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…
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…
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…
The trace reconstruction problem asks to reconstruct an unknown n-bit string x given independent random "traces" of x, where a random trace is obtained by first deleting each bit of…
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…
The travel time map of a compact length space with a closed measurement set takes any point of the space to the function which measures the distance from this point…
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…
During each 50-minute First Year Research Seminar, two faculty give our new graduate students a short (~20-25 minute), accessible talk about their research or research area. First Year Research Seminar…
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…
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,…
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.
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…
The Hilbert scheme of d points on a smooth variety X, denoted by Hilb^d(X), is an important moduli space with connections to various fields, including combinatorics, enumerative geometry, and complexity…
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…
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…
Given a set K in R^2 with Hausdorff dimension t \in , what can we say about a typical orthogonal projection of K? Marstrand (1954) proved that for Lebesgue almost…
(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…