Results 41 to 50 of about 162 (133)
Modular cocycles and cup product [PDF]
, 2019 The Eichler-Shimura isomorphism relates holomorphic modular cusps forms of positive even integral weight to cohomology classes. The Haberland formula uses the cup product to give a cohomological formulation of the Petersson scalar product.
YoungJu Choie +5 more
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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
ADE double scaled little string theories, mock modular forms and Umbral Moonshine [PDF]
, 2015 We consider double scaled little string theory on K3. These theories are labelled by a positive integer k ≥ 2 and an ADE root lattice with Coxeter number k.
Harvey, Jeffrey A. +5 more
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Explicit height estimates for CM curves of genus 2
Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.Abstract In this paper, we make explicit the constants of Habegger and Pazuki's work from 2017 on bounding the discriminant of cyclic Galois CM fields corresponding to genus 2 curves with CM and potentially good reduction outside a predefined set of primes. We also simplify some of the arguments.
Linda Frey +2 more
wiley +1 more source
Floer theory for the variation operator of an isolated singularity
Journal of Topology, Volume 18, Issue 4, December 2025.Abstract The variation operator in singularity theory maps relative homology cycles to compact cycles in the Milnor fiber using the monodromy. We construct its symplectic analog for an isolated singularity. We define the monodromy Lagrangian Floer cohomology, which provides categorifications of the standard theorems on the variation operator and the ...
Hanwool Bae +3 more
wiley +1 more source
The arithmetic of modular grids
, 2022 A modular grid is a pair of sequences $(f_m)_m$ and $(g_n)_n$ of weakly holomorphic modular forms such that for almost all $m$ and $n$, the coefficient of $q^n$ in $f_m$ is the negative of the coefficient of $q^m$ in $g_n$. Zagier proved this coefficient
Griffin, Michael +2 more
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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
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
Faber's socle intersection numbers via Gromov–Witten theory of elliptic curve
Bulletin of the London Mathematical Society, Volume 57, Issue 9, Page 2698-2707, September 2025.Abstract The goal of this very short note is to give a new proof of Faber's formula for the socle intersection numbers in the tautological ring of Mg$\mathcal {M}_g$. This new proof exhibits a new beautiful tautological relation that stems from the recent work of Oberdieck–Pixton on the Gromov–Witten theory of the elliptic curve via a refinement of ...
Xavier Blot +2 more
wiley +1 more source
On the Fourier coefficients of 2-dimensional vector-valued modular forms
, 2011 Let ρ : S L ( 2 , Z ) → G L ( 2 , C ) \rho : SL(2, \mathbb {Z}) \rightarrow GL(2, \mathbb {C ...
Geoffrey Mason
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