In this talk we present both numerical analysis and experiments to study a few basic computational issues in practice: (1) the numerical error one can achieve given a finite machine…
Consider a dense Erdös-Rényi random graph with parameters n and p, with p fixed in (0,1). Let H_n(p) be the hitting time between two distinct vertices: run simple random walk from…
PyOED is a highly extensible scientific package that enables developing and testing model-constrained optimal experimental design (OED) for inverse problems. Specifically, PyOED aims to be a comprehensive Python toolkit for…
This talk will focus on point-cloud data, their analysis and biological applications in which they naturally arise. In particular, I will introduce "optimal transport", which has evolved as one of…
Consider the affine Lie algebra $\mathfrak{g}$ associated with the simple Lie algebra $sl(n)$ consisting of $n\times n$ trace zero matrices over the field of complex numbers. For every dominant integral…
A hollow vortex is a region of constant pressure bounded by a vortex sheet and suspended inside a perfect fluid; we can think of it as a spinning bubble of…
Physics-Informed Neural Networks (PINNs) have received much attention recently due to their potential for high-performance computations for complex physical systems, including data-based computing, systems with unknown parameters, and others. The…
We investigate the long-time behavior and stationary fluctuations of an infinite-dimensional rank-based diffusion process, called the Atlas model, where particles move as independent Brownian motions, with the lowest ranked particle…
Speaker's website Zoom Link
Speaker’s webpage: https://spdaugherty.github.io/
We will consider various models in hydrodynamic, including the 2d Navier-Stokes, Boussinesq equations, and a Brinkman-Forchheimer-Navier-Stokes equations in 3d. These models are driven by an external stochastic Brownian perturbation. We…
Desmos Activity Builder is an online tool that can be used in a variety of ways in and out of the classroom. It can be used to introduce concepts or…
The structure of algebras of differential invariants, particularly their generators, is based on the symbolic invariant calculus provided by the method of equivariant moving frames. I will discuss a new…
Global sensitivity analysis (GSA) offers a flexible framework for understanding the structural importance of uncertain parameters in mathematical models. This dissertation focuses on forward and inverse problems arising in uncertainty…
This talk will be in person in Cox 306 where snacks and refreshments will be provided, there will also be a virtual option for those who cannot attend in person. Speaker's website…
We show how to use continued fraction representations of 2-bridge knots to compute the average value of different invariants of the set of 2-bridge knots with fixed crossing number c.…
In this talk we define a new category of matroids, by working on matroid polytopes and rank preserving weak maps. This lets us introduce the concept of categorical valuativity for…