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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Proofs of two or infinity conjectures for Reeb orbits and closed geodesics
Reeb轨道 闭测地线 两个 无穷大猜想
2023/11/29
In this talk, we give a proof of the conjecture of Hofer-Wysocki-Zehnder published in 2003 asserting that a smooth and autonomous Hamiltonian flow on R4 has either two or infinitely many simple period...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Some conjectures on real-rootedness
实根性 组合数学 大群多项式
2023/4/21
The real-rootedness has been drawing attention of many mathematicians to study them on a large group of polynomials in Combinatorics. This talk is concerned with some conjectures on the real-rootednes...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Unsolved conjectures in Mathematical General Relativity
数学 广义相对论 未解 猜想
2023/5/5
I will review the recent progress, including my own contribution, in addressing the Kerr Stability Conjecture (克尔时空稳定性猜想）and the Strong Cosmic Censorship Hypothesis (强宇宙监督假设)，both of which are among t...
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...
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...
Some duality conjectures for finite graphs and their group theoretic consequences
finite graphs group theoretic consequences
2015/8/26
We pose some graph theoretic conjectures about duality and the diameter of maximal trees in planar graphs, and we describe innovations in the following two topics in Geometric Group Theory, where the ...
For a non-CM elliptic curve E/Q, Lang and Trotter made very deep conjectures concerning the number of primes p ≤ x for which ap(E) is a fixed integer (and for which the Frobeniusfield at p is a fixed ...
Branden's Conjectures on the Boros-Moll Polynomials
Boros-Moll Polynomials Real-rootedness Sturm sequence 3-log-concavity
2014/6/3
We prove two conjectures of Brändén on the real-rootedness of polynomials Qn(x) and Rn(x) which are related to the Boros-Moll polynomials Pn(x). In fact, we show that both Qn(x) and Rn(x) form St...
PARTIAL GENERALIZATIONS OF SOME CONJECTURES IN LOCALLY SYMMETRIC LORENTZ SPACES
PARTIAL GENERALIZATIONS CONJECTURES SYMMETRIC LORENTZ SPACES
2018/4/19
Abstract. In this paper, first we give a notion for linear Weingarten spacelike hypersurfaces with P + aH = b in a locally symmetric Lorentz space Ln+11 . Furthermore, we study complete or compact lin...
Branden's Conjectures on the Boros-Moll Polynomials
Boros-Moll Polynomials Real-rootedness Sturm sequence, 3-log-concavity
2012/5/24
We prove two conjectures of Br\"{a}nd\'{e}n on the real-rootedness of polynomials $Q_n(x)$ and $R_n(x)$ which are related to the Boros-Moll polynomials $P_n(x)$. In fact, we show that both $Q_n(x)$ an...
A Note on Schanuel's Conjectures for Exponential Fields
Note Schanuel's Conjectures Exponential Fields
2012/4/18
We apply a result of J. Ax [On Schanuel's Conjectures, Annals of Mathematics 93 (1971), 252-268] to differential valued exponential fields. In particular, we establish Schanuel's conjecture regarding ...
(Self-)similar groups and the Farrell-Jones conjectures
(Self-)similar groups the Farrell-Jones conjectures K-Theory and Homology
2011/9/21
Abstract: We show that contracting self-similar groups satisfy the Farrell-Jones conjectures as soon as their universal contracting cover is non-positively curved. This applies in particular to bounde...
The generalized Hodge and Bloch conjectures are equivalent for general complete intersections
The generalized Hodge Bloch conjectures general complete intersections Algebraic Geometry
2011/9/5
Abstract: Let $X$ be a smooth complex projective variety with trivial Chow groups. (By trivial, we mean that the cycle class is injective.) We show (assuming the Lefschetz standard conjecture) that if...
Chromatic number, clique subdivisions, and the conjectures of Hajos and Erdos-Fajtlowicz
Chromatic number clique subdivisions Hajos and Erdos-Fajtlowicz Combinatorics
2011/9/1
Abstract: For a graph $G$, let $\chi(G)$ denote its chromatic number and $\sigma(G)$ denote the order of the largest clique subdivision in $G$. Let H(n) be the maximum of $\chi(G)/\sigma(G)$ over all ...
Large matchings in uniform hypergraphs and the conjectures of Erdos and Samuels
Large matchings uniform hypergraphs conjectures of Erdos and Samuels Combinatorics Probability
2011/8/26
Abstract: In this paper we study conditions which guarantee the existence of perfect matchings and perfect fractional matchings in uniform hypergraphs. We reduce this problem to an old conjecture by E...