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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Strong approximation and integral quadratic forms over affine curves
仿射曲线 强近似 积分二次形式
2023/5/9
Let $k$ be a field of characteristic 0 and let $C$ be the a smooth affine curve over $k$. We will first discuss applications of strong approximation to the theory of integral quadratic forms over $C$....
We prove that the essential dimension of the spinor group
Spinn grows exponentially with n and use this result to show that quadratic forms with trivial discriminant and Hasse-Witt invariant are more...
Universal quadratic forms and Whitney tower intersection invariants
Whitney towers twisted Whitney towers quadratic refinements Arf invariants Lie algebra
2012/7/11
The first part of this paper exposits a simple geometric description of the Kirby-Siebenmann invariant of a 4--manifold in terms of a quadratic refinement of its intersection form. This is the first i...
Deformation Expression for Elements of Algebras (III) --Generic product formula for *-exponentials of quadratic forms--
Weyl algebra Heisenberg Lie algebra meta-plectic groups spinor polar elements
2011/9/5
Abstract: In a noncommutative algebra there is no canonical way to express elements in univalent way, which is often called "ordering problem". In this note we give product formula of the Weyl algebra...
Concentration of points on Modular Quadratic Forms
modular equation quadratic form concentration of points
2011/2/21
Let Q(x, y) be a quadratic form with discriminant D 6= 0. We obtain non trivial upper
bound estimates for the number of solutions of the congruence Q(x, y) ≡ (mod p), where p is
a prime and x, y l...
Freeness of Linear and Quadratic Forms in von Neumann Algebras
Free random variables free convolutions a characterization of the semicircle law
2011/2/28
We characterize the semicircular distribution by freeness of linear and qua-dratic forms in noncommutative random variables from tracial W-probability spaces with relaxed moment conditions.
Clifford modules and invariants of quadratic forms
Clifford modules invariants of quadratic forms
2011/2/22
For any integer k > 0, the Bott class k in topological complex K-theory is well known [7], [12, pg. 259].
An Inequality on Ternary Quadratic Forms in Triangles
Positive semidefinite ternary quadratic form arithmetic-mean geometric-mean inequality Cauchy inequality triangle
2010/1/22
In this short note, we give a proof of a conjecture about ternary quadratic orms involving two triangles and several interesting applications.
Rank-one-convex and Quasiconvex Envelopes for Functions Depending on Quadratic Forms
rank-one-convex quasiconvex envelope quadratic form James-Ericksen function Pipkin's formula
2009/2/5
In this paper we are interested in functions defined, on a set of matrices, by the mean of quadratic forms and we compute the rank-one-convex, quasiconvex, polyconvex and convex envelopes of these fun...
Harmonic analysis, quadratic forms and asymptotic expansions of risk measures
Quadratic form Gaussian model stationary phase
2010/9/10
In this paper we develop asymptotic expansions of Conditional Value at Risk (CVaR), one of the most widely used risk measures in the financial industry, based on harmonic analysis and the method of st...
<正> Meyer proved in 1883 theTheorem M.ecery indetiuite quadratie form in more than fourrep(?)sents zero with the rariables not all zero.
Formulas for the Fourier Coefficients of Cusp Form for Some Quadratic Forms
representation of numbers quadratic forms generalized theta series Fourier coefficient of cusp forms
2010/2/26
In this paper, representations of positive integers by certain quadratic forms Qp defined for odd prime p are examined. The number of representations of positive integer n by the quadratic form Qp, is...
A correspondence between various Pin-type structures on a compact surface and quadratic (Iinear) forms on its homology is constructed. Sum of structures is defined and expressed in terms of these quad...