Accurate estimation of microseismic events (small earthquakes) generated during hydraulic fracturing of low permeability rocks such as shale enables important characterization of hydraulic fracture networks. Determining the orientation of the fracture is important in characterizing the effectiveness of the stimulation process. We consider the source as separable in time and space and invert for a…
The finite minuscule and d-complete posets generalize Young and shifted Young diagrams. They have many nice combinatorial properties; for example, minuscule posets are Gaussian and Sperner, and d-complete posets have the hook length and jeu de taquin properties. Infinite analogs of the colored minuscule posets were used by R.M. Green to construct representations of many…
Poro-elastic and poro-visco-elastic models describe fluid flow through porous, deformable media. They are relevant in many applications in bioengineering and medicine, such as tissue perfusion and fluid flow inside cartilages and bones. In this talk, I will discuss the application of these models specifically to optical perfusion and its relation to glaucoma, as well as…
Geophysical seismic exploration, as well as radar and sonar imaging, require the solution of large scale forward and inverse problems for hyperbolic systems of equations. In this talk, I will show how model order reduction can be used to address some intrinsic difficulties of these problems. In model order reduction, one approximates the response (transfer…
Inspired by Bar-Natan's description of Khovanov homology, we discuss thin posets and their capacity to support homology and cohomology theories which categorify rank-statistic generating functions. Additionally, we present two main applications. The first, a categorification of certain generalized Vandermonde determinants gotten from the Bruhat order on the symmetric group by applying a special TQFT to…
In fibroblasts responding to gradients of platelet-derived growth factor (PDGF), an important chemoattractant in development and wound healing, signaling through the phospholipase C (PLC)/protein kinase C (PKC) pathway proved necessary for chemotaxis, whereas pathways that collaborate to activate the Arp2/3 complex were found to be dispensable. PKC is activated through its binding to the lipid…
This talk focuses on differential problems describing the flow of a viscous fluid in deformable domains. Such problems include flow in compliant tubes, often adopted for the modeling of arterial blood flow, and flow through deformable porous media, often adopted for the modeling of tissue perfusion. The mixed hyperbolic-parabolic-elliptic nature of these systems guides the…
Anticipating abrupt changes in ecosystem state is key for ecosystem management and preservation. Detailed knowledge of ecological mechanisms behind a critical transition is often difficult to attain, and the theory of resilience - assessment of the ability of a system to withstand disturbances - provides a pathway to circumvent this problem. Loss of system resilience…
Target Audience: Third, Fourth, and Fifth Years
Multiline queues were introduced by Ferrari and Matrin as a tool for understanding the steady state of the Totally Asymmetric Simple Exclusion Process (TASEP) on a ring. Since then, they have attracted independent interest as combinatorial objects. A queue can be described as a transformation of words by a combinatorial rule (related to the Lascoux-Schützenberger action of the symmetric group). A…
We address global sensitivity analysis for models with high-dimensional inputs and function-valued (functional) outputs. Variance-based global sensitivity approaches based on Sobol' indices have been proven useful in a wide range of outputs. However, Sobol' indices can be challenging to compute for computationally intensive models with a large number of parameters. We propose derivative based global…
The Gordian distance between two knots is the fewest number of crossing changes necessary to transform one knot into the other. Khovanov homology is a categorification of the Jones polynomial that comes equipped with several spectral sequences. In this talk, we show that the page at which some of these spectral sequences collapse gives a…
Gene expression is a biochemical process driven by the chance collisions of molecules, which can result in strong stochastic signatures and cell-to-cell variability in gene network dynamics (e.g. oscillation). Biological oscillators co-exist in the same cell and can interact directly or indirectly through shared resources. Our lab uses modeling and experiments to understand how these…
The still open topological surgery conjecture for 4-manifolds is equivalent to the statement that all good boundary links are freely slice. In this talk, I will show that every good boundary link with a pair of derivative links on a Seifert surface satisfying a homotopically trivial plus assumption is freely slice. This subsumes all previously…
This talk will be devoted to a fundamental question on the compactness of sets of solutions. The key concept in this study is the Kolmogorov epsilon-entropy which is the logarithm of the minimum number of elements in an epsilon-covering of a given (totally bounded) set. I will use this concept to provide a sharp estimate…
In this talk, we analyze nonlinear differential equations subject to generalized boundary conditions. More specifically, I will provide a framework from which we can provide conditions, which are straightforward to check, for the solvability of a large number of nonlinear scalar boundary value problems. I will begin by giving the general strategy which involves a reformulation of our…
This will be the first seminar in the SIAM Industry series, which is focused on presenting information about research opportunities in business, industry, and government jobs. Speakers will discuss their career paths and speak on projects they have worked on at their current industrial institution. The DOE Exascale Computing Project (ECP), a collaborative effort between…