Guest lectures and seminars - Page 15
Active solids consume energy to allow for actuation and shape change not possible in equilibrium. In this talk, I will focus on the elasticity of systems as wide-ranging as far-from-equilibrium hydrogels, nanoparticles, and mechanical structures composed of active robotic components. First, I will introduce our recent work on hydrogel spheres being lowered onto a hot plate. As the bottom vaporises, the resulting flow couples tightly to elastic deformations within the sphere, giving either spontaneous bouncing or steady-state floating as manifestations of the so-called elastic Leidenfrost effect. I will present theory and simulations of the floating case, which demonstrate a remarkable phenomenon: the heavier the solid, the higher it floats. I will then discuss the general competition between active boundary stresses and an elastic bulk, giving rise to so-called active elastocapillarity. Finally, I will discuss our current work on using non-reciprocal interactions in active elastic media to program robust mechanical actuation and locomotion. In each case, our results provide theoretical underpinning for recent experimental advances, and point to the design of novel soft machines.
I will discuss the “geometric method” for syzygies and discuss applications to the study of tautological bundles of linear spaces. From this, I will explain how to pass from realizable matroids to all matroids via initial degenerations. This is joint work in progress with Alex Fink and Chris Eur.
A finite graph determines a Kirchhoff polynomial, which is a squarefree, homogeneous polynomial in a set of variables indexed by the edges. The Kirchhoff polynomial appears in an integrand in the study of particle interactions in high-energy physics, and this provides some incentive to study the motives and periods arising from the projective hypersurface cut out by such a polynomial.
From the geometric perspective, work of Bloch, Esnault and Kreimer (2006) suggested that the most natural object of study is a polynomial determined by a linear matroid realization, for which the Kirchhoff polynomial is a special case.
I will describe some ongoing joint work with Delphine Pol, Mathias Schulze, and Uli Walther on the interplay between geometry and matroid combinatorics for this family of objects.
QOMBINE seminar by Roy Araiza (University of Illinois Urbana-Champaign)