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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On cancellation laws in cardinal arithmetic without the axiom of choice
选择公理 基数算术 取消定律
2023/4/17
We survey known results concerning cancellation laws in cardinal arithmetic without the axiom of choice. These results include the cancellation law for Dedekind finite cardinals in cardinal addition a...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Arithmetic purity of strong approximation for complete toric varieties
完整 复曲面品种 强近似 算术纯度
2023/4/18
In this talk, I will discuss arithmetic purity of strong approximation : motivations and related results. Finally, for complete toric varieties, I will briefly explain my work on this topic.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Density of orbits and arithmetic degrees of automorphisms of projective threefolds
射影三重 轨道密度 自同构 算术度
2023/4/18
The Zariski dense orbit conjecture of the arithmetic dynamic is to study the existence of a rational point P with a Zariski dense orbit of a dominant rational self-map f of a projective variety X. Whe...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Arithmetic mixed Siegel-Weil formulas and modular forms of arithmetic divisors
算术混合 西格尔-威尔公式 算术除数 模形式
2023/5/5
The classical Siegel–Weil formula relates theta series to Eisenstein series and its arithmetic version is central in Kudla's program. I will discuss arithmetic mixed Siegel-Weil formulas. I will focus...
Let E : 0 ! S ! E ! Q ! 0 be a short exact sequence of
hermitian vector bundles with metrics on S and Q induced from that
on E. We compute the Bott-Chern form áe(E ) corresponding to any
characteri...
Let F be the complete °ag variety over SpecZ with the tautological
ˉltration 0 ½ E1 ½ E2 ½ ￠ ￠ ￠ ½ En = E of the trivial bundle E of rank
n over F. The trivial hermitian metric o...
Schubert Calculus on the Arithmetic Grassmannian
Arithmetic Grassmannian Schubert Calculus
2015/12/17
Let G be the arithmetic Grassmannian over SpecZ with the natural invariant KÄahler metric on G(C). We study the combinatorics of
the arithmetic Schubert calculus in the Arakelov Chow ring CH(G)
STANDARD CONJECTURES FOR THE ARITHMETIC GRASSMANNIAN G(2; N) AND RACAH POLYNOMIALS
STANDARD CONJECTURES RACAH POLYNOMIALS
2015/12/17
We prove the arithmetic Hodge index and hard Lefschetz conjectures for the Grassmannian G = G(2; N) parametrizing
lines in projective space, for the natural arithmetic Lefschetz operator de ned via t...
THE HODGE CONJECTURE AND ARITHMETIC QUOTIENTS OF COMPLEX BALLS
HODGE CONJECTURE ARITHMETIC QUOTIENTS COMPLEX BALLS
2015/10/14
Let S be a closed Shimura variety uniformized by the complex n-ball. The Hodge conjecture predicts that every Hodge class in H2k(S, Q), k = 0, . . . , n, is algebraic. We show that this holds for all ...
HODGE TYPE THEOREMS FOR ARITHMETIC MANIFOLDS ASSOCIATED TO ORTHOGONAL GROUPS
HODGE TYPE THEOREMS ARITHMETIC MANIFOLDS ORTHOGONAL GROUPS
2015/10/14
We show that special cycles generate a large part of the cohomology of locally symmetric spaces associated to orthogonal groups. We prove in particular that classes of totally geodesic submanifolds ge...
SPLITTING FIELDS OF CHARACTERISTIC POLYNOMIALS OF RANDOM ELEMENTS IN ARITHMETIC GROUPS
SPLITTING FIELDS CHARACTERISTIC POLYNOMIALS RANDOM ELEMENTS ARITHMETIC GROUPS
2015/8/26
We discuss rather systematically the principle, implicit in earlier works, that for a “random” element in an arithmetic subgroup of a (split, say) reductive algebraic group over a number field, the sp...
PROPER FORCING,CARDINAL ARITHMETIC,AND UNCOUNTABLE LINEAR ORDERS
PROPER FORCING CARDINAL ARITHMETIC UNCOUNTABLE LINEAR ORDERS
2015/8/17
In this paper I will communicate some new consequences of the Proper Forcing Axiom. First, the Bounded Proper Forcing Axiom implies that there is a well ordering of R which is Σ1-definable in (H(ω2), ...
ARITHMETIC PROPERTIES OF THE SHIMURA-SHINTANI-WALDSPURGER CORRESPONDENCE
ARITHMETIC PROPERTIE CORRESPONDENCE
2015/7/6
We prove that the theta correspondence for the dual pair (SLg2; P B￡), for B an indeˉnite
quaternion algebra over Q, acting on modular forms of odd square-free level, preserves
rationality and p-int...
Deligne and Rapoport developed the theory of generalized elliptic curves over
arbitrary schemes and they proved that various moduli stacks for (ample) “level-N” structures on generalized
elliptic cu...
An integer $n$ is said to be \textit{arithmetic} if the arithmetic mean of its divisors is an integer. In this paper, using properties of the factorization of values of cyclotomic polynomials, we char...