12 papers
Volume Growth under Positive Intermediate Curvature and a Ricci Lower Bound
Robert Koirala
Let be a complete Riemannian manifold with $\Ric\ge-kg$ and uniformly positive -intermediate curvature in the sense of Brendle--Hirsch--Johne. We prove that the Fisher…
The Fisher Metric of the Ricci Flow Heat Kernel
Bennett Chow, Robert Koirala
We introduce and study a Fisher information metric \(g^F_τ\) associated to the conjugate heat kernel of a Ricci flow \((M^n,g_t)\). This tensor measures, at a fixed scale, how the…
Unbounded Topology of Nodal Sets of Harmonic Functions
Robert Koirala
For every integer \(n\ge 3\), every \(1\le \ell\le n-2\), and every sufficiently large integer \(m\), we construct harmonic functions \(u_{m,\ell}\) on the unit ball \(B_1(0)\subse…
Sharp Gaussian Isoperimetry along a Ricci Flow
Robert Koirala
We prove the sharp Gaussian isoperimetric inequality for conjugate heat-kernel measures along a Ricci flow via a monotonicity formula. As consequences, we obtain the exact Gaussian…
IceCube Second Track Data Release IceTracks-DR2: Data from 2008-2022 for Neutrino Source Searches
R. Abbasi, M. Ackermann, J. Adams +412
We present IceCube's latest release of muon track data for neutrino point-source searches, extending the previously published 10-year dataset to cover 14 years of observations (Apr…
Nested nodal loops for sums of Laplace eigenfunctions
Robert Koirala
We study nested loops in zero sets of sums of Laplace eigenfunctions on closed surfaces. In the real-analytic category, answering a question of Logunov, we prove a uniform bound fo…
Nested nodal loops of biharmonic functions
Javier Gómez-Serrano, Robert Koirala, Alexander Logunov
Given any \(n\in\mathbb{N}\), we construct a real-valued biharmonic polynomial on \(\mathbb{R}^2\) whose zero set contains a nest of \(n\) smooth, disjoint topological loops, meani…
Sensitivity Projections for Low-Mass Dark Matter Annihilation with the IceCube Upgrade
R. Abbasi, M. Ackermann, J. Adams +412
The IceCube Upgrade, an extension designed to enhance the IceCube Neutrino Observatory's detection of neutrinos with energies between 1 GeV and 500 GeV, will markedly improve IceCu…
Equidistribution of Eigenfunctions of Quantum Cat Maps
Robert Koirala
We prove that the short-period eigenfunctions of quantum cat maps constructed by Kim and the author equidistribute on in the sense of semiclassical measures. We also…
On a Problem of M. Kac on Laplace Distributions
Robert Koirala
We give counterexamples to a problem of M. Kac in the Scottish Book, which asks whether a certain nonlinear operation on two characteristic functions characterizes Laplace distribu…
Structure Theory of Parabolic Nodal and Singular Sets
Max Hallgren, Robert Koirala, Zilu Ma
We establish new estimates for the size and structure of the nodal set and the singular set of solutions to parabolic inequalities with parabolic…
Notes on regularity of Anosov splitting
Robert Koirala
In these expository notes, we give a proof of regularity of Anosov splitting for Anosov diffeomorphisms in a torus. We also generalize the idea to higher dimensions and to Anosov f…