Wiley: Proceedings of the London Mathematical Society: Table of Contents
https://londmathsoc.onlinelibrary.wiley.com/journal/1460244x?af=R
Table of Contents for Proceedings of the London Mathematical Society. List of articles from both the latest and EarlyView issues.
enUS
wileyonlinelibrary@wiley.com (London Mathematical Society (LMS))
Mon, 04 Mar 2024 08:17:12 +0000
Mon, 04 Mar 2024 08:17:12 +0000
Atypon® Literatum™
https://validator.w3.org/feed/docs/rss2.html
10080
Wiley: Proceedings of the London Mathematical Society: Table of Contents
Wiley
Proceedings of the London Mathematical Society
Wiley: Proceedings of the London Mathematical Society: Table of Contents
https://londmathsoc.onlinelibrary.wiley.com/pbassets/journalbanners/1460244x.jpg
https://londmathsoc.onlinelibrary.wiley.com/journal/1460244x?af=R

https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/plms.12525?af=R
Mon, 19 Feb 2024 00:00:00 0800
20240219T12:00:0008:00
Wiley: Proceedings of the London Mathematical Society: Table of Contents
Thu, 01 Feb 2024 00:00:00 0800
Thu, 01 Feb 2024 00:00:00 0800
10.1112/plms.12525
Issue Information
Proceedings of the London Mathematical Society, Volume 128, Issue 2, February 2024.
ISSUE INFORMATION
Issue Information
10.1112/plms.12525
Proceedings of the London Mathematical Society
10.1112/plms.12525
https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/plms.12525?af=R
ISSUE INFORMATION
128
2

https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/plms.12585?af=R
Sun, 18 Feb 2024 00:00:00 0800
20240218T12:00:0008:00
Wiley: Proceedings of the London Mathematical Society: Table of Contents
Thu, 01 Feb 2024 00:00:00 0800
Thu, 01 Feb 2024 00:00:00 0800
10.1112/plms.12585
Boundary current fluctuations for the half‐space ASEP and six‐vertex model
Proceedings of the London Mathematical Society, Volume 128, Issue 2, February 2024.
Abstract
We study fluctuations of the current at the boundary for the half‐space asymmetric simple exclusion process (ASEP) and the height function of the half‐space six‐vertex model at the boundary at large times. We establish a phase transition depending on the effective density of particles at the boundary, with Gaussian symplectic ensemble (GSE) and Gaussian orthogonal ensemble (GOE) limits as well as the Baik–Rains crossover distribution near the critical point. This was previously known for half‐space last‐passage percolation, and recently established for the half‐space log‐gamma polymer and Kardar–Parisi–Zhang equation in the groundbreaking work of Imamura, Mucciconi, and Sasamoto. The proof uses the underlying algebraic structure of these models in a crucial way to obtain exact formulas. In particular, we show a relationship between the half‐space six‐vertex model and a half‐space Hall–Littlewood measure with two boundary parameters, which is then matched to a free boundary Schur process via a new identity of symmetric functions. Fredholm Pfaffian formulas are established for the half‐space ASEP and six‐vertex model, indicating a hidden free fermionic structure.
<h2>Abstract</h2>
<p>We study fluctuations of the current at the boundary for the halfspace asymmetric simple exclusion process (ASEP) and the height function of the halfspace sixvertex model at the boundary at large times. We establish a phase transition depending on the effective density of particles at the boundary, with Gaussian symplectic ensemble (GSE) and Gaussian orthogonal ensemble (GOE) limits as well as the Baik–Rains crossover distribution near the critical point. This was previously known for halfspace lastpassage percolation, and recently established for the halfspace loggamma polymer and Kardar–Parisi–Zhang equation in the groundbreaking work of Imamura, Mucciconi, and Sasamoto. The proof uses the underlying algebraic structure of these models in a crucial way to obtain exact formulas. In particular, we show a relationship between the halfspace sixvertex model and a halfspace Hall–Littlewood measure with two boundary parameters, which is then matched to a free boundary Schur process via a new identity of symmetric functions. Fredholm Pfaffian formulas are established for the halfspace ASEP and sixvertex model, indicating a hidden free fermionic structure.</p>
Jimmy He
RESEARCH ARTICLE
Boundary current fluctuations for the half‐space ASEP and six‐vertex model
10.1112/plms.12585
Proceedings of the London Mathematical Society
10.1112/plms.12585
https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/plms.12585?af=R
RESEARCH ARTICLE
128
2

