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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Number of rational points of difference varieties in finite difference fields
有限差分域 差分簇 有理点数
2023/4/13
A difference field is a field with a distinguished automorphism. Automorphisms of a finite field are powers of the Frobenius map. In this talk, I will discuss how to estimate the number of rational po...
THE IDEAL OF RELATIONS FOR THE RING OF INVARIANTS OF n POINTS ON THE LINE:INTEGRALITY RESULTS
RELATIONS FOR THE RING INVARIANTS OF n POINTS ON THE LINE INTEGRALITY RESULTS
2015/10/14
Consider the projective coordinate ring of the GIT quotient (P1)n//SL(2), with the usual linearization, where n is even. In 1894, Kempe proved that this ring is generated in degree one. In [HMSV2]we s...
ELLIPTIC CURVES WITH MAXIMAL GALOIS ACTION ON THEIR TORSION POINTS
ELLIPTIC CURVES MAXIMAL GALOIS ACTION TORSION POINTS
2015/8/26
Given an elliptic curve E over a number field k, the Galois action on the torsion points of E induces a Galois representation, ρE : Gal(k/k) → GL2(Z b). For a fixed number field k, we describe the ima...
DRINFELD MODULES WITH MAXIMAL GALOIS ACTION ON THEIR TORSION POINTS
DRINFELD MODULES MAXIMAL GALOIS ACTION TORSION POINTS
2015/8/26
To each Drinfeld module of generic characteristic defined over a finitely generated field, one can associate a Galois representation arising from the Galois action on its torsion points. Recent work o...
We consider the ring of invariants of n points on the projective line. The space (P
1)
n//PGL2 is
perhaps the first nontrivial example of a Geometry Invariant Theory quotient. The constructio...
Symbolic powers versus regular powers of ideals of general points in P^1 x P^1
symbolic powers multigraded points
2011/9/20
Abstract: Let I be a homogeneous ideal of R = k[x_0,...,x_n]. A current research theme is to compare the symbolic powers of I with the regular powers of I. In this paper, we investigate which ordinary...
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...
Random groups have fixed points on CAT(0) cube complexes
Random groups fixed points on CAT(0) cube complexes
2011/2/22
We prove that a random group has fixed points when it isometrically acts on a CAT(0) cube complex. We do not assume that the action is simplicial.
Fixed points subgroups $G^{\sigma,\sigma'}$ by two involutive automorphisms $\sigma$, $\sigma'$ of exceptional compact Lie group $G$, Part II, $G = E_8$
Exceptional Lie group Symmetric space
2011/2/21
For the simply connected compact exceptional Lie group E8, we determine the structure of subgroup (E8).
Fixed points subgroups by two involutive automorphisms $\sigma, \gamma$ of compact exceptional Lie groups $F_4, E_6$ and $E_7$
Fixed points subgroups by two involutive automorphisms $\sigma \gamma$ of compact exceptional Lie groups $F_4, E_6$ $E_7$
2011/2/21
For simply connected compact exceptional Lie groups G = F4,E6 and E7, we consider two involutions σ, γ and determine the group structure of subgroups G,of G which are the intersection G ∩ G of the ...
At which points exactly has Lebesgue's singular function the derivative zero ?
Takagi’s function Lebesgue’s singular function Nowhere-differentiable function
2011/2/28
Let La(x) be Lebesgue’s singular function with a real parameter a (0 < a < 1, a 6= 1/2). As is well known, La(x) is strictly increasing and has a derivative equal to zero almost everywhere.
On the $p$-adic closure of a subgroup of rational points on an Abelian variety
$p$-adic closure subgroup of rational points Abelian variety
2011/2/24
In 2007, B. Poonen (unpublished) studied the p{adic closure of a subgroup of rational points on a commutative algebraic group. More recently, J. Bellache asked the same question for the special case...
Categories of partial algebras for critical points between varieties of algebras
Partial algebra congruence relation gamp pregamp variety of algebras
2011/1/19
We denote by Conc A the (∨, 0)-semilattice of all finitely generated congruences of an algebra A. A lifting of a (∨, 0)-semilattice S is an algebra A such that S ∼=Conc A.
Critical Brownian sheet does not have double points
Brownian sheet multiple points capacity Hausdorff dimension
2010/11/26
We derive a decoupling formula for the Brownian sheet which has the following ready consequence: An N-parameter Brownian sheet in Rd has double points if and only if 2(d − 2N) < d. In particular...
Finite group actions, rational fixed points and weak Néron models
Finite group actions rational fixed points weak Néron models
2010/12/1
If G is a finite ℓ-group acting on an affine space An over a finite field K of cardinality prime to ℓ, Serre [29] shows that there exists a rational fixed point. We generalize this to the ...