Related papers: Root systems and hyperkahler varieties
We introduce a new Floer theory associated to a pair consisting of a Cartan hypercontact 3-manifold M and a hyperkaehler manifold X.
We show that birational hyper-K\"ahler varieties of $K3^{[n]}$-type are derived equivalent, establishing the D-equivalence conjecture in these cases. The Fourier-Mukai kernels of our derived equivalences are constructed from projectively…
We discuss the relationship between Hopf superalgebras and Hopf algebras. We list the braided vector spaces of diagonal type with generalized root system of super type and give the defining relations of the corresponding Nichols algebras.
We build an explicit link between coherent functors in the sense of Auslander and strict polynomial functors in the sense of Friedlander and Suslin. Applications to functor cohomology are discussed.
One can associate to a valued field an inverse system of valued hyperfields $(\mathcal{H}_i)_{i \in I}$ in a natural way. We investigate when, conversely, such a system arise from a valued field. First, we extend a result of Krasner by…
The concept of hierarchy in complex systems is tightly linked to co-evolutionary processes. We propose here to explore it in the case of the co-evolution between transportation networks and territories. More precisely, we extend a…
With any hyper-K\"ahler variety $K$ of generalized Kummer type is associated via Hodge theory a K3 surface $S_K$. We show how they are related geometrically through a moduli space of sheaves on $S_K$. As a consequence, building…
We discuss several numerical conditions for families of projective varieties or variations of Hodge structures.
Motivated by the famous Skolem-Mahler-Lech theorem we initiate in this paper the study of a natural class of determinantal varieties which we call {\em Vandermonde varieties}. They are closely related to the varieties consisting of all…
Hypertoric varieties are hyperk\"ahler analogues of toric varieties, and are constructed as abelian hyperk\"ahler quotients of a quaternionic affine space. Just as symplectic toric orbifolds are determined by labelled polytopes, orbifold…
We give an explicit integral formula for the Dunkl kernel associated to root system of type $A_2$ and parameter $k>0$, by exploiting recent result in [1].
There is a mysterious connection between the multiple polylogarithms at N-th roots of unity and modular varieties. In this paper we "explain" it in the simplest case of the double logarithm. We introduce an Euler complex data on modular…
We prove that characteristic equations of certain types of delay differential systems, under some mild conditions on their coefficients, can possess infinitely many complex roots.
We discuss the relationship between kernels, images and cokernels of morphisms between perverse sheaves and induced maps on stalk cohomology.
For a root system of type $B$ we study an algebra similar to a graded Hecke algebra, isomorphic to a subalgebra of the rational Cherednik algebra. We introduce principal series modules over it and prove an irreducibility criterion for these…
Recent advances in computational techniques for $K$-theory allow us to describe the $K$-theory of toric varieties in terms of the $K$-theory of fields and simple cohomological data.
We give a survey of elliptic hypergeometric functions associated with root systems, comprised of three main parts. The first two form in essence an annotated table of the main evaluation and transformation formulas for elliptic…
We investigate the roots of Hilbert quasipolynomials arising from certain rational generating functions.
We describe extension classes arising in the $\ell$-adic and Hodge cohomology of Hilbert modular varieties, generalising results of Caspar to arbitrary dimensions. We show that this description is consistent with the "plectic conjectures"…
This thesis is split up into two parts: The first one concerns (pseudo)-holomorphic Hamiltonian systems, while the second part is about K\"ahler structures of complex coadjoint orbits. We begin the first part by investigating basic…