Hot Research
Contraction rates for sparse variational approximations in Gaussian process regression
We study the theoretical properties of a variational Bayes method in the Gaussian Process regression model.
Statistics Theory Statistics Theory
Minimax Rates for Conditional Density Estimation via Empirical Entropy
Consequently, minimax rates for conditional density estimation cannot be characterized using these classical results.
Statistics Theory Statistics Theory
Canonical Heights on Shimura Varieties and the André-Oort Conjecture
The main purpose of this work is to prove the Andr\'e-Oort conjecture in full generality.
Number Theory Algebraic Geometry
G-invariant Spin Structures on Spheres
We examine which of the compact connected Lie groups that act transitively on spheres of different dimensions leave the unique spin structure of the sphere invariant.
Differential Geometry 53C27, 53C30, 57S15
An Overview of Penumbral Moonshine
As Mathieu moonshine is a special case of umbral moonshine, Thompson moonshine (in half-integral weight) is a special case of a family of similar relationships between finite groups and vector-valued modular forms of a certain kind.
Representation Theory High Energy Physics - Theory 11F22 (Primary) 11F27, 11F37, 11F50, 20C34 (Secondary)
A machine learning approach to commutative algebra: Distinguishing table vs non-table ideals
We propose a novel approach to distinguish table vs non-table ideals by using different machine learning algorithms.
Commutative Algebra
Khovanov-Lipshitz-Sarkar homotopy type for links in thickened surfaces and those in $S^3$ with new modulis
We define a family of Khovanov-Lipshitz-Sarkar stable homotopy types for the homotopical Khovanov homology of links in thickened surfaces indexed by moduli space systems.
Geometric Topology 57M25, 57M27
Linear independence of odd zeta values using Siegel's lemma
We prove that among 1 and the odd zeta values $\zeta(3)$, $\zeta(5)$, ..., $\zeta(s)$, at least $ 0. 21 \sqrt{s / \log s}$ are linearly independent over the rationals, for any sufficiently large odd integer $s$.
Number Theory 11J72 (Primary), 11M06 (Secondary)
On partial isometries with circular numerical range
In their LAMA'2016 paper Gau, Wang and Wu conjectured that a partial isometry $A$ acting on $\mathbb{C}^n$ cannot have a circular numerical range with a non-zero center, and proved this conjecture for $n\leq 4$.
Functional Analysis 47A12, 47A20, 30J10, 33E05, 51N15
A plagiarism-proof online examination format for calculus and elementary linear algebra using Microsoft Excel
As educational systems move from onsite to online due to the COVID-19 pandemic, teachers face the difficulty of designing online examination formats which minimise opportunities for dishonesty.
History and Overview 97U40
