Mesh-free methods for boundary value problems (BVPs) can be convenient on manifolds where generating a mesh may be difficult or when the manifold is not known explicitly but is determined by data. Moreover, BVPs are important in machine learning since they provide a rigorous method of regularization for many regression problems. In this talk we…
The question of measuring "handedness" is of some significance in both mathematics and in the real world. Propellors and screws, proteins and DNA, in fact *almost everything* is chiral. Can we quantify chirality? Or can we perhaps answer the question: "Are your shoes more left-or-right handed than a potato?" We can begin with the hydrodynamic…
Zoom ID: 936 5420 1948 Password: the last four digits of the Zoom ID in reverse order
Randomized methods are becoming increasingly popular in numerical linear algebra. However, few attempts have been made to use them in developing preconditioners. Our interest lies in solving large-scale sparse symmetric positive definite linear systems of equations where the system matrix is preordered to doubly bordered block diagonal form (for example, using a nested dissection ordering).…
Mean field game PDE systems were introduced by J-M. Lasry and P.-L. Lions to describe Nash equilibria in multi-agents dynamic optimization. In the simplest model, those are forward-backward systems coupling Hamilton-Jacobi with Fokker-Planck equations. In this talk I will discuss the long time behavior of second order systems in the periodic case under suitable stability…
Dustin Kapraun attained degrees in mathematics (B.S., 1998), physics (M.S., 2002), and applied mathematics (Ph.D., 2014), all from North Carolina State University. After finishing the Ph.D., he completed two postdoctoral research appointments at the U.S. Environmental Protection Agency (EPA) National Center for Computational Toxicology, during which he developed physiologically based pharmacokinetic (PBPK) models for human…
We show that every $n \times n$ real matrix $A$ is within distance $\delta \|A\|$ in the operator norm of an $n\times n$ real matrix $A'$ whose eigenvectors have condition number $\tilde{O}(\text{poly}(n)/\delta)$. In fact, we show that with high probability, an additive i.i.d. sub-Gaussian perturbation of $A$ has this property. Up to log factors, this…
Linear extensions of posets are important objects in enumerative and algebraic combinatorics that are difficult to count in general. Families of posets like straight shapes and $d$-complete posets have hook-length product formulas to count linear extensions, whereas families like skew shapes have determinant or positive sum formulas like the Naruse hook length formula from 2014.…
High intensity (focused) ultrasound HIFU is used in numerous medical and industrial applications ranging from lithotripsy and thermotherapy via ultrasound cleaning and welding to sonochemistry. The relatively high amplitudes arising in these applications necessitate modeling of sound propagation via nonlinear wave equations and in this talk we will first of all dwell on this modeling aspect. Then…
One approach to studying symplectic manifolds with contact boundary is to consider Lagrangian submanifolds with Legendrian boundary; in particular, one can study exact Lagrangian fillings of Legendrian links. There are still many open questions on the spaces of exact Lagrangian fillings of Legendrian links in the standard contact 3-sphere, and one can use Floer theoretic…
Machine learning has blown up in popularity in the past decade, with applications from healthcare to self-driving cars, being used to create art, play video games, and act as customer service representatives. One of the most common and useful tools for these applications are neural networks: universal function approximators. This interactive workshop is meant for…
In this “something for everyone” talk, we will place the matrix decompositions that are so valuable in all fields of computation in a historical abstract context. It is well known that the singular value decomposition was discussed as far back as the 19th century by Beltrami and Jordan. Lesser known is that Cartan had a blueprint…
In this talk, I'll survey recent progress on problems in additive combinatorics, harmonic analysis, and ergodic theory related to Bergelson and Leibman's polynomial generalization of Szemer\'edi's theorem. Zoom ID: 980 3116 7550 Passcode: last 4 digits of the Zoom ID in reverse order
Counterexamples to some old-standing optimization problems in the smooth convex coercive setting are provided. Block-coordinate, steepest descent with exact search or Bregman descent methods do not generally converge. Other failures of various desirable features are established: directional convergence of Cauchy’s gradient curves, convergence of Newton’s flow, finite length of Tikhonov path, convergence of central paths,…
Congratulations, you are graduating with a PhD! You have done fantastic work in your thesis and are ready to take on the world. What is going to happen now? Should you go to industry or academia? You probably heard a lot about both job choices. In this lecture, the speakers, Andrea Klaiber-Langen and Vakhtang Putkaradze,…
Consider the geometric inverse problem: There is a set of delta-sources in spacetime that emit waves travelling at unit speed. If we know all the arrival times at the boundary cylinder of the spacetime, can we reconstruct the space, a Riemannian manifold with boundary? With a finite set of sources we can only hope to…