This final talk in the series shall discuss the problem of geodesic deviation for the sub-Riemannian metric on the three-sphere, and how it relates to the problem of null geodesic deviation on the non-commutative gravitomagnetic monopole.
The calculation of optimal feedback controllers for nonlinear systems remains elusive since it requires the solution or approximation of the Hamilton-Jacobi-Bellman equations. By restricting our attention to quadratic regulator problems and polynomial systems, we are able to calculate polynomial feedback laws for systems with hundreds of states. We describe our approximation algorithm, which relies on introducing a Kronecker structure and provide examples for discretized PDEs such as Burgers, Chafee-Infante, Kuramoto-Sivashinsky, etc.
The discretization of the Euler equations of gas dynamics (“compressible hydrodynamics”) in a moving material frame is at the heart of many multi-physics simulation codes. The Arbitrary Lagrangian-Eulerian (ALE) framework is frequently applied in these settings in the form of a Lagrange phase, where the hydrodynamics equations are solved on a moving mesh, followed by a three-part “advection phase” involving mesh optimization, field remap and multi-material zone treatment.
In a series of 2-3 talks we will discuss the abelian sandpile
model (ASM for short). The ASM is a growth model in which grains of sand
are placed at the vertices of a graph, and they spread according to a
toppling rule. A site topples if its amount of sand is at least as large
as the degree of the underlying vertex, in which case it sends one grain
of sand to each neighbor.
The first talks will consist of an informal introduction to the model,
We focus this term on graph expanders, Ramanujan graphs, optimal connected graphs and Schur-convex functions, maximal and minimal complexity, networks that quickly induce brain synchrony, and number theoretic conjectures associated to Hadamard codes. We may or may not cover all this but we are in no rush. The spirit of the Seminar is to give several talks introducing the research topic, present some fundamental results, then lead to new research and open questions.
The Graphs and Networks seminar will meet Mondays at 9:30 am via Microsoft Teams.
Greg Constantine will start by giving 3 talks on classification attempts of graphs of maximal complexity. The triangle-free strongly regular graphs -- all subgraphs of the Higman-Sims graph -- are proved to be instances of such graphs of maximal complexity. A series of conjectures and some stubborn research issues will be brought to attention.
Jon Rubin will then give several talks on networks. Sevak Mkrtchyan will also present a series of talks.
In this talk, we shall present a gravitational vacuum Hamiltonian other than Schwarzschild that is invariant under SU(2), the spin group of the three-dimensional rotation group, based on the sub-Riemannian structure on the three-sphere. We will also discuss the structure of its null geodesics.
Starting in 2021, the University of Pittsburgh AWM Chapter hosts the Pitt AWM Student Seminar Series, held on the first Fridays of each month at 4:45pm. Every meeting features two 30 minute long talks by female PhD students, each presenting the speaker's research outcomes. Our seminar is hoped to give a platform to female students-researchers, to promote the spirit of collegiality and collaboration, and to recognize the hard work of students during this pandemic time.
Starting in 2021, the University of Pittsburgh AWM Chapter hosts the Pitt AWM Student Seminar Series, held on the first Fridays of each month at 4:45pm. Every meeting features two 30 minute long talks by female PhD students, each presenting the speaker's research outcomes. Our seminar is hoped to give a platform to female students-researchers, to promote the spirit of collegiality and collaboration, and to recognize the hard work of students during this pandemic time.
Starting in 2021, the University of Pittsburgh AWM Chapter hosts the Pitt AWM Student Seminar Series, held on the first Fridays of each month at 4:45pm. Every meeting features two 30 minute long talks by female PhD students, each presenting the speaker's research outcomes. Our seminar is hoped to give a platform to female students-researchers, to promote the spirit of collegiality and collaboration, and to recognize the hard work of students during this pandemic time.