Related papers: On $BP\langle 2\rangle$-cooperations
We analyze the ring tmf_*tmf of cooperations for the connective spectrum of topological modular forms (at the prime 2) through a variety of perspectives: (1) the E_2-term of the Adams spectral sequence for tmf ^ tmf admits a decomposition…
We compute topological Hochschild homology of $\mathbb{E}_3$-MU-algebra forms of the second truncated Brown-Peterson spectrum with Adams summand coefficients at $p=2$ and conditionally at arbitrary primes. We also provide a new…
We construct spectrum-level splittings of $BPGL \langle 1 \rangle \wedge BPGL \langle 1 \rangle$ at all primes $p$, where $BPGL \langle 1 \rangle$ is the first truncated motivic Brown--Peterson spectrum. Classically, $BP\langle 1 \rangle…
We calculate the mod (p, v_1, v_2) homotopy V(2)_* TC(BP<2>) of the topological cyclic homology of the truncated Brown--Peterson spectrum BP<2>, at all primes p\ge7, and show that it is a finitely generated and free F_p[v_3]-module on 12p+4…
We compute the $\mathrm{MU}$-based syntomic cohomologies, mod $(p,v_1,\cdots,v_{n})$, of all $\mathbb{E}_1$ $\mathrm{MU}$-algebra forms of the truncated Brown--Peterson spectrum $\mathrm{BP}\langle n\rangle$. As qualitative consequences, we…
The aim of this paper is to gain explicit information about the multiplicative structure of l_*l, where l is the connective Adams summand. Our approach differs from Kane's or Lellmann's because our main technical tool is the MU-based…
A classical theorem of Adams, Harris, and Switzer states that the 0th grading of complex $K$-theory cooperations, $KU_0ku$ is isomorphic to the space of numerical polynomials. The space of numerical polynomials has a basis provided by the…
The E_1-term of the (2-local) bo-based Adams spectral sequence for the sphere spectrum decomposes into a direct sum of a v_1-periodic part, and a v_1-torsion part. Lellmann and Mahowald completely computed the d_1-differential on the…
We study a correlated Brownian motion in two dimensions, which is reflected, stopped or killed in a wedge represented as the intersection of two half spaces. First, we provide explicit density formulas, hinted by the method of images. These…
In the 1980's, Mahowald and Kane used integral Brown--Gitler spectra to decompose $ku \wedge ku$ as a sum of finitely generated $ku$-module spectra. This splitting, along with an analogous decomposition of $ko \wedge ko,$ led to a great…
We show that given a Frobenius algebra there is a unique notion of its second quantization, which is the sum over all symmetric group quotients of n--th tensor powers, where the quotients are given by symmetric group twisted Frobenius…
A structure theorem for bounded-below modules over the subalgebra A(1) of the mod 2 Steenrod algebra generated by Sq^1, Sq^2 is proved; this is applied to prove a classification theorem for a family of indecomposable A(1)-modules. The…
A two-point algebra is a set of bounded analytic functions on the unit disk that agree at two distinct points $a,b \in \mathbb{D}$. This algebra serves as a multiplier algebra for the family of Hardy Hilbert spaces $H^2_t := \{ f\in H^2 :…
We produce refinements of the known multiplicative structures on the Brown--Peterson spectrum $BP$, its truncated variants $BP\langle n \rangle$, Ravenel's spectra $X(n)$, and evenly graded polynomial rings over the sphere spectrum.…
We study the fractionalization of space group symmetries in two-dimensional topologically ordered phases. Specifically, we focus on Z2-fractionalized phases in two dimensions whose deconfined topological excitations transform trivially…
We present a new tensor network algorithm for calculating the partition function of interacting quantum field theories in 2 dimensions. It is based on the Tensor Renormalization Group (TRG) protocol, adapted to operate entirely at the level…
The Goodwillie derivatives of the identity functor on pointed spaces form an operad in spectra. Adapting a definition of Behrens, we introduce mod 2 homology operations for algebras over this operad and prove these operations account for…
We briefly report on our result that the braided tensor product algebra of two module algebras $A_1,A_2$ of a quasitriangular Hopf algebra $H$ is equal to the ordinary tensor product algebra of $H_1$ with a subalgebra isomorphic to $A_2$…
We present a mode-coupling theory (MCT) for the high-density dynamics of two-dimensional spherical active Brownian particles (ABP). The theory is based on the integration-through-transients (ITT) formalism and hence provides a starting…
In the previous paper, we studied obstructions to the existence of complex sections on almost complex manifolds up to cobordism. We determined the obstruction rationally, in terms of the Chern classes. In this paper, we study the torsion…