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Geometry and Topology Seminar: Marithania Silvero Casanova, Universidad de Sevilla, Positivity, fiberedness and link homology

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Khovanov homology is a link invariant which categorifies Jones polynomial. In this talk we present several results concerning Khovanov homology of fibered positive links; in particular, we extend the result by Stosic stating that braid positive links have vanishing Khovanov homology in homological grading 1. We also explore Khovanov homology of certain cable links and…

Applied Math Graduate Student Seminar:John Darges, NC State, Goal-Oriented Variance-Based Sensitivity Analysis for Uncovering Prior Hyperparameter Importance in Bayesian Inverse Problems s

SAS 4201

The formulation of Bayesian inverse problems involves choosing prior distributions; choices that seem equally reasonable may lead to significantly different conclusions. We develop a computational approach to better understand the impact of the hyperparameters defining the prior on the posterior statistics of the quantities of interest. Our approach relies on global sensitivity analysis (GSA) of…

Algebra and Combinatorics Seminar: Mark Skandera, Lehigh University, Type-BC analogs of codominant permutations and unit interval orders

SAS 4201

Permutations $w$ in $S_n$ for which the (type-A) Schubert variety $\Omega_w$ is smooth are characterized by avoidance of the patterns 3412 and 4231.  The smaller family of codominant permutations, those avoiding the pattern 312, seems to explain a lot about character evaluations at Kazhdan-Lusztig basis elements $C'_w(q)$ of the (type-A) Hecke algebra. In particular, for…

Differential Equations Seminar and Nonlinear Analysis Seminar: Weinan Wang, University of Oklahoma, Global well-posedness and the stabilization phenomenon for some two-dimensional fluid equations

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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 Boussinesq equations with fractional dissipation. For the Oldroyd-B model, we show that small smooth data lead to global and stable solutions. When Navier-Stokes is coupled…

Geometry and Topology Seminar: Daniel Weser, UNC, A Heintze-Karcher inequality with free boundaries and applications to capillarity theory

SAS 1216

 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 to classify the shape of global minimizers and (in the case without free boundary) critical points. In this talk, I will discuss joint work with…

Differential Equations Seminar and Nonlinear Analysis Seminar: Eduardo Casas Renteria, University of Cantabria, Second Order Analysis for Optimal Control Problems

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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 respect to small perturbations of the data. It is also crucial for proving superlinear or quadratic convergence of numerical algorithms for solving the problem, as…

Computational and Applied Mathematics Seminar: Dimitris Giannakis, Dartmouth, Quantum Information Science for Modeling Classical Dynamics

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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 spaces of observables. These methods leverage the linearity of the associated evolution operators, namely the Koopman and transfer operators, to carry out tasks such as…

Differential Equations and Nonlinear Analysis Seminar: Giuseppe Buttazzo, University of Pisa, Italy, Antagonistic cost functionals in shape optimization

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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 and $\Omega$ varies in the class of domains with prescribed measure. In particular, the cost functional ${\cal F}(\Omega)$ is not monotone with respect to $\Omega$…

Computational and Applied Mathematics Seminar:Tibor Illés, Corvinus University, Budapest, Hungary, Sufficient linear complementarity problems: pivot versus interior point algorithms

SAS 4201

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 of applications in economics, engineering, science, and many other fields. After all these, it is not surprising that LCPs are usually NP-complete problems (S.J. Chung,…

Applied Math Graduate Student Seminar: Abhijit Chowdhary, NC State, Scalable Sensitivity Analysis and Optimal Design for Bayesian Inverse Problems

SAS 4201

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 important tool in uncertainty quantification. However, performing uncertainty quantification tasks on top of this posterior is difficult to formulate and often computationally intractable. Hence, for…

Colloquium: Moody Chu, NC State, Optimal Hamiltonian Synthesis for Quantum Computing

SAS 4201

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 constituents, let alone integrating its equations of motion. Hamiltonian simulation on a quantum machine is a possible solution to this challenge. Assuming that a quantum…

Biomathematics Seminar: Yutong Sha, University of California Irvine, Reconstructing transition dynamics from static single-cell genomic data

Cox 306

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 to obtain their collective dynamical information remains an unexplored area. One major challenge to connecting temporal snapshots is that cells measured at one temporal point…

Algebra and Combinatorics Seminar: Joel Brewster Lewis, George Washington University, Bargain hunting in a Coxeter group

SAS 4201

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 permutation into transpositions. We generalize that cost function to the other classical (finite and affine) Weyl groups, letting the cost of an individual reflection t…