In this talk, I will talk about some recent well-posedness and stability results for several fluid models in 2D. More precisely, I will discuss the global well-posedness for the 2D…
In volume-constrained capillarity problems, minimizers may have free boundaries adhering to the container. Recent work in the study of capillarity problems has utilized stability theory for the volume-constrained isoperimetric problem…
In this talk, we discuss second-order optimality conditions for optimal control problems. This analysis is very important when we study the stability of the solution to the control problem with…
Over the past three decades, a fruitful approach for analysis and data-driven modeling of dynamical systems has been to consider the action of (nonlinear) dynamics in state space on linear…
Zoom Meeting: https://ncsu.zoom.us/j/93046132033?pwd=dkZiTjlKazgzK2Q3aXJra1g2R1Q0dz09 Meeting ID: 930 4613 2033 Passcode: 075251
In several shape optimization problems one has to deal with cost functionals of the form ${\cal F}(\Omega)=F(\Omega)+kG(\Omega)$, where $F$ and $G$ are two shape functionals with a different monotonicity behavior…
Linear complementarity problems (LCP) generalizes some fundamental problems of mathematical optimization like linear programming (LP) problem, linearly constrained quadratic programming (LQP) problem and some others. It admits an enormous number…
Inverse problems are an expanding field with many practical applications in scientific computing and engineering. Their Bayesian enhancement encodes prior knowledge and data uncertainties into a posterior. This is an…
Simulating the time evolution of a Hamiltonian system on a classical computer is hard—the computational power required to even describe a quantum system scales exponentially with the number of its…
Recently, single-cell transcriptomics has provided a powerful approach to investigate cellular properties in unprecedented resolution. However, given a small number of temporal snapshots of single-cell transcriptomics, how to connect them…
Petersen and Tenner defined the depth statistic for Coxeter group elements which, in the symmetric group, can be described in terms of a cost-minimization problem over the factorizations of a…
I will describe how an invariant measure with Cauchy-distributed marginals arises from a supercritical stochastic heat equation with an additional, independent additive noise. Joint work with Chiranjib Mukherjee. Zoom meeting: Link
Once per semester, the Teaching and Learning Seminar will host 10-minute "lightning talks" in which graduate students and/or faculty members will talk about some element of their teaching that they'd…
Deep neural networks (DNNs) have been a successful model across diverse machine learning tasks, increasingly capturing the interest for their potential in engineering problems where PDEs have long been the…
Schoen-Yau proved the spacetime positive energy theorem by reducing it to the time-symmetric (Riemannian) case using the Jang equation. To acquire solutions to the Jang equation, they introduced a family of regularized equations and took the limit of regularized solutions,…
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…
Zoom Meeting: https://ncsu.zoom.us/j/93046132033?pwd=dkZiTjlKazgzK2Q3aXJra1g2R1Q0dz09 Meeting ID: 930 4613 2033 Passcode: 075251