https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/plms.12583?af=R
Wed, 14 Feb 2024 00:00:00 0800
20240214T12:00:0008:00
Wiley: Proceedings of the London Mathematical Society: Table of Contents
Thu, 01 Feb 2024 00:00:00 0800
Thu, 01 Feb 2024 00:00:00 0800
10.1112/plms.12583
Simple spines of homotopy 2‐spheres are unique
Proceedings of the London Mathematical Society, Volume 128, Issue 2, February 2024.
Abstract
A locally flatly embedded 2‐sphere in a compact 4‐manifold X$X$ is called a spine if the inclusion map is a homotopy equivalence. A spine is called simple if the complement of the 2‐sphere has abelian fundamental group. We prove that if two simple spines represent the same generator of H2(X)$H_2(X)$ then they are ambiently isotopic. In particular, the theorem applies to simple shake‐slicing 2‐spheres in knot traces.
<h2>Abstract</h2>
<p>A locally flatly embedded 2sphere in a compact 4manifold X$X$ is called a spine if the inclusion map is a homotopy equivalence. A spine is called simple if the complement of the 2sphere has abelian fundamental group. We prove that if two simple spines represent the same generator of H2(X)$H_2(X)$ then they are ambiently isotopic. In particular, the theorem applies to simple shakeslicing 2spheres in knot traces.</p>
Patrick Orson,
Mark Powell
RESEARCH ARTICLE
Simple spines of homotopy 2‐spheres are unique
10.1112/plms.12583
Proceedings of the London Mathematical Society
10.1112/plms.12583
https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/plms.12583?af=R
RESEARCH ARTICLE
128
2

https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/plms.12586?af=R
Wed, 14 Feb 2024 00:00:00 0800
20240214T12:00:0008:00
Wiley: Proceedings of the London Mathematical Society: Table of Contents
Thu, 01 Feb 2024 00:00:00 0800
Thu, 01 Feb 2024 00:00:00 0800
10.1112/plms.12586
On the number of high‐dimensional partitions
Proceedings of the London Mathematical Society, Volume 128, Issue 2, February 2024.
Abstract
Let Pd(n)$P_{d}(n)$ denote the number of n×…×nd$n \times \ldots \times n \ d$‐dimensional partitions with entries from {0,1,…,n}$\lbrace 0,1,\ldots,n\rbrace$. Building upon the works of Balogh–Treglown–Wagner and Noel–Scott–Sudakov, we show that when d→∞$d \rightarrow \infty$,
Pd(n)=2(1+od(1))6(d+1)π·nd$$\begin{equation*} \hspace*{56pt}P_{d}(n) = 2^{(1+o_{d}(1)) \sqrt {\frac{6}{(d+1)\pi }} \cdot n^{d}} \end{equation*}$$holds for all n⩾1$n \geqslant 1$. This makes progress toward a conjecture of Moshkovitz–Shapira [Adv. in Math. 262 (2014), 1107–1129]. Via the main result of Moshkovitz and Shapira, our estimate also determines asymptotically a Ramsey‐theoretic parameter related to Erdős–Szekeres‐type functions, thus solving a problem of Fox, Pach, Sudakov, and Suk [Proc. Lond. Math. Soc. 105 (2012), 953–982]. Our main result is a new supersaturation theorem for antichains in [n]d$[n]^{d}$, which may be of independent interest.
<h2>Abstract</h2>
<p>Let Pd(n)$P_{d}(n)$ denote the number of n×…×nd$n \times \ldots \times n \ d$dimensional partitions with entries from {0,1,…,n}$\lbrace 0,1,\ldots,n\rbrace$. Building upon the works of Balogh–Treglown–Wagner and Noel–Scott–Sudakov, we show that when d→∞$d \rightarrow \infty$,
Pd(n)=2(1+od(1))6(d+1)π·nd$$\begin{equation*} \hspace*{56pt}P_{d}(n) = 2^{(1+o_{d}(1)) \sqrt {\frac{6}{(d+1)\pi }} \cdot n^{d}} \end{equation*}$$holds for all n⩾1$n \geqslant 1$. This makes progress toward a conjecture of Moshkovitz–Shapira [<i>Adv. in Math</i>. 262 (2014), 1107–1129]. Via the main result of Moshkovitz and Shapira, our estimate also determines asymptotically a Ramseytheoretic parameter related to Erdős–Szekerestype functions, thus solving a problem of Fox, Pach, Sudakov, and Suk [<i>Proc. Lond. Math. Soc</i>. 105 (2012), 953–982]. Our main result is a new supersaturation theorem for antichains in [n]d$[n]^{d}$, which may be of independent interest.</p>
Cosmin Pohoata,
Dmitrii Zakharov
RESEARCH ARTICLE
On the number of high‐dimensional partitions
10.1112/plms.12586
Proceedings of the London Mathematical Society
10.1112/plms.12586
https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/plms.12586?af=R
RESEARCH ARTICLE
128
2

