Related papers: Ziggurat fringes are self-similar
We compute the coherent cohomology of the structure sheaf of complex periplectic Grassmannians. In particular, we show that it can be decomposed as a tensor product of the singular cohomology ring of a Grassmannian for either the symplectic…
We study varieties of certain ordered $\Sigma$-algebras with restricted completeness and continuity properties. We give a general characterization of their free algebras in terms of submonads of the monad of $\Sigma$-coterms. Varieties of…
We construct spherical harmonics for fuzzy spheres of even and odd dimensions, generalizing the correspondence between finite matrix algebras and fuzzy two-spheres. The finite matrix algebras associated with the various fuzzy spheres have a…
We study consequences and applications of the folklore statement that every double complex over a field decomposes into so-called squares and zigzags. This result makes questions about the associated cohomology groups and spectral sequences…
We prove the conjectures on dimensions and characters of some quadratic algebras stated by B$.$L$.$Feigin. It turns out that these algebras are naturally isomorphic to the duals of the components of the bihamiltonian operad.
We classify (up to quasi-isomorphism) the free differential modules whose homology is equal to a given module $M$ by developing a theory for deforming an arbitrary free complex into a differential module. We use an iterative approach to…
Recent years have seen a surprising connection between the physics of scattering amplitudes and a class of mathematical objects--the positive Grassmannian, positive loop Grassmannians, tree and loop Amplituhedra--which have been loosely…
We show that 4--dimensional conformal field theory is most naturally formulated on Kulkarni 4--folds, i. e. real 4--folds endowed with an integrable quaternionic structure. This leads to a formalism that parallels very closely that of…
A description of the Ziegler spectrum is given for trivial extensions of tubular algebras and related self-injective algebras of tubular type.
We consider algebras of rational power series over an alphabet $\Sigma$ with coefficients in a commutative semiring $K$ and characterize them as the free algebras in various classes of algebraic structures.
Motivated by the work of Leininger on hyperbolic equivalence of homotopy classes of closed curves on surfaces, we investigate a similar phenomenon for free groups. Namely, we study the situation when two elements $g,h$ in a free group $F$…
We introduce a twisted relative trace formula which simultaneously generalizes the twisted trace formula of Langlands et.al. (in the quadratic case) and the relative trace formula of Jacquet and Lai. Certain matching statements relating…
We prove that the cyclic chain complex of the categorical coalgebra of singular chains on an arbitrary topological space $X$ is naturally quasi-isomorphic to the $S^1$-equivariant chains of the free loop space of $X$. This statement does…
A characterization of freeness for plane curves in terms of the Hilbert function of the associated Milnor algebra is given as well as many new examples of rational cuspidal curves which are free. Some stronger properties are stated as…
We investigate homological properties of perfect algebras of prime characteristic. The principle is as follows: perfect algebras resolve the singularities. For example, we show any module over the ring of absolute integral closure has…
We review the properties of quantum groups occurring as Kazhdan--Lusztig dual to logarithmic conformal field theory models. These quantum groups at even roots of unity are not quasitriangular but are factorizable and have a ribbon…
We investigate actions of cyclic groups on polynomial rings with two variables, and the minimal free resolution of the corresponding invariant ring. In particular, we fully classify several cases, including the case the defining ideal has…
The first half of this mostly expository note reviews some notions of joint spectrum of linear operators, and it gives a new characterization of amenable groups in terms of projective spectrum. The second half revisits an application of…
Inspired by a question raised by Eisenbud-Musta\c{t}\u{a}-Stillman regarding the injectivity of maps from ${\rm Ext}$ modules to local cohomology modules and the work by the third author with Pham, we introduce a class of rings which we…
In this paper we study algebras of modular forms on unitary groups of signature $(n,1)$. We give a necessary and sufficient condition for an algebra of unitary modular forms to be free in terms of the modular Jacobian. As a corollary we…