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Applied Math Graduate Student Seminar: Harley Hanes, NC State, Boundary Penalties, Sensitivity Equation Projection, and Optimal Sample Identification in Reduced-Order Models

SAS 4201

Reduced-order models (ROMs) are a critical tool for sensitivity analysis, parameter inference, and uncertainty quantification where high-fidelity models would be computationally intractable. Galerkin POD-ROMs are one particular class of ROMs which project high-fidelity model equations onto a set of model solutions to construct ROMs retaining original model parameters and physics, enabling accurate sensitivity analysis, parameter inference,…

Biomathematics Seminar: Jichun Xie, Duke, Disentangling Cellular Heterogeneities and Activities from the Topology Structures of Single-cell Co-expression Graphs

Cox 306

Gene co-expression graphs are a rich source of information, revealing critical insights into cellular functions, states, and activities. Yet, extracting meaningful signals from these graphs presents a formidable challenge. This complexity arises due to the presence of multiple, overlapping sources of information and the inherent noise, which is particularly pronounced in data derived from single-cell…

Geometry and Topology Seminar: Salem Selim, UC Irvine, Partial data inverse problems for magnetic Schrödinger operators with potentials of low regularity.

SAS 4201

In this talk we discuss partial data inverse boundary problems for magnetic Schrödinger operators on bounded domains in the Euclidean space as well as some Riemannian manifolds with boundary. In particular, we show that the knowledge of the set of the Cauchy data on a portion of the boundary of a domain in the Euclidean…

Algebra and Combinatorics Seminar: Emily Barnard, DePaul University, Pop-stack sorting and pattern-avoiding permutations

SAS 4201

The pop-stack sorting method takes an ordered list or permutation and reverses each descending run without changing their relative positions. In this talk we will review recent combinatorial results on the pop-stack sorting method, and we will extend the pop-stack sorting method to certain pattern avoiding permutations, called c-sortable. If time permits, we will describe…

Nonlinear Analysis Seminar and Differential Equation Seminar: Hung Tran, University of Wisconsin Madison, Periodic homogenization of Hamilton-Jacobi equations: some recent progress

Zoom

I first give a quick introduction to front propagations, Hamilton-Jacobi equations, level-set forced mean curvature flows, and homogenization theory. I will then show the optimal rates of convergence for homogenization of both first-order and second-order Hamilton-Jacobi equations. Based on joint works with J. Qian, T. Sprekeler, and Y. Yu. Zoom meeting: Link

Computational and Applied Mathematics Seminar: Wenjing Liao, Georgia Institute of Technology, Exploiting Low-Dimensional Data Structures in Deep Learning

SAS 4201

In the past decade, deep learning has made astonishing breakthroughs in various real-world applications. It is a common belief that deep neural networks are good at learning various geometric structures hidden in data sets. One of the central interests in deep learning theory is to understand why deep neural networks are successful, and how they…

Nonlinear Analysis Seminar and Differential Equation Seminar: Jameson Graber, Baylor University, The Master Equation in Mean Field Game Theory

Zoom

Mean field game theory was developed to analyze Nash games with large numbers of players in the continuum limit. The master equation, which can be seen as the limit of an N-player Nash system of PDEs, is a nonlinear PDE equation over time, space, and measure variables that formally gives the Nash equilibrium for a given…

Stochastics Seminar: Grigory Terlov, UNC-Chapel Hill, Random optimization problems at fixed temperatures

SAS 4201

We consider a class of disordered mean-field combinatorial optimization problems, focusing on the Gibbs measure, where the inverse temperature does not vary with the size of the graph and the edge weights are sampled from a general distribution. We prove Central Limit Theorems for the log-partition function, the weight of a typical configuration, and the…

Applied Math Graduate Student Seminar: Julia Sanger, NC State, Modeling interactions between platelet-like particles and fibrin matrix for wound healing applications

SAS 4201

In wound healing applications, platelet-like particles (PLPs) are engineered biomaterials that aim to mimic the behavior of natural platelets. Platelets play an essential role in the successful formation of the extracellular fibrin matrix in blood clots, aiding in both fibrin polymerization and clot retraction. We consider techniques for data driven mathematical and computational modeling of…

Geometry and Topology Seminar: Tye Lidman, NC State, Cosmetic surgeries and gauge theory

SAS 4201

The famous knot complement theorem of Gordon and Luecke states that two knots in the three-sphere are equivalent if and only if the complements are homeomorphic. This was proved more than 30 years ago using combinatorial methods. In this talk, we will prove some extended results using techniques from gauge theory. If there is time…

Nonlinear Analysis Seminar and Differential Equation Seminar: Olivier Glass, Université Paris-Dauphine, Small solids in Euler flows

SAS 4201

In this talk, I will discuss the evolution of rigid bodies in a perfect incompressible fluid, and the limit systems that can be obtained as the bodies shrink to points. The model is as follows: the fluid is driven by the incompressible Euler equation, while the solids evolve according Newton’s equations under the pressure force on…

Computational and Applied Mathematics Seminar: Saviz Mowlavi, MERL, Model-based and data-driven prediction and control of spatio-temporal systems

Zoom

Spatio-temporal dynamical systems, such as fluid flows or vibrating structures, are prevalent across various applications, from enhancing user comfort and reducing noise in HVAC systems to improving cooling efficiency in electronic devices. However, these systems are notoriously hard to optimize and control due to the infinite dimensionality and nonlinearity of their governing partial differential equations…

Stochastics Seminar: Nick Cook, Duke, Branching Brownian motion and the Road-Field Model

SAS 4201

The Fisher-KPP equation was introduced in 1937 to model the spread of an advantageous gene through a spatially distributed population. Remarkably precise information on the traveling front has been obtained via a connection with branching Brownian motion, beginning with works of McKean and Bramson in the 70s. I will discuss an extension of this probabilistic…

Applied Math Graduate Student Seminar: Walker Powell, Sensitivity Analysis of Attracting Dynamical Systems via Optimal Transport of Invariant Measures

SAS 4201

Determining the sensitivity of model outputs to input parameters is an important precursor to developing informative parameter studies, building surrogate models, and performing rigorous uncertainty quantification. A prominent class of models in many applications is dynamical systems whose trajectories lie on or near some attracting set after a sufficiently long time, and many quantities of…

Colloquium: Nikolaos Kapouleas, Brown University, Minimal Surface Doublings and Their Geometry

SAS 4201

Minimal surfaces are fundamental geometric objects which have been studied intensively since the 1700's. Classes of minimal surfaces of particular interest are the complete embedded ones in Euclidean space, closed (compact boundaryless) embedded in the round three-sphere, free boundary compact embedded ones in the unit Euclidean three-ball, and self-shrinkers of the mean curvature flow. Since…

Symbolic Computation Seminar: Sriram Gopalakrishnan, Sorbonne Université, The arithmetic complexity of computing Grobner bases of determinantal systems

SAS 4201

Determinantal systems are systems of polynomial equations which encode a rank deficiency of a given matrix with polynomial entries over the solution set to other polynomial equations. Such systems arise in a number of areas of computational mathematics such as polynomial optimization, real algebraic and enumerative geometry and engineering sciences such as robotics and biology.…