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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Introduction to Bourguignon-Gauduchon's variation formula for Dirac operators
Dirac算子 Bourguignon-Gauduchon 变分公式
2023/11/13
我们将介绍由Bar-Gauduchon-Moroianu给出的spin流形上Dirac算子在度量变化时一阶变分公式的证明。作为应用，我们将计算Dirac算子沿Ricci flow的一阶变分。
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Ambartzumian combinatorial formula and its applications
Ambartzumian 组合公式 有限线段集
2023/11/6
Consider a finite set of segments on a plane with endpoints in the general position. In [1] Sylvester posted a problem of finding the measure of the set of lines intersecting all of this segments. In ...
Turning a circle into a square is possible with this kirigami-inspired formula（图）
kirigami 圆形 正方形 几何
2023/6/5
Kirigami takes pop-up books to a whole new level. The Japanese paper craft involves cutting patterns in paper to transform a two-dimensional sheet into an intricate, three-dimensional structure when p...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Gauss-Bonnet formula beyond the aspherical conjecture
超越非球面猜想 Gauss-Bonnet 曲面
2023/4/21
In this talk, I'll make a discussion on recent progress in the research of scalar curvature. I'll review the backgrounds from Gauss-Bonnet formula to the aspherical conjecture, and then focus on the f...
We use the Pieri and Giambelli formulas of [BKT1, BKT3] and
the calculus of raising operators developed in [BKT2, T1] to prove a tableau
formula for the eta polynomials of [BKT3] and the Stanley sym...
A GIAMBELLI FORMULA FOR EVEN ORTHOGONAL GRASSMANNIANS
ORTHOGONAL GRASSMANNIANS GIAMBELLI FORMULA
2015/12/17
Let X be an orthogonal Grassmannian parametrizing isotropic
subspaces in an even dimensional vector space equipped with a nondegenerate
symmetric form. We prove a Giambelli formula which expresses a...
A GIAMBELLI FORMULA FOR ISOTROPIC GRASSMANNIANS
ISOTROPIC GRASSMANNIANS GIAMBELLI FORMULA
2015/12/17
Let X be a symplectic or odd orthogonal Grassmannian. We prove
a Giambelli formula which expresses an arbitrary Schubert class in H∗
(X, Z)
as a polynomial in certain special Schubert classes...
Energy of Harmonic Maps and Gardiner’s Formula
Harmonic maps Teichmuller space measured foliation
2015/12/17
It is shown that the usual first variational formula for the energy of a harmonic map (or equivariant harmonic map) with respect to the conformal structure on a two dimensional domain extends to case ...
In the famous papers [1] and [2], J Cheeger, S Chern and J Simons define characteristic
classes for flat G–bundles. Each such characteristic class is given by a corresponding
universal c...
Hopf bifurcation formula for first order differential-delay equations
Hopf bifurcation Differential delay equation DDE Retarded functional differential equation RFDE
2015/8/27
This work presents an explicit formula for determining the radius of a limit cycle which is born in a Hopf bifurcation in a class of first order constant coefficient differential-delay equations. The ...
ON THE VORONO˘I FORMULA FOR GL(n)
Automorphic forms Voronoi formula L-functions Whittaker functions
2015/8/25
We prove a general Vorono˘ı formula for cuspidal automorphic representations of GL(n) over number fields. This generalizes recent work by Miller-Schmid and Goldfeld-Li on Maass forms. Our me...
Analysis of Belief Propagation for Non-Linear Problems: The Example of CDMA (or: How to Prove Tanaka’s Formula)
Binary signal and white gaussian noise spread sequence scheme of linear time
2015/8/21
We consider the CDMA (code-division multipleaccess) multi-user detection problem for binary signals and additive white gaussian noise. We propose a spreading sequences scheme based on random sparse si...
We suppose that the statistician observes some large number of estimates zi
, each with
its own unobserved expectation parameter i
. The largest few of the zi
's are likely to
substantially over...
Trace formula for the Sturm-Liouville eigenvalue problem with its applications to n-body problem
Sturm-Liouville eigenvalue applications n-body problem
2015/3/18
Trace formula for the Sturm-Liouville eigenvalue problem with its applications to n-body problem.
Let G be a classical complex Lie group, P any parabolic subgroup
of G, and G/P the corresponding partial flag variety. We prove an explicit
combinatorial Giambelli formula which expresses an a...