Related papers: Strictly Commutative Complex Orientations of $Tmf_…

We introduce a method to construct special holomorphic tensors on orthogonal modular varieties from scalar-valued modular forms, and give applications to the Lang conjecture on the birational type of subvarieties of orthogonal modular…

A geometric construction of Z_2-graded orthogonal modular categories is given. Their 0-graded parts coincide with categories previously obtained by Blanchet and the author from the category of tangles modulo the Kauffman skein relations.…

We compute the mod $2$ homology of the spectrum $\mathrm{tmf}$ of topological modular forms by proving a 2-local equivalence $\mathrm{tmf} \wedge DA(1) \simeq \mathrm{tmf}_1(3) \simeq BP\left \langle 2\right\rangle$, where $DA(1)$ is an…

The numerical complex coupled-mode method used in a metal thin-film optic element is applied to a planar multilayer optical waveguide. All modes are required to satisfy Helmholtz Vectorial equation in an optical waveguide including bound…

We investigate the structure of graded commutative exponential functors. We give applications of these structure results, including computations of the homology of the symmetric groups and of extensions in the category of strict polynomial…

This article is about 1-forms on complex analytic varieties and it is particularly relevant when the variety has non-isolated singularities. We first show how the radial extension technique of M.-H. Schwartz can be adapted to 1-forms,…

We compute the homotopy groups of the $C_2$ fixed points of equivariant topological modular forms at the prime $2$ using the descent spectral sequence. We then show that as a $\mathrm{TMF}$-module, it is isomorphic to the tensor product of…

We investigate the complexity of states and operators evolved with the modular Hamiltonian by using the Krylov basis. In the first part, we formulate the problem for states and analyse different examples, including quantum mechanics,…

We construct local charts for the ramified cusps of the Hilbert modular variety of level $\Gamma_1(\mathfrak{c},\mathfrak{n})$. This allows us, following closely M. Rapoport and C.-L. Chai, to construct arithmetic toroidal and minimal…

We consider the three new crossing probabilities for percolation recently found via conformal field theory by Simmons, Kleban and Ziff. We prove that all three of them (i) may be simply expressed in terms of Cardy's and Watts' crossing…

We study the coherent orientations of the moduli spaces of holomorphic curves in Symplectic Field Theory, generalizing a construction due to Floer and Hofer. In particular we examine their behavior at multiple closed Reeb orbits under…

We study three connective versions of the spectrum for topological modular forms of level 3. All three were described briefly by Mahowald and Rezk in [Pure Appl Math Quar (2009)], but we add much detail to their discussion. Letting tmf(3)…

We extend the method for constructing symmetry operators of higher order for two-dimensional quantum Hamiltonians by Kalnins, Kress and Miller (2010). This expansion method expresses the integral in a finite power series in terms of lower…

We construct bases for the spaces of higher order modular forms of all orders and weights. We also provide a cohomological interpretation of these forms.

We construct fixed-point wave functions and exactly solvable commuting-projector Hamiltonians for a large class of bosonic symmetry-enriched topological (SET) phases, based on the concept of equivalent classes of symmetric local unitary…

For any truncated path algebra $\Lambda$, we give a structural description of the modules in the categories ${\cal P}^{<\infty}(\Lambda\text{-mod})$ and ${\cal P}^{<\infty}(\Lambda\text{-Mod})$, consisting of the finitely generated (resp.…

We study versions of strict Mittag-Leffler modules relativized to a class $\cK$ (of modules), that is, \emph{strict} versions (in the technical sense of Raynaud and Gruson) of $\cK$-Mittag-Leffler modules, as investigated in the preceding…

We prove the Gap Theorem for the spectrum of topological modular forms $\mathrm{Tmf}$. This removes a longstanding circularity in the literature, thereby confirming the computation of $\pi_\ast \mathrm{tmf}$ from over two decades ago by…

This work deals with the topological classification of singular foliation germs on $(\mathbb C^{2},0)$. Working in a suitable class of foliations we fix the topological invariants given by the separatrix set, the Camacho-Sad indices and the…

We show that the first-order symmetry operators of twistor spinors can be constructed from conformal Killing-Yano forms in conformally-flat backgrounds. We express the conditions on conformal Killing-Yano forms to obtain mutually commuting…