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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Rational points and homogeneous spaces over function fields of curves
曲线函数场 有理点 齐次空间
2023/4/17
In the last decade, there has been a growing interest in the study of rational points on homogeneous spaces of linear algebraic groups defined over fields having good arithmetical properties other tha...
Quadrature rules and distribution of points on manifolds
Quadrature discrepancy harmonic analysis
2011/2/28
We study the error in quadrature rules on a compact manifold, XN j=1 !jf (zj) − Z
M f(x)dx ≤ cD {zj} V {f} .
We obtain an upper bound for the derivative of a Blaschke product, whose zeros lie in a certain Stolz-type region. We show that the derivative belongs to the space of analytic functions in the unit di...
A sharp bound on fixed points of surface symplectomorphisms in each mapping class
sharp bound fixed points of surface symplectomorphisms
2010/11/29
Given a closed, oriented surface , possibly with boundary, and a mapping class, we obtain sharp lower bounds on the number of xed points of a surface symplectomorphism (i.e. area-preserving map) in ...
Asymptotic of geometrical navigation on a random set of points of the plane
Asymptotic of geometrical navigation random set of points plane
2010/12/10
A navigation on a set of points is a rule for choosing which point to move to from the
present point in order to progress toward a specified target. In the present paper we study
some “geometrical b...
Let f be a transcendental entire function and let A(f) denote the set of points that escape to infinity ‘as fast as possible’ under iteration. By writing A(f) as a countable union of closed sets, call...
On 1-point Gromov-Witten invariants of the Hilbert schemes of points on surfaces
Hilbert schemes projective surfaces Gromov-Witten invariants
2010/3/1
We compute certain 1-point genus-0 Gromov-Witten invariants of the Hilbert scheme of points on a simply-connected smooth projective surface.
Denting Points in Bochner Banach Ideal Spaces X(E)
Denting Points Bochner Banach Ideal Spaces X(E)
2009/1/20
Let $(X, \|.\|_{X})$ be an order-continuous Banach ideal space over a $\sigma-$ finite measure space $(\Omega,\Sigma,\mu)$ and $E$ a Banach space. We prove that a function $f$ of the vector Banach ide...
Solutions Near Singular Points to the Eikonal and Related First Order Non-linear Partial Differential Equations in Two Independent Variables
Singular Points Eikonal Partial Differential Equations
2010/11/1
A detailed study of solutions to the first order partial differential equation H(x,y,z_x,z_y)=0, with special emphasis on the eikonal equation z_x^2+z_y^2=h(x,y), is made near points where the equatio...