Recently Peltola and Wang introduced the multiple SLE(0) process as the deterministic limit of the random multiple SLE(kappa) curves as kappa goes to zero. They prove this result by means of a ``small kappa’’ large deviations principle, but the limiting curves also turn out to have important geometric characterizations that are independent of their relation to SLE(kappa). In particular, they show that the SLE(0) curves can be generated by a deterministic Loewner evolution driven by multiple points, and the vector field describing the evolution of these points must satisfy a particular system of algebraic equations. We show how to generate solutions to these algebraic equations in two ways: first in terms of the poles and critical points of an associated real rational function, and second via the well-known Caloger-Moser integrable system with particular initial velocities. Although our results are purely deterministic they are again motivated by taking limits of probabilistic constructions, which I will explain.

Joint work with Nam-Gyu Kang (KIAS) and Nikolai Makarov (Caltech).

Flexible fibers have a powerful role in microscopic biological phenomena. They can take the form of beating flagella that propel sperm cells and bacteria, or they can tangle into the vast, interconnected networks that make up the cellular cytoskeleton. In this talk I’ll discuss methods to numerically simulate flexible, inextensible microfilaments which are suspended in a viscous fluid; with special care taken to account for thermal fluctuations from the solvent. I’ll introduce a method where fibers are treated as a chain of beads and use it to interrogate experimental observations on magnetic filaments which are made to swim using an applied field.  I’ll present ongoing work concerning a method more suited to fiber networks, in which inextensible fiber motions are parametrized as curves on the unit sphere. After writing down a stochastic differential equation governing the fluctuating fiber dynamics in the new, constrained coordinates, I’ll discuss temporal integration schemes which linearly scale in complexity with the number of fibers.

Zoom:  https://arizona.zoom.us/j/94534134312   
Password:  “arizona” (all lower case)

Adaptation requires a new genotype to fully replace a population of individuals with different genotypes, and this replacement process imposes a cost on the population. J.B.S. Haldane quantified this cost in terms of deaths the population sustains in order for a new genotype to fully replace a population. Since populations can only sustain so many deaths per generation without going extinct, the cost imposed by natural selection sets an upper bound to the rate at which adaptation can proceed. This speed limit on adaptation is known as Haldane's Dilemma. The correct way to calculate this speed limit and whether existing populations break this speed limit or not have been the subject of a great deal of controversy and confusion. We clarify an important way to quantify the cost of natural selection in terms of reproductive excess, and explore Haldane's Dilemma and the cost of natural selection using an extensive dataset of Arabidopsis thaliana, collected by Exposito-Alonso et al. 2019.

Zoom:  https://asu.zoom.us/j/85049043960 
  

In this talk I will introduce 3 main tools: network epidemic simulations, SINDy (a model discovery tool), and the ICC curve. With these tools for simulating and analyzing epidemics, I will explore the impact of network structure on the stochastic simulations, the associated discovered models and theoretical explanations for these results. Finally, we will see what impact the structure has on the associated ICC curves and the statistical analysis.

Zoom: https://arizona.zoom.us/j/98593835992     Password: 021573

The Euler equations describe the dynamics of an inviscid and incompressible fluid on a Riemannian manifold. In this context, Arnold's structure theorem marked the birth of the modern field of Topological Hydrodynamics. This theorem provides an almost complete description of the rigid behavior of a solution whose Bernoulli function is analytic or Morse-Bott on a three dimensional manifold. However, only a few examples of such fluids exist in the literature. We will address the inverse problem to Arnold's theorem, proving a realization and topological classification theorem for non-vanishing Eulerisable flows (steady solutions for some metric) with a Morse-Bott Bernoulli function. The proofs combine the geometry of the equations for a varying metric with the theory of Hamiltonian integrable systems. Lastly, we drop the non-vanishing assumption and investigate how the topology of the ambient manifold can be an obstruction to the existence of any Bott integrable fluid for any metric.

The talk will be via Zoom at: https://utoronto.zoom.us/j/99576627828

Passcode: 448487

Since its introduction in the 1980s, the Jones polynomial and its refinements have repeatedly revolutionized knot theory. This talk will start by recalling some basic notions and questions about knots. We will then recall the Jones polynomial and some of its applications to these questions. We will then discuss two refinements of the Jones polynomial: Khovanov homology and the Khovanov spectrum, and some of their recent applications, particularly to questions at the overlap of 3- and 4-dimensional topology. Most of the talk focuses on work of other people, but part is joint with Tyler Lawson and Sucharit Sarkar.

TBA

TBA

There are two classes of interesting, at least to me, physical behavior that follow from the impossibility of integrating some formulas that involve derivatives. I learned of both of them from Tom Kane. First, systems with wheels or ice skates can conserve energy yet still act damped. This occurs despite the supposed theorem that conservative systems cannot have such stability. In fact (energy conserving) cars, flying arrows, skateboards and bicycles can have this stability. Second is the well-known possibility that a system with zero angular momentum can, by appropriate deformations, rotate without any external torque. It is not rotating, it has zero angular momentum, yet it gets rotated.  This is the falling cat problem: a cat dropped upside down can turn over.  

Both rolling contact and constancy of angular momentum are examples of  "non-integrability" of a "non-holonomic" equation. There are various simple demonstrations of these phenomena that can go bad. Cars can crash, bikes can fall over. And, in terrestrial angular-momentum experiments, various sometimes-subtle effects can swamp that which one wants to demonstrate. The talk describes the basic theory and also various simple experiments that fail various ways for various reasons.

With luck, the talk will be somewhat accessible to perky undergraduates, while still being somewhat amusing to those more technically savvy.

TBA

This event will be held at 11am.

TBA

TBA

TBA

TBA

TBA

TBA