Samuel Lin
Real-world software engineering tasks require coding agents that can operate on massive repositories, sustain long-horizon sessions, and reliably coordinate complex toolchains at test time. Existing research-grade coding agents offer…
We show that singular Riemannian foliations, or, more generally, manifold submetries, defined on a compact normal homogeneous space, have algebraic nature. Moreover, in this case there exists a one-to-one correspondence between algebras of…
We prove a version of Weyl's Law for the basic spectrum of a closed singular Riemannian foliation $(M,\mathcal{F})$ with basic mean curvature. In the special case of $M=\mathbb{S}^n$, this gives an explicit formula for the volume of the…
Traditional approaches to network management have been accessible only to a handful of highly-trained network operators with significant expert knowledge. This creates barriers for lay users to easily manage their networks without resorting…
Strain-level identification of viruses is critical for effective public health responses to potential outbreaks, yet current diagnostic methods often lack the necessary speed or sensitivity. Surface-enhanced Raman spectroscopy (SERS) offers…
Detecting anomalies in multivariate time series(MTS) data plays an important role in many domains. The abnormal values could indicate events, medical abnormalities,cyber-attacks, or faulty devices which if left undetected could lead to…
Let a torus $T$ act freely on a closed manifold $M$ of dimension at least two. We demonstrate that, for a generic $T$-invariant Riemannian metric $g$ on $M$, each real $\Delta_g$-eigenspace is an irreducible real representation of $T$ and,…
Considerable financial resources are allocated for measuring ambient air pollution in the United States, yet the locations for these monitoring sites may not be optimized to capture the full extent of current pollution variability. Prior…
We continue our exploration of the extent to which the spectrum encodes the local geometry of a locally homogeneous three-manifold and find that if $(M,g)$ and $(N,h)$ are a pair of locally homogeneous, locally non-isometric isospectral…
Inspired by the role geometric structures play in our understanding of surfaces and three-manifolds, and Berger's observation that a surface of constant sectional curvature is determined up to local isometry by its Laplace spectrum, we…
We construct examples of complete Riemannian manifolds having the property that every geodesic lies in a totally geodesic hyperbolic plane. Despite the abundance of totally geodesic hyperbolic planes, these examples are not locally…
We prove two rigidity results for complete Riemannian three-manifolds of higher rank. Complete three-manifolds have higher spherical rank if an only if they are spherical space forms. Complete finite volume three-manifolds have higher…