Symplectic capacities are symplectic invariants that measure the “size” of symplectic manifolds and are designed to capture phenomena of symplectic rigidity.

In this talk, I will focus on symplectic capacities of fiberwise convex domains in cotangent bundles. This setting provides a natural link to the systolic geometry of the base manifold. I will survey current results and discuss the variety of techniques used to compute symplectic capacities, ranging from billiard dynamics to pseudoholomorphic curves and symplectic homology. I will illustrate these techniques using disk tangent bundles of ellipsoids as an example.

TBA 

I will discuss an ongoing joint work with Luigi Appolloni and Andrea Malchiodi concerning the above objects. Minimal surfaces are critical points of the area functional, which is analytic in this case, so we should expect critical points (minimal surfaces) to be either isolated or to belong to smooth nearby minimal foliations. On the other hand, the flat plane of multiplicity two in $\mathbb{R}^3$ can be (in compact regions) approximated by a blown-down catenoid, which will converge back to the plane with multiplicity two in the limit. Hence a plane of multiplicity two cannot be thought of as being isolated, or belonging solely to a smooth family, because there are “nearby” minimal surfaces of distinct topology weakly converging to it. We will nevertheless prove that, when the ambient manifold is closed and analytic, this type of local degeneration is impossible amongst closed and embedded minimal surfaces of bounded topology: such surfaces, even with multiplicity are either isolated or belong to smooth families of nearby minimal surfaces.  

Dr Steph Foulds will talk about; 'Lazy Quantum Walks with Native Multiqubit Gates'

Quantum walks, the quantum analogue to the classical random walk, have been shown to deliver the Dirac equation in the continuum limit. Recent work has shown that 'lazy', open quantum walks can be mapped to computational methods for fluid simulation such as lattice Boltzmann method, quantum fluid dynamics, and smoothed-particle hydrodynamics. This work concerns evaluating the ability of near-term hardware to perform small, proof-of-concept quantum walks - but crucially with the inclusion of a rest state to encompass 'lazy' quantum walks, providing an integral step towards quantum walks for fluid simulation.

Neutral atom hardware is a promising choice of platform for implementing quantum walks due to its ability to implement native multiqubit gates and to dynamically re-arrange qubits. Using detail realistic modelling for near-term multiqubit Rydberg gates via two-photon adiabatic rapid passage, SPAM, and passive error, we present the gate sequences and final state fidelities for quantum walks with and without a rest state on 4 to 16-node rings. This, along with results of an error model with improved two- and three-qubit gate fidelities, leads us to conclude that a native four-qubit gate is required for the near-term implementation of interesting quantum walks on neutral atom hardware.

Please note; this talk is hosted by Rutherford Appleton Laboratory, Harwell Campus, Didcot, OX11 0QX