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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Rational points and homogeneous spaces over function fields of curves
曲线函数场 有理点 齐次空间
2023/4/17
In the last decade, there has been a growing interest in the study of rational points on homogeneous spaces of linear algebraic groups defined over fields having good arithmetical properties other tha...
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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Birkhoff genericity for points on curves in expanding horospheres and Diophantine applications
星座图 曲线 Birkhoff泛型 丢番图应用
2023/5/16
Let $\{a(t):t \in \mathbb{R}\}$ be a diagonalizable subgroup of $SL(d,\mathbb{R})$ for which the expanded horosphere $U$ is abelian. By the Birkhoff ergodic theorem, for any point $x \in SL(d,\mathbb{...
THE RING OF PROJECTIVE INVARIANTS OF EIGHT POINTS ON THE LINE VIA REPRESENTATION THEORY
PROJECTIVE INVARIANTS EIGHT POINTS ON THE LINE VIA
2015/10/14
The ring of projective invariants of eight ordered points on the line is a quotient of the polynomial ring on V , where V is a fourteen-dimensional representation of S8, by an ideal I8, so the modular...
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...
THE RELATIONS AMONG INVARIANTS OF POINTS ON THE PROJECTIVE LINE
RELATIONS AMONG INVARIANTS POINTS ON THE PROJECTIVE LINE
2015/10/14
THE RELATIONS AMONG INVARIANTS OF POINTS ON THE PROJECTIVE LINE.
THE IDEAL OF RELATIONS FOR THE RING OF INVARIANTS OF n POINTS ON THE LINE
RELATIONS FOR THE RING INVARIANTS OF n POINTS THE LINE
2015/10/14
The ring of projective invariants of n ordered points on the projective line is one of the most basic and earliest studied examples in Geometric Invariant Theory. It is a remarkable fact and the point...
THE EQUATIONS FOR THE MODULI SPACE OF n POINTS ON THE LINE
MODULI SPACE n POINTS ON THE LINE
2015/10/14
A central question in invariant theory is that of determining the relations among invariants. Geometric invariant theory quotients come with a natural ample line bundle, and hence often a natural proj...
JOINTLY PERIODIC POINTS IN CELLULAR AUTOMATA:COMPUTER EXPLORATIONS AND CONJECTURES
JOINTLY PERIODIC POINTS CELLULAR AUTOMATA COMPUTER EXPLORATIONS AND CONJECTURES
2015/9/29
We develop a rather elaborate computer program to investigate the jointly periodic points of one-dimensional cellular automata. The experimental results and mathematical context lead to questions, con...
PARAMETER CHOICE FOR FAMILIES OF MAPS WITH MANY CRITICAL POINTS
PARAMETER CHOICE MAPS WITH MANY CRITICAL POINTS
2015/9/25
We consider families of smooth one-dimensional maps with several critical points and outline the main ideas of the construction in the parameter space that allows to get infinite Markov Partitions and...
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...
Adaptive Multiscale Detection of Filamentary Structures Embedded in a Background of Uniform Random Points
Multiscale Geometric Analysis Pattern Recognition
2015/8/21
We are given a set of n points that appears uniformly distributed in the unit square [0,1]2.
We wish to test whether the set actually is generated from a non-uniform distribution having
a small frac...
The ring of projective invariants of n ordered points on the projective line is one of the most
basic and earliest studied examples in Geometric Invariant Theory. It is a remarkable fact and the poin...
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...