Results 61 to 70 of about 6,496 (142)

W‐algebras, Gaussian free fields, and g$\mathfrak {g}$‐Dotsenko–Fateev integrals

Proceedings of the London Mathematical Society, Volume 131, Issue 6, December 2025.
Abstract Based on the intrinsic connection between Gaussian free fields and the Heisenberg vertex algebra, we study some aspects of the correspondence between probability theory and W$W$‐algebras. This is first achieved by providing a construction of the W$W$‐algebra associated to a complex simple Lie algebra g$\mathfrak {g}$ by means of Gaussian free ...
Baptiste Cerclé
wiley   +1 more source

Persistence of unknottedness of clean Lagrangian intersections

Journal of Topology, Volume 18, Issue 4, December 2025.
Abstract Let Q0$Q_0$ and Q1$Q_1$ be two Lagrangian spheres in a six‐dimensional symplectic manifold. Assume that Q0$Q_0$ and Q1$Q_1$ intersect cleanly along a circle that is unknotted in both Q0$Q_0$ and Q1$Q_1$. We prove that there is no nearby Hamiltonian isotopy of Q0$Q_0$ and Q1$Q_1$ to a pair of Lagrangian spheres meeting cleanly along a circle ...
Johan Asplund, Yin Li
wiley   +1 more source

Weakly special threefolds and nondensity of rational points

Journal of the London Mathematical Society, Volume 112, Issue 5, November 2025.
Abstract We verify part of a conjecture of Campana predicting that rational points on the weakly special nonspecial simply connected smooth projective threefolds constructed by Bogomolov–Tschinkel are not dense. To prove our result, we establish fundamental properties of moduli spaces of orbifold maps, and prove a dimension bound for such moduli spaces
Finn Bartsch, Ariyan Javanpeykar, Erwan Rousseau   +2 more
wiley   +1 more source

Holomorphic field theories and higher algebra

Bulletin of the London Mathematical Society, Volume 57, Issue 10, Page 2903-2974, October 2025.
Abstract Aimed at complex geometers and representation theorists, this survey explores higher dimensional analogs of the rich interplay between Riemann surfaces, Virasoro and Kac‐Moody Lie algebras, and conformal blocks. We introduce a panoply of examples from physics — field theories that are holomorphic in nature, such as holomorphic Chern‐Simons ...
Owen Gwilliam, Brian R. Williams
wiley   +1 more source

Dirac–Schrödinger operators, index theory and spectral flow

Journal of the London Mathematical Society, Volume 112, Issue 4, October 2025.
Abstract In this article, we study generalised Dirac–Schrödinger operators in arbitrary signatures (with or without gradings), providing a general KK$\textnormal {KK}$‐theoretic framework for the study of index pairings and spectral flow. We provide a general Callias Theorem, which shows that the index (or the spectral flow, or abstractly the K ...
Koen van den Dungen
wiley   +1 more source

Taking limits in topological recursion

Journal of the London Mathematical Society, Volume 112, Issue 3, September 2025.
Abstract When does topological recursion applied to a family of spectral curves commute with taking limits? This problem is subtle, especially when the ramification structure of the spectral curve changes at the limit point. We provide sufficient (straightforward‐to‐use) conditions for checking when the commutation with limits holds, thereby closing a ...
Gaëtan Borot, Vincent Bouchard, Nitin Kumar Chidambaram, Reinier Kramer, Sergey Shadrin   +4 more
wiley   +1 more source

Real Quadratic Analogs of Traces of Singular Moduli [PDF]

, 2017
In this paper, regularized Petersson inner products of certain weight weakly holomorphic (or harmonic) modular forms are expressed in terms of real quadratic analogs of traces of singular moduli.
Duke, W., Imamoḡlu, Ö., Tóth, Á.
core  

Modular differential equations for characters of RCFT

, 2010
We discuss methods, based on the theory of vector-valued modular forms, to determine all modular differential equations satisfied by the conformal characters of RCFT; these modular equations are related to the null vector relations of the operator ...
D Eisenbud, EP Verlinde, F Diamond, G Anderson, G Mason, G Shimura, GW Moore, J-P Serre, JL Cardy, M Knopp, M Knopp, MR Gaberdiel, MR Gaberdiel, N Koblitz, P Bántay, P Bántay, P Francesco Di, P. Bantay, RC Gunning, S Lang, SD Mathur, SD Mathur, TM Apostol, W Eholzer, W Kohnen, Y Zhu   +25 more
core   +1 more source

Triple sums of Kloosterman sums and the discrepancy of modular inverses

Journal of the London Mathematical Society, Volume 112, Issue 3, September 2025.
Abstract We investigate the distribution of modular inverses modulo positive integers c$c$ in a large interval. We provide upper and lower bounds for their box, ball, and isotropic discrepancy, thereby exhibiting some deviations from random point sets. The analysis is based, among other things, on a new bound for a triple sum of Kloosterman sums.
Valentin Blomer, Morten S. Risager, Igor E. Shparlinski   +2 more
wiley   +1 more source

Weakly holomorphic modular forms and rank two hyperbolic Kac-Moody algebras

Transactions of the American Mathematical Society, 2015
In this paper, we compute basis elements of certain spaces of weight 0 0 weakly holomorphic modular forms and consider the integrality of Fourier coefficients of the modular forms. We use the results to construct automorphic correction of the rank 2 2 hyperbolic Kac-Moody algebras H
Kim, Henry H., Lee, Kyu-Hwan, Zhang, Yichao   +2 more
openaire   +3 more sources