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In this paper, we extend some classes of structured matrices to higher order tensors. We discuss their relationships with positive semi-definite tensors and some other structured tensors. We show that every principal sub-tensor of such a…
Connected Shimura varieties are the quotients of hermitian symmetric domains by discrete groups defined by congruence conditions. We examine their relation with moduli varieties. (Handbook of Moduli).
In this paper we introduce the concepts of higher equivariant and invariant topological complexity; and study their properties. Then we compare them with equivariant LS-category. We give lower and upper bounds for these new invariants. We…
In this paper, we prove the existence of an efficient algorithm for the computation of $q$-expansions of modular forms of weight $k$ and level $\Gamma$, where $\Gamma \subseteq SL_{2}({\mathbb{Z}})$ is an arbitrary congruence subgroup. We…
We define a class of multiparameter persistence modules that arise from a one-parameter family of functions on a topological space and prove that these persistence modules are stable. We show that this construction can produce…
We prove a formula of Petersson's type for Fourier coefficients of Siegel cusp forms of degree 2 with respect to congruence subgroups, and as a corollary, show upper bound estimates of individual Fourier coefficient. The method in this…
A composite Higgs boson is likely to be accompanied by additional light states generated by the same dynamics. This expectation is substantiated when realising the composite Higgs mechanism by an underlying gauge theory. We review the…
We prove the basic properties of determinantal semi-invariants for presentation spaces over any finite dimensional hereditary algebra over any field. These include the virtual generic decomposition theorem, stability theorem and the…
In this paper, we will introduce the concept of 2-absorbing (resp. strongly 2-absorbing) secondary submodules of modules over a commutative ring as a generalization of secondary modules and investigate some basic properties of these classes…
The main aim of this paper to show how commutative algebra is connected to topology. We give underlying topological idea of some results on completable unimodular rows.
We define and study a higher-dimensional version of model theoretic internality, and relate it to higher-dimensional definable groupoids in the base theory.
We obtain a small improvement of Gallagher's larger sieve and we extend it to higher dimensions. We also obtain two interesting upper bounds for the number of solutions to polynomial congruences.
Using the modern perspective of noncommutative algebraic geometry we survey some recent progress in the theory of stability conditions and moduli spaces with applications in hyperk\"ahler geometry and classical algebraic geometry.
We introduce and analyze a new geometric structure on topological surfaces generalizing the complex structure. To define this so called higher complex structure we use the punctual Hilbert scheme of the plane. The moduli space of higher…
We obtain new recurrence relations, an explicit formula, and convolution identities for higher order geometric polynomials. These relations generalize known results for geometric polynomials, and lead to congruences for higher order…
We define abelian extensions of algebras in congruence-modular varieties. The theory is sufficiently general that it includes, in a natural way, extensions of R-modules for a ring R. We also define a cohomology theory, which we call clone…
We introduce the notion of non commutative truncated polynomial extension of an algebra A. We study two families of these extensions. For the first one we obtain a complete classification and for the second one, which we call upper…
Direct and indirect information on the top quark mass and its decay modes is reviewed. The theory of top production in hadron- and electron-positron-colliders is presented.
We give a proof of the Thom-Sebastiani theorem for mixed Hodge modules using a compatibility with Verdier specialization.
Congruence families, i.e., $\ell$-adic convergence for well-defined arithmetic subsequences, is a commonplace phenomenon for the coefficients of modular forms. Such families superficially resemble one another, but they often vary…