In this paper we explore the relationships between the motivic and simplicial cohomology operations defined on mod-l motivic cohomology. We also explore similar relationships in étale cohomology and conclude by considering certain operations that commute with proper push-forwards.

Using local cohomology and algebraic D-Modules, we generalize a comparison theorem between relative de Rham cohomology and Dwork cohomology due to N. Katz, A. Adolphson and S. Sperber.

We show that Haefliger’s cohomology for étale groupoids, Moore’s cohomology for locally compact groups and the Brauer group of a locally compact groupoid are all particular cases of sheaf (or Čech) cohomology for topological simplicial spaces.

For a smooth manifold equipped with a compact Lie group action, we construct an equivariant cohomology theory which takes values in a vertex algebra, and contains the classical equivariant cohomology as a subalgebra. The main idea is to synthesize the algebraic approach to the classical equivariant cohomology theory due to H. Cartan and Guillemin-Sternberg, with the chiral de Rham algebra of Ma...

States obtained by projecting boundary states, associated with D-branes, to fixed mass-level and momentum generically define non-trivial cohomology classes. For on-shell states the cohomology is the standard one, but when the states are off-shell the relevant cohomology is defined using a BRST operator with ghost zero modes removed. The zero momentum cohomology falls naturally into multiplets o...

We define the cohomology of a tiling as the cocycle cohomology of its associated groupoid and consider this cohomology for the class of tilings which are obtained from a higher dimensional lattice by the canonical projection method in Schlottmann’s formulation. We prove the cohomology to be equivalent to a certain cohomology of the lattice. We discuss one of its qualitative features, namely tha...

We define an integer graded symplectic Floer cohomology and a Fintushel–Stern type spectral sequence which are new invariants for monotone Lagrangian sub–manifolds and exact isotopes. The Z–graded symplectic Floer cohomology is an integral lifting of the usual ZΣ(L) –graded Floer–Oh cohomology. We prove the Künneth formula for the spectral sequence and an ring structure on it. The ring structur...

In this paper we develop a Conditional Least Squares (CLS) procedure for estimating bilinear time series models. We apply this method to two general types of bilinear models. A model of type I is a special superdiagonal bilinear model which includes the linear ARMA model as a submodel. A model of type II is a standardized version of the popular bilinear BL(p, 0, p, 1) model (see e.g. Liu and Ch...

In this paper, we determine the $L^p(\mathbb{R})\times L^q(\mathbb{R})\rightarrow L^r(\mathbb{R})$ boundedness of bilinear Hilbert transform $H_{\gamma}(f,g)$ along a convex curve $\gamma$ $$H_{\gamma}(f,g)(x):=\mathrm{p.\,v.}\int_{-\infty}^{\infty}f(x-t)g(x-\gamma(t)) \,\frac{\textrm{d}t}{t},$$ where $p$, $q$, and $r$ satisfy $\frac{1}{p}+\frac{1}{q}=\frac{1}{r}$, $r>\frac{1}{2}$, $p>1$, $q>1$...