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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Invariant Geometric Flows in Affine-related Geometries
仿射 相关几何 不变几何流
2023/4/26
In this talk, we are mainly concerned with invariant geometric flows in affine-related geometries including centro-equiane, centro-affine, affine and affine-symplectic geometries. First, we show that ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Some geometry of affine Deligne-Lusztig varieties
仿射 Deligne-Lusztig变种 几何
2023/5/17
The mod p points of a Shimura variety have a conjectural description called the Langlands-Rapoport conjecture. In accordance with the conjecture, Rapoport defined (generalized) affine Deligne-Lusztig ...
AFFINE CUBIC SURFACES AND RELATIVE SL(2)-CHARACTER VARIETIES OF COMPACT SURFACES
AFFINE CUBIC SURFACES RELATIVE SL(2)-CHARACTER
2015/9/29
A natural family of affine cubic surfaces arises from
SL(2)-characters of the 4-holed sphere and the 1-holed torus. The
ideal locus is a tritangent plane which is generic in the sense that
the...
FINITE-SIDED DEFORMATION SPACES OF COMPLETE AFFINE 3-MANIFOLDS
3-MANIFOLDS DEFORMATION SPACES
2015/9/29
A Margulis spacetime is a complete affine 3-manifold
M with nonsolvable fundamental group. Associated to every Margulis spacetime is a noncompact complete hyperbolic surface S.
We show that eve...
THE RADIANCE OBSTRUCTION AND PARALLEL FORMS ON AFFINE MANIFOLDS
RADIANCE OBSTRUCTION PARALLEL FORMS
2015/9/29
A manifold M is affine if it is endowed with a distinguished atlas whose
coordinate changes are locally affine. When they are locally linear M is called
radiant. The obstruction to radiance is a o...
Those groups r which act properly discontinuously and aillnely on II?’ with
compact fundamental domain are classified. First it is shown that such a group f
contains a solvable subgroup of finite ...
An affine manifold is a manifold with a distinguished
system of affine coordinates, namely, an open covering by
charts which map homeomorphically onto open sets in an
affine space E such that on ov...
It is well known that the real cohomology of a compact Riemannian manifold
M is isomorphic to the algebra of its harmonic forms. When M is a fiat
Riemannian manifold, i.e. a Euclidean manifold, a ...
Geometry of optimal control for control-affine systems
affine distributions optimal control theory Cartan's method of equivalence
2012/6/21
Motivated by the ubiquity of control-affine systems in optimal control theory, we investigate the geometry of point-affine control systems with metric structures in dimensions two and three. We comput...
Quasi-umbilical affine hypersurfaces congruent to their centre map
affine differential geometry quasi-umbilical center map Differential Geometry
2012/6/12
In this paper, we study strictly convex affine hypersurfaces centroaffinely congruent to their centre map, in the case when the shape operator has two distinct eigenvalues: one of multiplicity 1, and ...
In this paper, we give a characterization of existence of a dense orbit for the action on Cn of an abelian affine subgroup G of GA(n,C). We prove in particular that if G has a dense orbit then the clo...
Shape theory via affine transformation: Some generalisations
Jacobians Jack polynomials generalised hypergeometric functions
2011/2/28
This work sets the statistical affine shape theory in the context of real normed divi-sion algebras. The general densities apply for every field: real, complex, quaternion,octonion, and for any noncen...
On affine maps on non-compact convex sets and some characterizations of finite-dimensional solid ellipsoids
affine maps non-compact convex sets characterizations of finite-dimensional solid ellipsoids
2011/2/25
In recent studies, properties of the set of affine maps between two convex sets have been
investigated with intensive motivation from quantum physics, but in those preceding works
the underlying con...
Infinite loop spaces associated to affine Kac-Moody groups
generalized Cartan matrix infinite loop space affine Kac-Moody group
2011/2/25
It is well known that to each infinite class of classical groups over a commutative ring R, we can associate an infinite loop space by Quillen’s plus construction. In this paper we generalize this fac...
Integrable defects in affine Toda field theory and infinite dimensional representations of quantum groups
Integrable defects affine Toda field theory infinite dimensional representations quantum groups
2011/3/3
Transmission matrices for two types of integrable defect are calculated explicitly, first by solving directly the nonlinear transmission Yang-Baxter equations.