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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Gibbons' conjecture and Liouville theorem for master equations
主方程 Gibbons猜想 Liouville定理
2023/11/29
In this talk, we will discuss some of our recent work on the master equation involving the fully fractional heat operator. Specifically, we will present two main results. The first one pertains to a g...
Stam’s Conjecture and Threshold Phenomena in Collision Resistance
Stam’s Threshold Phenomena Collision Resistance
2012/12/4
At CRYPTO 2008 Stam [8] conjectured that if an (m+s)- bit to s-bit compression function F makes r calls to a primitive f of n-bit input, then a collision for F can be obtained (with high probability) ...
Lehmer's conjecture for Hermitian matrices over the Eisenstein and Gaussian integers
Lehmer's conjecture Hermitian matrices Eisenstein and Gaussian integers Number Theory
2012/6/29
We solve Lehmer's problem for a class of polynomials arising from Hermitian matrices over the Eisenstein and Gaussian integers, that is, we show that all such polynomials have Mahler measure at least ...
Modularity lifting results in parallel weight one and applications to the Artin conjecture: the tamely ramified case
Modularity lifting results parallel weight one Artin conjecture tamely ramified case Number Theory
2012/4/18
We extend the modularity lifting result of the arXiv:1111.2804 to allow Galois representations with some ramification at p. We also prove modularity mod 2 and 5 of certain Galois representations. We u...
On Zagier's conjecture for base extensions of elliptic curves
Zagier's conjecture base extensions of elliptic curves Number Theory
2012/4/18
Let E be an elliptic curve over Q, and let F be a finite abelian extension of Q. Using Beilinson's theorem on a suitable modular curve, we prove a weak version of Zagier's conjecture for L(E/F,2), whe...
A new two-dimension sieve method and the proof of the Goldbach's conjecture
sieve Goldbach conjecture
2011/9/21
This paper advanced a new two-dimension sieve method of using some deleted lines to sum formulae with some odd composites in formula columns for every even number >6, and proved a stronger Goldbach\&#...
The proofs of twin prime conjecture and weaker Polignac's conjecture
prime distribution of primes twin primes Polignac's conjecture Goldbach-type problem
2011/9/18
This paper advanced a new method of appointedly covering prime circles with level colors of black degree, and showed twin prime conjecture and weaker Polignac's conjecture to be true with the proof by...
In this paper, the Goldbach Conjecture﹛1, 1﹜ is proved by the complex variable integration. To prove the conjecture, a new function is introduced into Dirichlet series. And then, by using the Perron F...
On the Mumford-Tate conjecture for 1-motives
Mumford-Tate conjecture Number Theory Algebraic Geometry
2011/9/21
Abstract: We show that the statement analogous to the Mumford-Tate conjecture for abelian varieties holds for 1-motives on unipotent parts. This is done by comparing the unipotent part of the associat...
Abstract: We say that k is a P-integer if the first phi(k) primes coprime to k form a reduced residue system modulo k. In 1980 Pomerance proved the finiteness of the set of P-integers and conjectured ...
Algorithmic Proof of the Epsilon Constant Conjecture
epsilon constant conjecture local fundamental classes Number Theory
2011/9/6
Abstract: In this paper we will algorithmically prove the local and global epsilon constant conjectures for all fields of absolute degree lower or equal to 15. To this end we will present an efficient...
Agoh's conjecture: its proof, its generalizations, its analogues
Agoh's conjecture its generalizations its analogues Number Theory
2011/9/9
Abstract: In this paper we formulate some generalizations of Agoh's conjecture. We provide a proof of one of them. We also formulate conjectures involving congruence modulo primes about hyperbolic sec...
The Gross - Kuz'min conjecture for CM fields
The Gross - Kuz'min conjecture CM fields Number Theory
2011/8/26
Abstract: Let $A' = \varprojlim_n$ be the projective limit of the $p$-parts of the ideal class groups of the $p$ integers in the $\Z_p$-cyclotomic extension $\K_{\infty}/\K$ of a CM number field $\K$....
Toda Molecule and Tomimatsu-Sato Solution $\sim$ Toward the complete proof of Nakamura's conjecture$\sim$
Toda Molecule Tomimatsu-Sato Solution $\sim$
2010/12/28
We discuss the Nakamura’s conjecture stating that the Tomimatsu-Sato black hole solution with deformation parameter n is composed of the special solutions of the Toda molecule equation at the n-th lat...