Research
Research
Research
Research
85+ open-access research outputs.
We provide a positive answer to an old problem of Jonathan K. Simon: if $K$ and $K'$ are two knots such that there is an epimorphism from the knot group of $K$ to the knot group of $K'$, then the genu…
The world of primes has many gaps between evidence and theorems. Here, we review Legendre's conjecture on primes between consecutive squares and recent progress on the weaker question of primes betwee…
About 40 years ago Jonathan and Peter Borwein discovered the series identity $$ \sum_{n=0}^\infty \frac{(-1)^n(6n)!}{(3n)!(n!)^3} \frac{(A+nB)}{C^{n+1/2}} = \frac{1}{12\pi} $$ where \begin{align*} A&=…
Let $(M^5,g)$ be a five-dimensional non-trivial simply-connected compact quasi-Einstein manifold with boundary. If $M$ has constant scalar $R$, Johnatan Costa, Ernani Ribeiro Jr, and Detang Zhou show …
For a set $E \subseteq \mathbb{F}_q^d$, the distance set is defined as $\Delta(E) := \{\|\mathbf{x} - \mathbf{y}\| : \mathbf{x}, \mathbf{y} \in E\}$, where $\|\cdot\|$ denotes the standard quadratic f…
We introduce a new group action on set systems, constructed as a semidirect product of a permutation group and a group generated by twist and loop complementation operations on a single element. This …
We address a problem posed by Nathan Kaplan in the 2014 Combinatorial and Additive Number Theory session: finding the largest subset $H \subseteq (\mathbb{Z}/4\mathbb{Z})^n$ with no distinct $x, y, z …
The purpose of this paper is to translate the expression of rank 2 cluster scattering diagrams via dilogarithm elements into via formal power series. As a corollary, we prove some conjectures introduc…
In recent work, the author, in collaboration with Allen, Long, and Tu, developed the Explicit Hypergeometric Modularity Method (EHMM), which establishes the modularity of a large class of hypergeometr…
The ribbon group action extends geometric duality and Petrie duality by defining two embedded graphs as twisted duals precisely when they lie within the same orbit under this group action. Twisted dua…
We prove that a family of complex hyperbolic ultra-parallel $[m_1, m_2, m_3]$-triangle group representations, where \( m_3 > 0 \), is discrete and faithful if and only if the isometry \( R_1(R_2R_1)^n…
These notes were intended as support material for a minicourse on Anosov flows in the conference "Symplectic geometry and Anosov flows'' which took place in Heidelberg in July 2024 organized by Peter …
In the study of ribbon knots, Lamm introduced symmetric unions inspired by earlier work of Kinoshita and Terasaka. We show an identity between the twisted Alexander polynomials of a symmetric union an…
Borwein integrals are one of the most popularly known phenomena in contemporary mathematics. They were found in 2001 by David Borwein and Jonathan Borwein and consist of a simple family of integrals i…
An alleged opposition between David Hilbert and Felix Klein as modern vs countermodern has been pursued by marxist historian Herbert Mehrtens and others. Scholars such as Epple, Grattan-Guinness, Gray…
The following document is a translation (from French to English) of: Gabriele H. Greco, Sur la mesurabilit\'e d'une fonction num\'erique par rapport \`a une famille d'ensembles, Rendiconti del Seminar…
The Quillen-McCord theorem (aka Quillen fiber lemma) gives a sufficient condition on a map between classifying spaces of posetal categories to be a homotopy equivalence. Jonathan Ariel Barmak in his p…
Let $\widehat{\mathcal{C}}_\mathbb{Z}$ be the group consists of manifold-knot pairs $(Y,K)$ modulo homology concordance, where $Y$ is an integer homology sphere bounding an integer homology ball, and …
Motivated by the goal of studying cluster algebras in infinite type, we study the stability domains of modules for the preprojective algebra in the corresponding infinite types. Specifically, we study…
We use knowledge of local fields to adapt Jonathan Lubin and Michael Rosen's proof of Mazur's Proposition 4.39. This changes the result about abelian varieties from only working over local fields with…
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