Title: Introduction to Monte Carlo methods for Advection Diffusion Abstract: My thesis work concerns analyzing how the shape of a tracer distribution in a steady pipe flow is influenced by the shape of the pipe. To numerically study this, I … Read more
Title: Low-dimensional topology and (categorified) quantum groups Abstract: We'll explore the relation between 3-dimensional topology and representation theory. More explicitly, we'll see how certain algebra (quantum groups) lead to polynomial invariants of knots, and to invariants of 3-manifolds. Motivated by … Read more
Title: A Kernel PCA-Based Adjoint Method and Its Goal-Oriented Extensions Abstract: The adjoint state method is a staple technique for efficiently computing gradients involved in numerical optimization, and continues to be applied to inverse problems in a broad array of fields … Read more
Title/Abstract
Title: Introduction to Mathematical Modeling of Plasticity Abstract: Complete mathematical formulations of plasticity are rarely taught in a formal class setting. In this lecture, I will provide a basic introduction for students who may work in modeling plasticity in the … Read more
Title: $d$-complete Posets and Representations of Lie Algebras Abstract: In the first part of this talk, I will give the definition of $d$-complete poset as well as some of the basic properties. This will be in the context of general, … Read more
Title: Reduced modeling of cell mechanics Abstract: As can be discerned by the brief overview above of the current state of experimental and computational techniques, there is considerable scope at present to provide quantitative links between atomistic scales and biological functions at … Read more
Title: Modeling Polymer Nanocomposites Abstract: Carbon Nanotubes (CNT's) are potentially extremely valuable vehicles for mechanical reinforcement in the synthesis of new materials--individual CNT's have an elastic modulus of ~1 TPa and tensile strength up to 63 GPa. In addition, they have desirable thermal and … Read more
Title: Eigenfunctions and waves for domains with corners. Abstract: I will discuss some results about the effects of corners on eigenfunctions and waves. This includes some now older results on eigenfunction concentration, some basic things about simple linear evolution equations … Read more
Title: Fluid-structure interaction for the people! Abstract: The development of fluid-structure interaction (FSI) software involves trade-offs between ease of use, generality, performance, and cost. Typically there are large learning curves when using low-level software to model the interaction of an elastic … Read more
Title: Topological Data Analysis: A Survey Abstract: With the advent of computers followed a boom in data sets; in practical terms, the growing sizes of data sets outpaced the growing computational power. This made it infeasible to analyze large data sets … Read more
Title: Surface Waves Generated by Fluid Flow Abstract: Fluid flow past an obstacle and the resulting free surface profile are considered. Special attention is paid to cases in the long wave asymptotic limit in which the Froude number is close to one … Read more
