Sean Li

activity

20092025

most citedCharacterizations of rectifiable metric measure spaces

28 citations · 102 across the 27 of their papers we have counts for

collaborators

30 papers

math.MG2025

Characterizing rectifiability via biLipschitz pieces of Lipschitz mappings on the space

Sean Li, Raanan Schul

We give the following characterization of rectifiable metric spaces. A metric space with positive lower Hausdorff density is rectifiable if and only if, for any subset $F$ and $f:F…

math.MG2023

Notions of null sets in infinite-dimensional Carnot groups

Nathaniel Eldredge, Maria Gordina, Enrico Le Donne +1

We study several notions of null sets on infinite-dimensional Carnot groups. We prove that a set is Aronszajn null if and only if it is null with respect to measures that are convo…

math.MG2023

The strong geometric lemma in the Heisenberg group

Vasileios Chousionis, Sean Li, Robert Young

We prove that in the first Heisenberg group, unlike Euclidean spaces and higher dimensional Heisenberg groups, the best possible exponent for the strong geometric lemma for intrins…

math.CO2022

On the number of generalized numerical semigroups

Sean Li

Let $r_{k}$ be the unique positive root of $x^{k} - (x + 1)^{k - 1} = 0$ . We prove the best known bounds on the number $n_{g, d}$ of $d$ -dimensional generalized numerical semigroup…

math.CO2022

Counting numerical semigroups by Frobenius number, multiplicity, and depth

Sean Li

In 1990, Backelin showed that the number of numerical semigroups with Frobenius number $f$ approaches $C_{i} \cdot 2^{f /2}$ for constants $C_{0}$ and $C_{1}$ depending on the parity of $…

math.MG2022

The Riesz tranform on intrinsic Lipschitz graphs in the Heisenberg group

Vasileios Chousionis, Sean Li, Robert Young

We prove that the Heisenberg Riesz transform is $L_{2}$ --unbounded on a family of intrinsic Lipschitz graphs in the first Heisenberg group $H$ . We construct this family by c…

math.MG2021

Identifying 1-rectifiable measures in Carnot groups

Matthew Badger, Sean Li, Scott Zimmerman

We continue to develop a program in geometric measure theory that seeks to identify how measures in a space interact with canonical families of sets in the space. In particular, ex…

math.NT2021★ 1 cited

Tamagawa Products for Elliptic Curves Over Number Fields

Yunseo Choi, Sean Li, Apoorva Panidapu +1

In recent work, Griffin, Ono, and Tsai constructs an $L -$ series to prove that the proportion of short Weierstrass elliptic curves over $Q$ with trivial Tamagawa product is…

cs.LG2021★ 25 cited

Beyond Low-Pass Filters: Adaptive Feature Propagation on Graphs

Sean Li, Dongwoo Kim, Qing Wang

Graph neural networks (GNNs) have been extensively studied for prediction tasks on graphs. As pointed out by recent studies, most GNNs assume local homophily, i.e., strong similari…

math.CO2020

The Penney's Game with Group Action

Tanya Khovanova, Sean Li

Consider equipping an alphabet $A$ with a group action that partitions the set of words into equivalence classes which we call patterns. We answer standard questions for…

math.MG2020

The strong geometric lemma for intrinsic Lipschitz graphs in Heisenberg groups

Vasileios Chousionis, Sean Li, Robert Young

We show that the $β$ --numbers of intrinsic Lipschitz graphs of Heisenberg groups $H_{n}$ are locally Carleson integrable when $n \geq 2$ . Our technique relies on a recent Do…

math.CA2020

Singular integrals on $C^{1, α}$ regular curves in Carnot groups

Vasileios Chousionis, Sean Li, Scott Zimmerman

Let $G$ be any Carnot group. We prove that if a convolution type singular integral associated with a $1$ -dimensional Calderón-Zygmund kernel is $L^{2}$ -bounded on horizontal…

math.MG2019★ 5 cited

Stratified $β$ -numbers and traveling salesman in Carnot groups

Sean Li

We introduce a modified version of P. Jones's $β$ -numbers for Carnot groups which we call {\it stratified $β$ -numbers}. We show that an analogue of Jones's traveling salesman theor…

math.MG2018

Bi-Lipschitz embeddings of Heisenberg submanifolds into Euclidean spaces

Vasileios Chousionis, Sean Li, Vyron Vellis +1

The Heisenberg group $H$ equipped with a sub-Riemannian metric is one of the most well known examples of a doubling metric space which does not admit a bi-Lipschitz embedd…

math.FA2018★ 2 cited

Gâteaux differentiability on infinite-dimensional Carnot groups

Enrico Le Donne, Sean Li, Terhi Moisala

This paper contributes to the generalization of Rademacher's differentiability result for Lipschitz functions when the domain is infinite dimensional and has nonabelian group struc…

