Providing equitable access to education involves academic disability accommodations. Alison will discuss the barriers to college students receiving their school-approved disability accommodations in math classrooms.

I will review two combinatorial constructions of integrable systems: Goncharov-Kenyon construction based on counting perfect matchings in bipartite graphs, and Gekhtman-Shapiro-Tabachnikov-Vainshtein construction based on counting paths in networks. After that I will outline the proof of equivalence of those constructions. The talk is based on my recent preprint arXiv:2108.04975.

We use techniques from Iwasawa theory to study the growth of the
Mordell Weil group and Tate-Shafarevich groups of elliptic curves in cyclic
extensions of prime degree. This is joint work with Lea Beneish and
Debanjana Kundu.

This talk concerns a hyperbolic model of cell-cell repulsion with a dynamics in the population of cells. More precisely, we consider a population of cells producing a field (the ''pressure'') which induces a motion of the cells following the opposite of the gradient. The field indicates the local density of population and we assume that cells try to avoid crowded areas and prefer locally empty spaces which are far away from the carrying capacity. We analyze the well-posedness property of the associated Cauchy problem on the real line. We start from bounded initial conditions and we consider some invariant properties of the initial conditions such as the continuity, smoothness and monotony. We also describe in detail the behavior of the level sets near the propagating boundary of the solution and we find that an asymptotic jump is formed on the solution for a natural class of initial conditions. Finally, we prove the existence of sharp traveling waves for this model, which are particular solutions traveling at a constant speed, and argue that sharp traveling waves are necessarily discontinuous. This analysis is confirmed by numerical simulations of the PDE problem.

This is a joint work with Xiaoming Fu and Pierre Magal.

Please join us (and bring your questions!) for a wide-ranging discussion with NREL, regarding:

•           Research at NREL

•           Opportunities for grad students!

•           The day-to-day of internships at NREL

•           Prospects/Results from internships with NREL

•           Where to find more information and apply!

Place: Zoom:   https://arizona.zoom.us/j/82075792519 
Password:  150721

Each speaker will give a 20 minute talk, with 5 minutes for questions.  Full titles and abstracts to be announced. 

We examine the problem of real-time optimization of networked systems and develop online algorithms that steer the system towards the optimal system trajectory. Zero-order algorithms are considered, wherein the primal step that involves the gradient of the objective function (and hence requires networked systems model) is replaced by its zero-order approximation with two function evaluations using a deterministic perturbation signal. The evaluations are performed using the measurements of the system output, hence giving rise to a feedback interconnection, with the optimization algorithm serving as a feedback controller. We provide insights on the stability and tracking properties of this interconnection. Finally, we apply this methodology to a real-time optimal power flow problem in power systems, for reference power tracking and voltage regulation.

We are witnessing a revolutionary transition of energy infrastructure around the world. As infrastructure systems transform, they will be required to deliver critical services reliably, resiliently, securely, affordably, and in an environmentally responsible fashion. Additionally, advances in computation and connectivity have enabled emerging opportunities and challenges for system integration to support these requirements of modern infrastructure. Infrastructure modernization is disrupting the status quo of markets, planning, and operational procedures. NREL strives to address these challenges and help evaluate and understand energy infrastructure transformation across a broad technology landscape through the development and analysis of leading-edge modeling tools, solution methods, and datasets. This presentation will showcase key NREL modeling and analysis activities focusing on NRELs open-access datasets and a new suite of open-source infrastructure system models.

Each speaker will give a 20-minute talk, with 5 minutes for questions.  Full titles and abstract are to be announced. 

What do ultra-secure communications, a longstanding open problem in operator algebra and boson sampling have in common? These are all problems that are solved using quantum techniques.  In this colloquium aimed at a general mathematical audience, we discuss how quantum information resembles more a physical object than a digital one, and how this translates to a method for unforgeable money and ultra-secure communications. We then link this to quantum interactive proofs, the study of which have recently led to the unravelling of a 50-year old mathematical puzzle called the Connes embedding problem. Finally, we present boson sampling as the first ever demonstration of a computational advantage of quantum computers over conventional ones.

The recursive structure of butterfly matrices has been exploited to accelerate common methods in computational linear algebra. Recent interest in butterfly matrices has spiked in the machine learning and AI communities, where butterfly structures have been integrated into architecture used in learning fast solvers for large linear systems and in image recognition. These growing applications have often eclipsed the mathematical understanding on how or why butterfly matrices are able to accomplish these tasks. I will focus on the particular application to remove the need for pivoting in Gaussian elimination. I will explore the impact of preconditioning a linear system by butterfly matrices on the growth factor, which controls the numerical stability of Gaussian elimination. These results will be compared to other common methods found in randomized linear algebra.

 Reduced-order models of time-dependent partial differential equations (PDEs) where the solution is assumed as a linear combination of prescribed modes are rooted in a well-developed theory. However, more general models where the reduced solutions depend nonlinearly on time-dependent variables have thus far been derived in an ad hoc manner. I introduce Reduced-order Nonlinear Solutions (RONS): a unified framework for deriving reduced-order models that depend nonlinearly on a set of time-dependent variables. The set of all possible reduced-order solutions are viewed as a manifold immersed in the function space of the PDE. The variables are evolved such that the instantaneous discrepancy between reduced dynamics and the full PDE dynamics is minimized. This results in a set of explicit ordinary differential equations on the tangent bundle of the manifold. In the special case of linear parameter dependence, our reduced equations coincide with the standard Galerkin projection. Furthermore, any number of conserved quantities of the PDE can readily be enforced in our framework. Since RONS does not assume an underlying variational formulation for the PDE, it is applicable to a broad class of problems.

Thermodynamics provides a robust conceptual framework and set of laws that govern the exchange of energy and matter. Although these laws were originally articulated for macroscopic objects, nanoscale systems also exhibit “thermodynamic¬-like” behavior – for instance, biomolecular motors convert chemical fuel into mechanical work, and single molecules exhibit hysteresis when manipulated using optical tweezers. To what extent can the laws of thermodynamics be scaled down to apply to individual microscopic systems, and what new features emerge at the nanoscale? I will describe some of the challenges and recent progress – both theoretical and experimental – associated with addressing these questions.  Along the way, my talk will touch on non-equilibrium fluctuations, “violations” of the second law, the thermodynamic arrow of time, nanoscale feedback control, strong system-environment coupling, and quantum thermodynamics.

Each speaker will give a 30 minute talk with 5 minutes for questions at the end.  Full title and abstracts are to be announced.

Hybrid: Math, 501 and Zoom https://arizona.zoom.us/j/86997964863     Password:   Locute

I will report a joint work with Tong, concerning the structure of a certain submodule inside prismatic cohomology of a smooth proper scheme over a p-adic ring of integers. I will explain how this part of prismatic cohomology causes various pathologies, then say a few corresponding consequences of our structural result. If time permits, I shall also mention an interesting example.