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We define a variant of intersection space theory that applies to many compact complex and real analytic spaces $X$, including all complex projective varieties; this is a significant extension to a theory which has so far only been shown to…
Properties of Hermitian forms are used to investigate several natural questions from CR Geometry. To each Hermitian symmetric polynomial we assign a Hermitian form. We study how the signature pairs of two Hermitian forms behave under the…
The following paper is inspired by Efimov's problem - an undecided problem of whether there exists an infinite compact topological space that does not contain neither non-trivial convergent sequences nor a copy of $\beta\omega$. After…
We present an alternative account of the problem of classifying and finding normal forms for arbitrary bilinear forms. Beginning from basic results developed by Riehm, our solution to this problem hinges on the classification of…
We study finite systems of subspaces of a complex Hilbert space such that each pair of subspaces satisfies a certain condition as described in the following. For each subspace excepting the first one an angle between this subspace and the…
We give an elementary construction of symplectic connections through reduction. This provides an elegant description of a class of symmetric spaces and gives examples of symplectic connections with Ricci type curvature, which are not…
We give an elementary proof of the Pieri-type formula in the cohomology of a Grassmannian of maximal isotropic subspaces of an odd orthogonal or symplectic vector space. This proof proceeds by explicitly computing a triple intersection of…
There is a deep connection between permutations and trees. Certain sub-structures of permutations, called sub-permutations, bijectively map to sub-trees of binary increasing trees. This opens a powerful tool set to study enumerative and…
Employing the currently discussed notion of pseudo-Hermiticity, we define a pseudo-unitary group. Further, we develop a random matrix theory which is invariant under such a group and call this ensemble of pseudo-Hermitian random matrices as…
In this article, we study geometric aspects of semi-arithmetic Riemann surfaces by means of number theory and hyperbolic geometry. First, we show the existence of infinitely many semi-arithmetic Riemann surfaces of various shapes and prove…
In this paper, for symplectic and split odd special orthogonal groups, we develop an account of theory on the intersection problem of local Arthur packets. Specifically, following Atobe's reformulation on M{\oe}glin's construction of local…
Let $M$ be a complex manifold. We prove that a compact submanifold $S\subset M$ with splitting tangent sequence (called a splitting submanifold) is rational homogeneous when $M$ is in a large class of rational homogeneous spaces of Picard…
Under ABC, Silverman showed that there are infinitely many non-Wieferich primes with respect to any (non-trivial) base $a$. Recently Srinivas and Subramani proved an analogous result over number fields with trivial class group. In the first…
A permutation $\sigma\in S_n$ is said to be $k$-universal or a $k$-superpattern if for every $\pi\in S_k$, there is a subsequence of $\sigma$ that is order-isomorphic to $\pi$. A simple counting argument shows that $\sigma$ can be a…
Following our approach to metric Lie algebras developed in math.DG/0312243 we propose a way of understanding pseudo-Riemannian symmetric spaces which are not semi-simple. We introduce cohomology sets (called quadratic cohomology) associated…
By using unramified cohomology groups, we construct a full sequence of cohomological invariants for hermitian forms of any type (orthogonal, symplectic or unitary) that can be used to detect hyperbolicity. The base central simple algebras…
We introduce and explore a new concept of evasive subspace with respect to a collection of subspaces sharing a common dimension, most notably partial spreads. We show that this concept generalises known notions of subspace scatteredness and…
Having developed a description of indefinite extrinsic symmetric spaces by corresponding infinitesimal objects in the preceding paper we now study the classification problem for these algebraic objects. In most cases the transvection group…
We study statistical properties of the random variables $X_{\sigma}(\pi)$, the number of occurrences of the pattern $\sigma$ in the permutation $\pi$. We present two contrasting approaches to this problem: traditional probability theory and…
In this paper, a supersymmetric extension of the minimal surface equation is formulated. Based on this formulation, a Lie superalgebra of infinitesimal symmetries of this equation is determined. A classification of the one-dimensional…