From swarms of swimming bacteria to the moving contents of cells, biology is replete with active systems whose microscopic constituents interact by performing mechanical work on a surrounding fluidic medium. This can lead to large-scale, sometimes functional, self-organized structures and complex dynamics. I'll overview the modeling of such systems, focusing first on continuum kinetic theories that couple the micro and macroscopic scales to describe how suspensions of active particles, such as swimming microorganisms, evolve in time. While high-dimensional (5+1) these models have been used to understand observations of novel instabilities, turbulent-like dynamics, and strange rheology, and have been incorporated into more complex models of biological systems. I'll then pivot to describe the emergence of large scale, spontaneously appearing transport flows in developing egg cells. Building on a conception of molecular motors carrying payloads on a flexible polymer assembly, I'll develop an active porous medium model whose instabilities naturally drive the system towards large-scale "twister" flows consistent with experiments.

Bio:  Dr. Michael J. Shelley is an applied mathematician who works on the modeling and simulation  of complex systems arising in physics and biology. He is the Lyttle Professor of Applied Mathematics at the Courant Institute, co-founder of the Courant Institute's Applied Mathematics Lab, and is the Director of the Center for Computational Biology at the Flatiron Institute.  He holds a B.A. in mathematics from the University of Colorado and a Ph.D. in applied mathematics from the University of Arizona. He was a postdoctoral researcher at Princeton University and a member of the mathematics faculty at the University of Chicago before joining NYU. Shelley has received the François Frenkiel Award from the American Physical Society and the Julian Cole Lectureship from the Society for Industrial and Applied Mathematics, and he is a Fellow of both societies. He is also a Fellow of the American Academy of Arts and Sciences and a member of the National Academy of Sciences.
PSB = Physical Science Building
 

I will present some introductory notions of integrability and discuss their application to some important models in condensed matter physics such as the Hubbard model, the Heisenberg spin chain and the Kondo model.

Thomas Gomez ^1,2*
1University of Colorado
²National Solar Observatory
^*Hale Fellow

The equation of state (EOS) is one of the outstanding challenges in neutron star (NS) astrophysics. Accurate determination of their masses and radii will constrain the EOS of nuclear matter. There are multiple efforts underway to determine mass and radius, such as using observations of hot spot radiation being gravitationally bent around the NS. This goal can also be accomplished by measuring the spectrum of the NS directly. In dense plasmas, the widths of spectral lines are dominated by pressure broadening and can therefore be used to determine a star’s gravity. However, the high magnetic field in a NS atmosphere complicates the physics of line broadening creating competing broadening mechanisms. Theoretical developments of line broadening in high magnetic fields indicate that collisions with plasma particles exceed the broadening from the motional Stark effect from the magnetic field. Contrary to past results, this means that spectral lines from neutron star atmospheres can be used to directly determine mass and radius. Recent measurements from the Chandra X-ray telescope give us a clue as to the feasibility of this method.

After a brief introduction to soft condensed matter physics, I will describe work from my lab with colloids and liquid crystals. The colloid experiments explore novel phases, phase transition mechanisms, and relaxation in crystal films and glasses that are relevant to a broad range of hard and soft materials. In a different vein, experiments with liquid crystal drops reveal remarkable “almost biological” shape transformation behaviors.

Band theory, one of the enduring successes of the quantum revolution of the past century, has given us a purview into the physics of electrons in solids and has been extensively probed through linear response, and particularly, charge current response.

Here, I will show that nonlinear responses such as optical rectification and second harmonic generation offer a unique window into quantum observables that encode the basic elements of “quantum geometry”, a feature of multiband solids with broken symmetries. Such signals are only measurable going beyond linear response.

I will demonstrate that familiar analogues from the world of differential geometry -- curvatures and metrics – naturally appear in the nonlinear response regime and give rise to currents forbidden in linear response. As direct applications, I will present the mechanism for rectified current generation in twisted Moire superlattices, the Hall current in topological antiferromagnets, the role of quantum geometry in sliding ferroelectricity and time-reversal odd rectification in crystals.

I will conclude with an overview of the many prospective uses of the quantum geometric viewpoint on light-matter interaction, touching on how nonlinear signals can diagnose the order parameter of a topological superconductor, in a manner accessible only beyond the linear regime.