相关论文: The Gauss-Manin connection and noncommutative tori
We consider the compactification of Matrix theory on tori with background antisymmetric tensor field. Douglas and Hull have recently discussed how noncommutative geometry appears on the tori. In this paper, we demonstrate the concrete…
The subject of the present work is the de Rham part of non-commutative Hodge structures on the periodic cyclic homology of differential graded algebras and categories. We discuss explicit formulas for the corresponding connection on the…
In this article, we prove nonlinear orbital stability for steadily translating vortex pairs, a family of nonlinear waves that are exact solutions of the incompressible, two-dimensional Euler equations. We use an adaptation of Kelvin's…
We prove the Gersten conjecture for $p$-adic \'etale Tate twists for a smooth scheme $X$ in mixed characteristic in the Nisnevich topology. Our main observation is that, while $p$-adic \'etale Tate twists are not $\mathbb A^1$-invariant,…
Khovanov homology for knots has generated a flurry of activity in the topology community. This paper studies the Khovanov type cohomology for graphs with a special attention to torsions. When the underlying algebra is $\mathbb{Z}[x]/(x^2)$,…
Under certain regularity conditions, we establish quasi-invariance of Gaussian measures on periodic functions under the flow of cubic fractional nonlinear Schr\"{o}dinger equations on the one-dimensional torus.
We consider synchrony patterns in coupled phase oscillator networks that correspond to invariant tori. For specific nongeneric coupling, these tori are equilibria relative to a continuous symmetry action. We analyze how the invariant tori…
We introduce a framework for coverings of noncommutative spaces. Moreover, we study noncommutative coverings of irrational quantum tori and characterize all such coverings that are connected in a reasonable sense.
We examine some recent developments in noncommutative geometry, including spin geometries on noncommutative tori and their quantization by the Shale-Stinespring procedure, as well as the emergence of Hopf algebras as a tool linking index…
We consider the noncommutative extension of Chern-Simons theory. We show the the theory can be fully expanded in power series of the noncommutative parameter theta and that no non-analytical sector exists. The theory appears to be unstable…
This paper aims to study the Betti homology and de Rham cohomology of twisted symmetric powers of the Kloosterman connection of rank two on the torus. We compute the period pairing and, with respect to certain bases, interpret these…
We analyze the breakup of invariant tori in Hamiltonian systems with two degrees of freedom using a combination of KAM theory and renormalization-group techniques. We consider a class of Hamiltonians quadratic in the action variables that…
We indicate two short proofs of the Goresky-MacPherson topological invariance of intersection homology. One proof is very short but requires the Goresky-MacPherson support and cosupport axioms; the other is slightly longer but does not…
We give a topological interpretation of the space of $L^2$-harmonic forms on Manifold with flat ends. It is an answer to an old question of J. Dodziuk. We also give a Chern-Gauss-Bonnet formula for the $L^2$-Euler characteristic of some of…
We prove the conjectural relation between the Stokes matrix for the quantum cohomology and an exceptional collection generating the derived category of coherent sheaves in the case of smooth cubic surfaces. The proof is based on a toric…
We form real-analytic Eisenstein series twisted by Manin's noncommutative modular symbols. After developing their basic properties, these series are shown to have meromorphic continuations to the entire complex plane and satisfy functional…
We construct parity and time reversal invariant Maxwell-Chern-Simons gauge theory coupled to fermions with adding the parity partner to the matter and the gauge fields, which can give nontopological vortex solutions depending on the sign of…
In this note, we establish a relationship between fractional Dehn twist coefficients of Riemann surface automorphisms and modular invariants of holomorphic families of algebraic curves. Specially, we give a characterization of…
We show that the cohomology intersection number of a twisted Gauss-Manin connection with regularization condition is a rational function. As an application, we obtain a new quadratic relation associated to period integrals of a certain…
Classical differential geometry can be encoded in spectral data, such as Connes' spectral triples, involving supersymmetry algebras. In this paper, we formulate non-commutative geometry in terms of supersymmetric spectral data. This leads…