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We deduce a formula enumerating the isomorphism classes of extensions of a $\kp$-adic field $K$ with given ramification $e$ and inertia $f$. The formula follows from a simple group-theoretic lemma, pl...
The quaternionic Grassmannian HGr(r,n) is the affine open subscheme of the ordinary Grassmannian parametrizing those 2r-dimensional subspaces of a 2n-dimensional symplectic vector space on which the ...
In 1974, S.-S. Chern and J. Simons published a paper where they defined a new type of characteristic class - one that depends not just on the topology of a manifold but also on the geometry. The goal...
Conjugacy classes in Weyl groups and q-W algebras     Conjugacy classes  Weyl groups  q-W algebras       font style='font-size:12px;'> 2010/11/17
We define noncommutative deformations W_q^s(G) of algebras of regular functions on certain transversal slices to the set of conjugacy classes in an algebraic group G which play the role of Slodowy sl...
Conditions are provided under which lack of domination of a homoclinic class yields robust heterodimensional cycles. Moreover, so-called viral homoclinic classes are studied. Viral classes have the p...
Classes of extension modules by Serre subcategories     extension modules  Serre subcategories       font style='font-size:12px;'> 2010/11/9
In this paper, to find a way of constructing Serre subcategories of the modules category, we consider classes of extension modules of Serre subcategory by another one and study when these classes are ...
Transcription factors (TF) play an essential role in the cell as locus- and condition-specific recruiters of transcriptional machinery or chromatin-modifying complexes. However, predicting the in vivo...
Two classes of slant surfaces in nearly Kahler six sphere      slant surfaces  K¨ahler angle  octonions  six sphere       font style='font-size:12px;'> 2010/12/14
In this paper we find examples of slant surfaces in the nearly K¨ahler six sphere. First, we characterize two-dimensional small and great spheres which are slant.
Given a pair (G, a) where G is a finitely presentable group and a is an integer homology class of this group, Gromov defined in [Gro83] a new numerical invariant associated to this pair called systoli...
It is well known that the Hodge conjecture with rational coefficients holds for degree 2n − 2 classes on complex projective n-folds. In this paper we study the more precise question if on a rati...
An Asymptotic for the Number of Solutions to Linear Equations in Prime Numbers from Specified Chebotarev Classes.
On Approximations and Ergodicity Classes in Random Chains      Approximations  Ergodicity Classes  Random Chains        font style='font-size:12px;'> 2010/11/30
We study the limiting behavior of a random dynamic system driven by a stochastic chain. Our main interest is in the chains that are not necessarily er godic but rather decomposable into ergodic classe...
We show the q-analog of a well-known result of Farahat and Higman: in the center of the Iwahori-Hecke algebraHn,q, if (a  μ(n, q)) is the set of structure constants involved in the product of two G...
We fix a non-zero integer a and consider arithmetic progressions a mod q, with q varying over a given range. We show that for certain specific values of a, the arithmetic progressions a mod q contain,...
By resolving any perfect derived object over a Deligne-Mumford stack, we define its Euler class. We then apply it to define the Euler numbers for a smooth Calabi-Yau threefold in P4. These numbers are...

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