math.MG2018

The Traveling Salesman Theorem in Carnot Groups

Vasileios Chousionis, Sean Li, Scott Zimmerman

Let $G$ be any Carnot group. We prove that, if a subset of $G$ is contained in a rectifiable curve, then it satisfies Peter Jones' geometric lemma with some natur…

math.CA2016★ 8 cited

Nonnegative kernels and $1$ -rectifiability in the Heisenberg group

Vasileios Chousionis, Sean Li

Let $E$ be an $1$ -Ahlfors regular subset of the Heisenberg group $H$ . We prove that there exists a $- 1$ -homogeneous kernel $K_{1}$ such that if $E$ is contained in a $1$ -reg…

math.CA2016

Some remarks on the Lipschitz regularity of Radon transforms

Jonas Azzam, Jonathan Hickman, Sean Li

A set in the Euclidean plane is constructed whose image under the classical Radon transform is Lipschitz in every direction. It is also shown that, under mild hypotheses, for any s…

math.MG2016

Separated Nets in Nilpotent Groups

Tullia Dymarz, Michael Kelly, Sean Li +1

In this paper we generalize several results on separated nets in Euclidean space to separated nets in connected simply connected nilpotent Lie groups. We show that every such group…

math.FA2015★ 3 cited

Quantitative affine approximation for UMD targets

Tuomas Hytönen, Sean Li, Assaf Naor

It is shown here that if $(Y, ∥ \cdot ∥_{Y})$ is a Banach space in which martingale differences are unconditional (a UMD Banach space) then there exists $c = c (Y) \in (0, \infty)$ with th…

math.MG2015

Ahlfors-regular distances on the Heisenberg group without biLipschitz pieces

Enrico Le Donne, Sean Li, Tapio Rajala

We show that the Heisenberg group is not minimal in looking down. This answers Problem 11.15 in `Fractured fractals and broken dreams' by David and Semmes, or equivalently, Questio…

math.MG2015★ 14 cited

Differentiability and Poincaré-type inequalities in metric measure spaces

David Bate, Sean Li

We demonstrate the necessity of a Poincaré type inequality for those metric measure spaces that satisfy Cheeger's generalization of Rademacher's theorem for all Lipschitz functions…

math.MG2015★ 2 cited

BiLipschitz decomposition of Lipschitz maps between Carnot groups

Sean Li

Let $f : G \to H$ be a Lipschitz map between two Carnot groups. We show that if $B$ is ball of $G$ , then there exists a subset $Z \subset B$ , whose image in $H$ under $f$ has small…

math.MG2014★ 28 cited

Characterizations of rectifiable metric measure spaces

David Bate, Sean Li

We characterize $n$ -rectifiable metric measure spaces as those spaces that admit a countable Borel decomposition so that each piece has positive and finite $n$ -densities and one of…

Characterizing rectifiability via biLipschitz pieces of Lipschitz mappings on the space

Notions of null sets in infinite-dimensional Carnot groups

The strong geometric lemma in the Heisenberg group

On the number of generalized numerical semigroups

Counting numerical semigroups by Frobenius number, multiplicity, and depth

The Riesz tranform on intrinsic Lipschitz graphs in the Heisenberg group

Identifying 1-rectifiable measures in Carnot groups

Tamagawa Products for Elliptic Curves Over Number Fields

Beyond Low-Pass Filters: Adaptive Feature Propagation on Graphs

The Penney's Game with Group Action

The strong geometric lemma for intrinsic Lipschitz graphs in Heisenberg groups

Singular integrals on C1,α regular curves in Carnot groups

Stratified β-numbers and traveling salesman in Carnot groups

Bi-Lipschitz embeddings of Heisenberg submanifolds into Euclidean spaces

Gâteaux differentiability on infinite-dimensional Carnot groups

The Traveling Salesman Theorem in Carnot Groups

Nonnegative kernels and 1-rectifiability in the Heisenberg group

Some remarks on the Lipschitz regularity of Radon transforms

Separated Nets in Nilpotent Groups

Quantitative affine approximation for UMD targets

Ahlfors-regular distances on the Heisenberg group without biLipschitz pieces

Differentiability and Poincaré-type inequalities in metric measure spaces

BiLipschitz decomposition of Lipschitz maps between Carnot groups

Characterizations of rectifiable metric measure spaces

Singular integrals on $C^{1, α}$ regular curves in Carnot groups

Stratified $β$ -numbers and traveling salesman in Carnot groups

Nonnegative kernels and $1$ -rectifiability in the Heisenberg group