https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/plms.12582?af=R
Tue, 13 Feb 2024 00:00:00 0800
20240213T12:00:0008:00
Wiley: Proceedings of the London Mathematical Society: Table of Contents
Thu, 01 Feb 2024 00:00:00 0800
Thu, 01 Feb 2024 00:00:00 0800
10.1112/plms.12582
The Loewner–Kufarev energy and foliations by Weil–Petersson quasicircles
Proceedings of the London Mathematical Society, Volume 128, Issue 2, February 2024.
Abstract
We study foliations by chord–arc Jordan curves of the twice punctured Riemann sphere C∖{0}$\mathbb {C} \setminus \lbrace 0\rbrace$ using the Loewner–Kufarev equation. We associate to such a foliation a function on the plane that describes the “local winding” along each leaf. Our main theorem is that this function has finite Dirichlet energy if and only if the Loewner driving measure ρ$\rho$ has finite Loewner–Kufarev energy, defined by
S(ρ)=12∫∫S1×Rνt′(θ)2dθdt$$\begin{equation*} \hspace*{58pt}S(\rho) = \frac{1}{2}\iint\nolimits _{S^1 \times \mathbb {R}} \nu _t^{\prime }(\theta)^2 \, d \theta d t \end{equation*}$$whenever ρ$\rho$ is of the form νt(θ)2dθdt$\nu _t(\theta)^2 d \theta d t$, and set to ∞$\infty$ otherwise. Moreover, if either of these two energies is finite, they are equal up to a constant factor, and in this case, the foliation leaves are Weil–Petersson quasicircles. This duality between energies has several consequences. The first is that the Loewner–Kufarev energy is reversible, that is, invariant under inversion and time reversal of the foliation. Furthermore, the Loewner energy of a Jordan curve can be expressed using the minimal Loewner–Kufarev energy of those measures that generate the curve as a leaf. This provides a new and quantitative characterization of Weil–Petersson quasicircles. Finally, we consider conformal distortion of the foliation and show that the Loewner–Kufarev energy satisfies an exact transformation law involving the Schwarzian derivative. The proof of our main theorem uses an isometry between the Dirichlet energy space on the unit disc and L2(2ρ)$L^2(2\rho)$ that we construct using Hadamard's variational formula expressed by means of the Loewner–Kufarev equation. Our results are related to κ$\kappa$‐parameter duality and large deviations of Schramm–Loewner evolutions coupled with Gaussian random fields.
<h2>Abstract</h2>
<p>We study foliations by chord–arc Jordan curves of the twice punctured Riemann sphere C∖{0}$\mathbb {C} \setminus \lbrace 0\rbrace$ using the Loewner–Kufarev equation. We associate to such a foliation a function on the plane that describes the “local winding” along each leaf. Our main theorem is that this function has finite Dirichlet energy if and only if the Loewner driving measure ρ$\rho$ has finite Loewner–Kufarev energy, defined by
S(ρ)=12∫∫S1×Rνt′(θ)2dθdt$$\begin{equation*} \hspace*{58pt}S(\rho) = \frac{1}{2}\iint\nolimits _{S^1 \times \mathbb {R}} \nu _t^{\prime }(\theta)^2 \, d \theta d t \end{equation*}$$whenever ρ$\rho$ is of the form νt(θ)2dθdt$\nu _t(\theta)^2 d \theta d t$, and set to ∞$\infty$ otherwise. Moreover, if either of these two energies is finite, they are equal up to a constant factor, and in this case, the foliation leaves are Weil–Petersson quasicircles. This duality between energies has several consequences. The first is that the Loewner–Kufarev energy is reversible, that is, invariant under inversion and time reversal of the foliation. Furthermore, the Loewner energy of a Jordan curve can be expressed using the minimal Loewner–Kufarev energy of those measures that generate the curve as a leaf. This provides a new and quantitative characterization of Weil–Petersson quasicircles. Finally, we consider conformal distortion of the foliation and show that the Loewner–Kufarev energy satisfies an exact transformation law involving the Schwarzian derivative. The proof of our main theorem uses an isometry between the Dirichlet energy space on the unit disc and L2(2ρ)$L^2(2\rho)$ that we construct using Hadamard's variational formula expressed by means of the Loewner–Kufarev equation. Our results are related to κ$\kappa$parameter duality and large deviations of Schramm–Loewner evolutions coupled with Gaussian random fields.</p>
Fredrik Viklund,
Yilin Wang
RESEARCH ARTICLE
The Loewner–Kufarev energy and foliations by Weil–Petersson quasicircles
10.1112/plms.12582
Proceedings of the London Mathematical Society
10.1112/plms.12582
https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/plms.12582?af=R
RESEARCH ARTICLE
128
2

