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Geometry and Topology Seminar: François Monard, UC Santa Cruz, The geodesic X-ray transform and boundary behavior

SAS 4201

On a Riemannian manifold with boundary, the X-ray transform integrates a function or a tensor field along all geodesics through the manifold. The reconstruction of the integrand of interest from its X-ray transform is the basis of important inverse problems in seismology and medical imaging. For this transform, statements of injectivity and microlocal stability in the interior of the domain were established some…

Algebra and Combinatorics Seminar: Hugh Thomas, Université du Québec à Montréal, Cyclic actions on noncrossing and nonnesting partitions

SAS 4201

Noncrossing partitions and nonnesting partitions are both counted by Catalan numbers. Noncrossing partitions on admit a natural cyclic action of order 2n, induced by the Kreweras complement. Nonnesting partitions admit a natural toggle-based action; in fact, they admit one such action for each choice of Coxeter element of the symmetric group. We prove that the latter actions all…

Special Event: Triangle Area Inverse Problems Weekend

SAS 4201

How to use mathematics to see inside something that is too large or too precious to be opened up? Would you like to learn about the mathematical theory behind medical and seismic imaging? Attend Triangle Area Inverse Problems Weekend at NC State University from Friday October 4 thru Sunday October 6 to learn more. The event is…

Applied Mathematics Graduate Student Seminar: Steven Maio, NC State, A Machine Learning Primal Heuristic for Mixed-Integer Programming

SAS 4201

Applications of machine learning (ML) in mixed-integer program (MIP) optimization is an active area of research. The human-designed heuristics used by MIP solvers rely on domain expertise and years of experience with the expectation of applicability to only a specific problem class. The underlying question is whether training can simulate expertise and experience. We consider…

Algebra and Combinatorics Seminar: John Graf, NC State, Symmetric Functions, Plethysm, and Schur’s Q-functions

SAS 4201

The Schur functions are an important basis of the ring of symmetric functions, and Schur’s Q-functions enjoy many analogous properties as a basis of the subring Gamma. We will begin by discussing various properties and bases of symmetric functions, before moving on to the comparisons between Schur functions and Schur’s Q-functions. In particular, plethysm is…

Differential Equations and Nonlinear Analysis Seminar: Silvia Villa, Università di Genova, Structured stochastic zeroth order optimization

Zoom

In the framework of black-box optimization, I will present new algorithms,  based on the stochastic estimation of the gradient via finite differences with structured directions. I will describe their convergence properties under various assumptions and show some numerical results. Speaker's website: https://www.dima.unige.it/~villa/ Zoom meeting: link

Computational and Applied Mathematics: Shixu Meng, Virginia Tech, Exploring low rank structures for inverse scattering problems

SAS 4201

Inverse problems are pivotal in a variety of applications, such as target identification, non-destructive testing, and parameter estimation. Among these, the inverse scattering problem in inhomogeneous media poses significant challenges, as it seeks to estimate unknown parameters from available measurement data. To understand the mathematics of machine learning approaches for inverse scattering, we develop a…

Quantum Groups and Representation Theory Conference

SAS Hall Lobby

Event webpage: https://sites.google.com/ncsu.edu/conf-quantum-groups-rep2024/home?pli=1   This conference is in celebration of Kailash Misra's 70th birthday.

Geometry and Topology Seminar: Amir Vig, University of Michigan, Potential Theory and Feynman Diagrams in Spectral Theory

Cox 306

In 1966, Mark Kac posed the famous question “Can you hear the shape of a drum?” Mathematically, this amounts to recovering the geometry of a Riemannian manifold from knowledge of its Laplace spectrum. In the case of strictly convex and smooth bounded planar domains, the problem is very much open. One technique for studying the…

Differential Equations and Nonlinear Analysis Seminar: Ziad Musslimani, Florida State University, Space-time nonlocal integrable systems

Zoom

In this talk I will review past and recent results pertaining to the emerging topic of integrable space-time nonlocal integrable nonlinear evolution equations. In particular, we will discuss blow-up in finite time for solitons and the physical derivations of many integrable nonlocal systems. Speaker's website: https://www.math.fsu.edu/~musliman/ Zoom meeting: link

Computational and Applied Mathematics: Jaeyong Lee, Chung-Ang University, Real-Time Solutions to PDEs with Neural Operators in SciML

SAS 4201

Recent advancements in deep learning have led to a surge in research focused on solving scientific problems under the "AI for Science." Among these efforts, Scientific Machine Learning (SciML) aims to address domain-specific data challenges and extract insights from scientific datasets through innovative methodological solutions. A particularly active area within SciML involves using neural operators…

Geometry and Topology Seminar: Saman Habibi Esfahani, Duke, Gauge theory beyond low dimensions: progress on compactness conjectures

SAS 4201

(Based on joint work with Yang Li). I will present an overview of Donaldson's program to extend the methods of gauge theory and Floer homology from 3- and 4-manifolds to higher dimensions, with a focus in this talk on Calabi-Yau 3-folds. After discussing the background material in gauge theory and Calabi-Yau geometry, I will highlight…