Related papers: Singular Light Leaves
We recast the classical notion of standard tableaux in an alcove-geometric setting and extend these classical ideas to all reduced paths in our geometry. This broader path-perspective is essential for implementing the higher categorical…
A novel and simple superbunching pseudothermal light source is introduced based on common instruments such as laser, lens, pinhole and groundglass. $g^{(2)}(0)=3.66 \pm 0.02$ is observed in the suggested scheme by employing two rotating…
We classify a class of complex representations of an arbitrary Coxeter group via characters of the integral homology of certain graphs. Such representations can be viewed as a generalization of the geometric representation and correspond to…
We study the symplectic leaves of the subvariety of fixed points of an automorphism of a Calogero-Moser space induced by an element of finite order of the normalizer of the associated complex reflection group $W$. We give a parametrization…
We construct real polarizable Hodge structures on the reduced leafwise cohomology of K\"ahler-Riemann foliations by complex manifolds. As in the classical case one obtains a hard Lefschetz theorem for this cohomology. Serre's K\"ahlerian…
For an isolated hypersurface singularity which is neither simple nor simple elliptic, it is shown that there exists a distinguished basis of vanishing cycles which contains two basis elements with an arbitrary intersection number. This…
The complex singlet-doublet model is a popular theory to account for dark matter and electroweak baryogenesis, wherein the Standard Model particle content is supplemented by a complex scalar gauge singlet, with certain discrete symmetries…
A planar (upper) semimodular lattice $L$ is slim if the five-element nondistributive modular lattice $M_3$ does not occur among its sublattices. (Planar lattices are finite by definition.) Slim rectangular lattices as particular slim planar…
We provide base change theorems, projection formulae and Verdier duality for both cohomology and homology in the context of finite topological spaces
There exist natural generalizations of the real moduli space of Riemann spheres based on manipulations of Coxeter complexes. These novel spaces inherit a tiling by the graph-associahedra convex polytopes. We obtain explicit configuration…
We enlarge a Coxeter group into a category, with one object for each finite parabolic subgroup, encoding the combinatorics of double cosets. This category, the singular Coxeter monoid, is connected to the geometry of partial flag varieties.…
The integral monodromy on the Milnor lattice of an isolated quasihomogeneous singularity is subject of an almost untouched conjecture of Orlik from 1972. We prove this conjecture for all iterated Thom-Sebastiani sums of chain type…
We refine Brieskorn's study of the cohomology of the complement of the reflection arrangement of a finite Coxeter group $W$. As a result we complete the verification of a conjecture by Felder and Veselov that gives an explicit basis of the…
Computing the extensions between Verma modules is in general a very difficult problem. Using Soergel bimodules, one can construct a graded version of the principal block of Category $\mathcal{O}$ for any finite coxeter group. In this…
A recent baryogenesis scenario [Phys. Rev. D 110, 023520 (2024)], rooted in a two-brane Universe model, proposed a solution to the matter-antimatter asymmetry through the dynamics of a new pseudo-scalar field. In the present paper, one…
In this paper we focus on various aspects of singular complex plane curves, mostly in the context of their homological properties and the associated combinatorial structures. We formulate some challenging open problems that can point to new…
A special subcomplex of the singular chain complex for a topological space, historically called oriented singular chain complex is used here with the new name "alternative" singular chain complex. It was already known that this subcomplex…
We prove the relative hard Lefschetz theorem for Soergel bimodules. It follows that the structure constants of the Kazhdan-Lusztig basis are unimodal. We explain why the relative hard Lefschetz theorem implies that the tensor category…
We develop the notion of singular support of a coherent sheaf on a quasi-smooth DG scheme or stack and use it to formulate the Geometric Langlands Conjecture.
An isolated hypersurface singularity comes equipped with many different pairings on different spaces, the intersection form and the Seifert form on the Milnor lattice, a polarizing form for a mixed Hodge structure on a dual space, and a…