Related papers: Periods for topological circle actions

In this paper we express the linearized dynamics of interacting interfacial waves in stratified shear flows in the compact form of action-angle Hamilton equations. The pseudo-energy serves as the Hamiltonian of the system, the action…

Acoustic waves in fluids undergoing the transition from sub- to supersonic flow satisfy governing equations similar to those for light waves in the immediate vicinity of a black hole event horizon. This acoustic analogy has been used by…

We compute the equivariant cohomology $H^*_{T_I}(\mathcal Z_K)$ of moment-angle complexes $\mathcal Z_K$ with respect to the action of coordinate subtori $T_I \subset T^m$. We give a criterion for the equivariant formality of $\mathcal Z_K$…

Numerous studies grounded on Hawkes processes have been carried out in many fields including finance, biology and social network. Hawkes processes form a class of selfexciting simple point processes. In this article, we consider a general…

We find the subgroup of classical acceleration-enlarged Newton-Hooke Hopf algebra which acts covariantly on the twisted acceleration-enlarged Newton-Hooke space-times. The case of classical acceleration-enlarged Galilei quantum group is…

This text presents some basic notions in symplectic geometry, Poisson geometry, Hamiltonian systems, Lie algebras and Lie groups actions on symplectic or Poisson manifolds, momentum maps and their use for the reduction of Hamiltonian…

Twisted K-theory has received much attention recently in both mathematics and physics. We describe some models of twisted K-theory, both topological and geometric. Then we state a theorem which relates representations of loop groups to…

After the torch of Anders Kock [Taylor series calculus for ring objects of line type, Journal of Pure and Applied Algebra, 12 (1978), 271-293], we will establish the Baker-Campbell-Hausdorff formula as well as the Zassenhaus formula in the…

For elliptic curves over rationals, there are a well-known conjecture of Sato-Tate and a new computational guided murmuration phenomenon, for which the abelian Hasse-Weil zeta functions are used. In this paper, we show that both the…

We study tautological cycle classes on the Jacobian of a curve. We prove a new result about the ring of tautological classes on a general curve that allows, among other things, easy dimension calculations and leads to some general results…

Spatio-temporal Hawkes point processes are a particularly interesting class of stochastic point processes for modeling self-exciting behavior, in which the occurrence of one event increases the probability of other events occurring. These…

We define topological invariants in terms of the ground states wave functions on a torus. This approach leads to precisely defined formulas for the Hall conductance in four dimensions and the topological magneto-electric $\theta$ term in…

We define twisted equivariant K-homology groups using geometric cycles. We compare them with approaches using Kasparov KK-Theory and (twisted) group C*-algebras.

Learning causal structure among event types on multi-type event sequences is an important but challenging task. Existing methods, such as the Multivariate Hawkes processes, mostly assumed that each sequence is independent and identically…

We construct a cohomology theory with compact support H^i_c(X_ar,Z(n))$ for separated schemes of finite type over a finite field, which should play a role analog to Lichtenbaum's Weil-etale cohomology groups for smooth and projective…

We apply the recently defined Lambert W function to some problems of classical statistical mechanics, i.e. the Tonks gas and a fluid of classical particles interacting via repulsive pair potentials. The latter case is considered both from…

For a given pseudo-Anosov homeomorphism $\varphi$ of a closed surface $S$, the action of $\varphi$ on the Teichm\"uller space $\mathcal T(S)$ preserves the Weil-Petersson symplectic form. We give explicit formulae for two invariant…

We suggest a method of derivation of the long-wave action of the model spin Hamiltonians using the non-linear partial differential equations of motions of the individual spins. According to the Vainberg's theorem the set of these equations…

We study K-theory classes of Hamiltonian loop group spaces represented by admissible Fredholm complexes. We prove various equivariant index formulae in this context. In a sequel to this article we show that, when specialized to a family of…

Kitchloo and Morava give a strikingly simple picture of elliptic cohomology at the Tate curve by studying a completed version of $S^1$-equivariant $K$-theory for spaces. Several authors (cf [ABG],[KM],[L]) have suggested that an equivariant…