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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The pseudoeffective cone on projective manifolds
射影流形 赝有效锥 全纯线丛
2023/5/15
We report the work of Boucksom-Demailly-Paun-Peternell, which shows that a holomorphic line bundle on a projective manifold is pseudoeffective iff its degree on any member of a covering family of curv...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Expanding cone and homogeneous dynamics
膨胀锥体 均匀动力学 非紧致简单李群
2023/4/17
We introduce the notion of expanding cone of a noncompact simple Lie group. This allows us to extend several results in homogeneous dynamics to more general settings. We show how this notion is used i...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Morrison-Kawamata cone conjecture for Calabi-Yau fiber spaces
Calabi-Yau fiber spaces 莫里森-川俣 锥猜想
2023/5/9
In this talk, I will explain the relationship between the Morrison-Kawamata cone conjecture for Calabi-Yau fiber spaces and the existence of Shokurov polytopes. For K3 fibrations, this enables us to e...
Applications of second-order cone programming
Second-order cone programming linear function affine sets linear nonlinear convex problem quadratic program
2015/8/11
In a second-order cone program (SOCP) a linear function is minimized over the intersection of an affine set and the product of second-order (quadratic) cones. SOCPs are nonlinear convex problems that ...
Geodesics in the space of Kahler cone metrics
Geodesics the space of Kahler cone metrics Analysis of PDEs
2012/5/9
In this paper, we prove the existence and uniqueness of the weak cone geodesics in the space of K\"ahler cone metrics by solving the singular, homogeneous complex Monge-Amp\`{e}re equation. As an appl...
Liouville-Arnold integrability for scattering under cone potentials
Liouville-Arnold integrability scattering cone potentials Dynamical Systems
2012/4/26
The problem of scattering of particles on the line with repulsive interactions, gives rise to some well-known integrable Hamiltonian systems, for example, the nonperiodic Toda lattice or Calogero's sy...
Reducing scattering problems under cone potentials to normal form by global canonical transformations
scattering problems cone normal form global canonical transformations Exactly Solvable and Integrable Systems
2012/4/26
We introduce a class of Hamiltonian scattering systems which can be reduced to the "normal form" $\dot P=0$, $\dot Q=P$, by means of a global canonical transformation $ (P,Q)=A(p,q), p,q\in R^n$, defi...
Complete Integrability for Hamiltonian Systems with a Cone Potential
Complete Integrability Hamiltonian Systems Cone Potential
2012/4/26
It is known that, if a point in $R^n$ is driven by a bounded below potential $V$, whose gradient is always in a closed convex cone which contains no lines, then the velocity has a finite limit as time...
Common fixed points theorem for two multivalued mappings in cone metric spaces
functional analysis common fixed point non normal cone multivalued mapping cone metric spaces
2011/10/20
In this paper, a new generalized contractive condition is introduced in metric space. By the condition and without the normality of the cone, the existence of common fixed points of multivalued mappin...
Birational automorphism groups and the movable cone theorem for Calabi-Yau manifolds of Wehler type via universal Coxeter groups
Birational automorphism groups movable cone theorem Calabi-Yau manifolds of Wehler type
2011/9/22
Abstract: We prove that the birational automorphism group of any Calabi-Yau manifold given by a generic hypersurface of multi-degree two in $({\mathbf P^1})^{n+1}$ is isomorphic to the universal Coxet...
$sl_2$ conformal block divisors and the nef cone of $\bar{M}_{0,n}$
the nef cone Algebraic Geometry
2011/9/21
Abstract: We show that $sl_2$ conformal block divisors do not cover the nef cone of $\bar{M}_{0,6}$, or the $S_9$-invariant nef cone of $\bar{M}_{0,9}$. A key point is to relate the nonvanishing of in...
Continuity of the cone spectral radius
Cone spectral radius, continuity, cone spectrum, nonlinear cone maps,fixed point index
2011/9/19
Abstract: This paper concerns the question whether the cone spectral radius of a continuous compact order-preserving homogenous map on a closed cone in Banach space depends continuously on the map. Us...
Asymptotic cone of semisimple orbits for symmetric pairs
asymptotic cone Richardson orbit nilpotent orbit symmetric pair
2011/2/21
Let G be a reductive algebraic group over C and denote its Lie algebra by g. Let Oh be a closed G-orbit through a semisimple element h ∈ g. By a result of Borho and Kraft [BK79], it is known that the ...
Energy estimate for initial data on a characteristic cone
Energy estimate initial data characteristic cone
2011/3/2
The Einstein equations in wave map gauge are a geometric second order system for a Lorentzian metric. To study existence of solutions of this hyperbolic quasi diagonal system with initial data on a ch...
The incenter of a triangle as a cone isoperimetric center
Incenter isoperimetric problem optimization center
2011/3/1
We show that the the image of the regular projection of a vertex of a cone over a triangle
that minimizes the ratio of the cube of the area of the boundary of the cone and the square
of the volume o...