Related papers: Toda brackets and congruences of modular forms
This work deals with the conformal transformations in six-dimensional spinorial formalism. Several conformally invariant equations are obtained and their geometrical interpretation are worked out. Finally, the integrability conditions for…
New invariants for 2-dimensional cell complexes are defined, which can be interpreted as curvature bounds. These invariants are proved to be rational and computable in a companion article. This document is a survey that collects theorems…
One of the oldest methods for computing invariants of ordinary differential equations is tested using the full Toda lattice model. We show that the standard method of undetermined coefficients and modern symbolic algebra tools together with…
We show a number of Toda brackets in the homotopy of the motivic bordism spectrum $MGL$ and of the Real bordism spectrum $MU_{\mathbb R}$. These brackets are "red-shifting" in the sense that while the terms in the bracket will be of some…
The problem of construction of the boundary conditions for the Toda lattice compatible with its higher symmetries is considered. It is demonstrated that this problem is reduced to finding of the differential constraints consistent with the…
This thesis investigates the quantum properties of T-duality invariant formalisms of String Theory. We introduce and review duality invariant formalisms of String Theory including the Doubled Formalism. We calculate the background field…
In~\cite{CS04}, Calegari and Stein studied the congruences between classical cusp forms $S_k(\Gamma_0(p))$ of prime level and made several conjectures about them. In~\cite{AB07} (resp., ~\cite{BP11}) the authors proved one of those…
A brief overview of dimensional reductions for diffeomorphism invariant theories is given. The distinction between the physical idea of compactification and the mathematical problem of a consistent truncation is discussed, and the typical…
We compute quantum corrections to soliton masses in affine Toda theories with imaginary exponentials based on the nonsimply-laced Lie algebras $c_n^{(1)}$. We find that the soliton mass ratios renormalize nontrivially, in the same manner as…
The superconformal algebras of Ademollo et al are generalised to a multi-index form. The structure obtained is similar to the Moyal Bracket analogue of the Neveu-Schwarz Algebra.
In this note we use Heegaard Floer homology to study smooth cobordisms of algebraic knots and complex deformations of cusp singularities of curves. The main tool will be the concordance invariant $\nu^+$: we study its behaviour with respect…
Modular invariance is a necessary condition for the consistency of any closed string theory. In particular, it imposes stringent constraints on the spectrum of orbifold theories, and in principle determines their spectrum uniquely up to…
We study integrals of the form $\int_{\Omega}f\left( d\omega\right)$, where $1\leq k\leq n$, $f:\Lambda^{k}\rightarrow\mathbb{R}$ is continuous and $\omega$ is a $\left(k-1\right)$-form. We introduce the appropriate notions of convexity,…
Meta-conformal invariance is a novel class of dynamical symmetries, with dynamical exponent $z=1$, and distinct from the standard ortho-conformal invariance. The meta-conformal Ward identities can be directly read off from the Lie algebra…
Attributed to J F Adams is the conjecture that, at odd primes, the mod-p cohomology ring of the classifying space of a connected compact Lie group is detected by its elementary abelian p-subgroups. In this note we rely on Toda's calculation…
T-duality (Fourier-Mukai duality) and properties of classical instanton moduli spaces can be used to deduce some properties of $\alpha^{\prime}$-corrected moduli spaces of branes for Type IIA string theory compactified on $K3$ or $T^4$.…
We define two new unstable n-fold Toda brackets for every composable sequence (f_n, ... ,f_1) of pointed maps f_i : X_i \to X_{i+1} between well-pointed spaces with n > 2. The brackets agree with the classical Toda bracket when n = 3, and…
Given a brane tiling, that is a bipartite graph on a torus, we can associate with it a quiver potential and a quiver potential algebra. Under certain consistency conditions on a brane tiling, we prove a formula for the Donaldson-Thomas type…
In this paper we present multidimensional analogues of both the continuous- and discrete-time Toda lattices. The integrable systems that we consider here have two or more space coordinates. To construct the systems, we generalize the…
This is Part II of the series of our papers under the title "Toward resolution of singularities over a field of positive characteristic (The Idealistic Filtration Program)". See http://arxiv.org/abs/math/0607009 for Part I.