https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/plms.12584?af=R
Tue, 13 Feb 2024 00:00:00 0800
20240213T12:00:0008:00
Wiley: Proceedings of the London Mathematical Society: Table of Contents
Thu, 01 Feb 2024 00:00:00 0800
Thu, 01 Feb 2024 00:00:00 0800
10.1112/plms.12584
A p$p$‐adic approach to the existence of level‐raising congruences
Proceedings of the London Mathematical Society, Volume 128, Issue 2, February 2024.
Abstract
We construct level‐raising congruences between p$p$‐ordinary automorphic representations, and apply this to the problem of symmetric power functoriality for Hilbert modular forms. In particular, we prove the existence of the nth$n\text{th}$ symmetric power lift of a Hilbert modular eigenform of regular weight for each odd integer n=1,3,⋯,25$n = 1, 3, \dots, 25$. In a future work with James Newton, we will use these results to establish the existence of the nth$n\text{th}$ symmetric power lift for all n⩾1$n \geqslant 1$.
<h2>Abstract</h2>
<p>We construct levelraising congruences between p$p$ordinary automorphic representations, and apply this to the problem of symmetric power functoriality for Hilbert modular forms. In particular, we prove the existence of the nth$n\text{th}$ symmetric power lift of a Hilbert modular eigenform of regular weight for each odd integer n=1,3,⋯,25$n = 1, 3, \dots, 25$. In a future work with James Newton, we will use these results to establish the existence of the nth$n\text{th}$ symmetric power lift for all n⩾1$n \geqslant 1$.</p>
Jack A. Thorne
RESEARCH ARTICLE
A p$p$‐adic approach to the existence of level‐raising congruences
10.1112/plms.12584
Proceedings of the London Mathematical Society
10.1112/plms.12584
https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/plms.12584?af=R
RESEARCH ARTICLE
128
2

https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/plms.12581?af=R
Sat, 10 Feb 2024 00:00:00 0800
20240210T12:00:0008:00
Wiley: Proceedings of the London Mathematical Society: Table of Contents
Thu, 01 Feb 2024 00:00:00 0800
Thu, 01 Feb 2024 00:00:00 0800
10.1112/plms.12581
Diophantine approximation, large intersections and geodesics in negative curvature
Proceedings of the London Mathematical Society, Volume 128, Issue 2, February 2024.
Abstract
In this paper, we prove quantitative results about geodesic approximations to submanifolds in negatively curved spaces. Among the main tools is a new and general Jarník–Besicovitch type theorem in Diophantine approximation. Our framework allows manifolds of variable negative curvature, a variety of geometric targets, and logarithm laws as well as spiraling phenomena in both measure and dimension aspect. Several of the results are new also for manifolds of constant negative sectional curvature. We further establish a large intersection property of Falconer in this context.
<h2>Abstract</h2>
<p>In this paper, we prove quantitative results about geodesic approximations to submanifolds in negatively curved spaces. Among the main tools is a new and general Jarník–Besicovitch type theorem in Diophantine approximation. Our framework allows manifolds of variable negative curvature, a variety of geometric targets, and logarithm laws as well as spiraling phenomena in both measure and dimension aspect. Several of the results are new also for manifolds of constant negative sectional curvature. We further establish a large intersection property of Falconer in this context.</p>
Anish Ghosh,
Debanjan Nandi
RESEARCH ARTICLE
Diophantine approximation, large intersections and geodesics in negative curvature
10.1112/plms.12581
Proceedings of the London Mathematical Society
10.1112/plms.12581
https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/plms.12581?af=R
RESEARCH ARTICLE
128
2