Related papers: Higher order spectra, equivariant Hodge-Deligne po…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
We propose a method for constructing systems of polynomial equations that define submanifolds of degenerate binary forms of an arbitrary degeneracy degree. It is appropriate to call these systems of equations "higher discriminants".
We construct hyper-homology spectral sequences of Z-graded and ROG-graded Mackey functors for Ext and Tor over G-equivariant S-algebras (A-infty ring spectra) for finite groups G. These specialize to universal coefficient and Kunneth…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
Solutions which are quasimodular forms to a second order differential equation attached to a triangular group are explicitly described in terms of certain orthogonal polynomials.
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
There are (at least) two different approaches to define equivariant analogue of the Euler charateristic for a space with a finite group action. The first one defines it as an element of the Burnside ring of the group. The second approach…
For a complex quasi-projective manifold with a finite group action, we define higher order generalized Euler characteristics with values in the Grothendieck ring of complex quasi-projective varieties extended by the rational powers of the…
J. Milnor introduced a specific class of codimension-$1$ submanifolds in the product of projective spaces, known as Milnor manifolds. This paper establishes precise bounds on the higher topological complexity of these manifolds and provides…
We define new higher-order Alexander modules $\mathcal{A}_n(C)$ and higher-order degrees $\delta_n(C)$ which are invariants of the algebraic planar curve $C$. These come from analyzing the module structure of the homology of certain…
We study the spectrum of prime ideals in the tensor-triangulated category of compact equivariant spectra over a finite group. We completely describe this spectrum as a set for all finite groups. We also make significant progress in…
We study finiteness (and vanishing) properties of the higher order degrees associated to complements of complex affine plane curves with mild singularities at infinity. Our results impose new obstructions on the class of groups that can be…
We present the theory of higher order invariants and higher order automorphic forms in the simplest case, that of a compact quotient. In this case many things simplify and we are thus able to prove a more precise structure theorem than in…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. The associated special functions are eigenfunctions of some shape invariant operators. These operators can…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
For any finite group G, there are several well-established definitions of a G-equivariant spectrum. In this paper, we develop the definition of a global orthogonal spectrum. Loosely speaking, this is a coherent choice of orthogonal…
Classical homological algebra considers chain complexes, resolutions, and derived functors in additive categories. We describe "track algebras in dimension n", which generalize additive categories, and we define higher order chain…
A survey of some results and open questions related to the following algebraic invariants of compact complex manifolds, that can be obtained from differential forms: cohomology groups, Chern classes, rational homotopy groups, and higher…
We describe a conjecture on the algebra of higher cohomology operations which leads to the computations of the differentials in the Adams spectral sequence. For this we introduce the notion of an n-th order track category which is suitable…
Higher order cohomology of arithmetic groups is expressed in terms of (g,K)-cohomology. Generalizing results of Borel, it is shown that the latter can be computed using functions of (uniform) moderate growth. A higher order versions of…