Guest lectures and seminars - Page 4
A liquid droplet placed on a rigid, planar surface has a captivating simplicity: its surface is a spherical cap and remains in equilibrium. In this talk, I’ll show that the addition of a deformable boundary leads to a range of new phenomena: evaporating droplets with an elastic skin may develop flat tops, but even without a complex rheology, reaching equilibrium can happen slowly, with the droplet’s contact ageing. I will discuss two specific examples, presenting a combination of theory and experiment for each.
The theory of flexible plates can be applied to models of floating solar panels. When wet, the structure vibrates with lower frequencies than when in vacuo. Our study is concerned with thin rectangular porous plates with free edge conditions in three dimensions exposed to incoming waves. We develop a complete hydrodynamical theory of the wave-flexible-structure interaction including the coupled radiation-diffraction problem. The formulation leads to a set of integral equations for the potentials on the wetted side of the plate. The Green function in three dimensions is implemented along the floating geometry. We use the beam method for the displacement of the rectangular free plate. A variational equation is minimized for the solutions of the interaction problem
Note the non-standard start time!
Abstract: We consider mirror pairs of Calabi-Yau hypersurfaces X and X’ in toric varieties associated to dual reflexive polytopes. We will give a proof through tropical geometry that the Hodge numbers of X and X’ are mirror symmetric. The proof goes by considering tropical homology, and works over the ring of integer numbers. In particular, we can use our spectral sequence with Kris Shaw to explore the connections between the topology of the real part of X and cohomological operations on X’.
This is based on joint work with Diego Matessi.
C*-algebra seminar by Sergey Neshveyev.
Structural equation models are simultaneous equation regression models, whose variables are latent, and measured via a confirmatory factor model (that is, with measurement error and repeated measurements). When the functional form of the simultaneous equation system is unknown, it has previously been observed in simulations that factor scores inputted into non-parametric regression methods approximate the true functional form. Factor scores estimate the latent variables (per person), and several types exist. We provide a theoretical (though population-based) analysis of this procedure, and provide assumptions under which it is theoretically justified in using Bartlett factor scores, which are simple linear transformations of the data. In simulations, we compare this suggestion to an already available though understudied non-linear and computationally heavy procedure, and observe that the simple Bartlett approach appears to work better.