface to admit boundary components tangent to the flow. Using Birkhoff sections, one can convert between dynamical information of 3-dimensional flows and 2-dimensional maps. A classical result of Fried states that every transitive Anosov flow admits a Birkhoff section. The natural next question is how simple of a Birkhoff section we can find. In this talk, we discuss some recent progress on this question. Location:
KT 207
10/29/2024 - 4:00pm This is a 30min slow-pace pre-seminar discussion aiming to familiarise early-career researchers with basic ideas used in Thursday Analysis Seminar talk. The focus will be put on ideas, and technicalities are kept to a minimum. Topics include: pseudodifferential operators, paradifferential operators. Location:
KT 906
10/29/2024 - 4:30pm I will give a short review of the physics-inspired approach to Donaldson theory based on topologically-twisted four-dimensional N=2 supersymmetric quantum field theory (SQFT) as propounded by Witten in 1988, and then describe some of my recent and ongoing work. One theme in particular is a generalization of Donaldson-Witten theory to describe invariants of smooth families of smooth, closed, oriented Riemannian 4-manifolds X using methods of SQFT and supergravity, and leading to physical derivations of relevant models of equivariant cohomology. Family Donaldson invariants are cohomology classes of the classifying space of orientation-preserving diffeomorphisms, i.e., elements of H*(BDiff^+(X)), and we propose path integral formulations of their cocycle representatives. Several interesting open questions arise concerning the observables and interpretation of the invariants, calling for a renewed math-physics dialog. I hope to (re?)ignite some interest in these issues through this talk. Time permitting, I will touch upon the second theme, a new perspective of topological twisting using the notion of ‘transfer of structure group’ associated with a continuous homomorphism between topological groups. This approach accounts for the global topology of the structure group of a quantum field theory, rather than just its simply connected cover, and leads to a proposal for twisting more general four-dimensional N=2 SQFTs. The talk will be based on collaborations with G. W. Moore, M. Roček, and R. K. Singh. Location:
KT 906
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