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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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Arnold conjecture and advances in Floer theory
阿诺德猜想 弗洛尔理论 哈密顿微分同胚
2023/5/4
In 1960s, Arnold conjectured that the number of fixed points of a Hamiltonian diffeomorphism of a symplectic manifold should be (much) greater than its counterpart for a general diffeomorphism. This c...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The logarithmic Brunn-Minkowski inequality conjecture in convex geometry
凸几何 对数 布伦-闵可夫斯基 不等式猜想
2023/4/21
The logarithmic Brunn-Minkowski inequality conjecture is one of the most intriguing challenges in convex geometry since 2012. Notably, this conjectured inequality is stronger than the celebrated Brunn...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Gauss-Bonnet formula beyond the aspherical conjecture
超越非球面猜想 Gauss-Bonnet 曲面
2023/4/21
In this talk, I'll make a discussion on recent progress in the research of scalar curvature. I'll review the backgrounds from Gauss-Bonnet formula to the aspherical conjecture, and then focus on the f...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The Lp-Brunn-Minkowski conjecture for 0
0
2023/4/21
The Lp-Brunn-Minkowski conjecture for 0 < p < 1 states that the volume functional is concave when origin-symmetric convex bodies are Lp-added, where 0 < p < 1. This conjecture has garnered significant...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Morrison-Kawamata cone conjecture for Calabi-Yau fiber spaces
Calabi-Yau fiber spaces 莫里森-川俣 锥猜想
2023/5/9
In this talk, I will explain the relationship between the Morrison-Kawamata cone conjecture for Calabi-Yau fiber spaces and the existence of Shokurov polytopes. For K3 fibrations, this enables us to e...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Some special cases of the three dimensional Kakeya conjecture and their application to the restriction conjecture
三维Kakeya猜想 特殊情况 限制猜想
2023/5/9
We will discuss two special cases of the three-dimensional Kakeya conjecture: SL_2 Kakeya and a refined Wolff's hairbrush result. As an application of the refined Wolff's hairbrush result, we will dis...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Borel conjecture for the torus and the splitting of surgery sets
环面 Borel猜想 外科手术集 分裂
2023/5/10
The Borel conjecture considers the obstruction from homotopy equivalence to homeomorphism for aspherical manifolds. The torus is the first computed case of Borel conjecture with the idea of splitting ...
Jinyoung Park and Huy Tuan Pham Prove the Kahn-Kalai Conjecture（图）
Kahn-Kalai Conjecture probabilistic combinatorics phase transition the expectation threshold conjecture
2022/4/25
Past Member (2020–21) Jinyoung Park, a Szegö Assistant Professor at Stanford University, and Huy Tuan Pham, a Stanford Ph.D. student, proved the Kahn-Kalai Conjecture, a central problem in probab...
2018 Workshop on New Methods for Zimmer’s Conjecture
2018 Workshop New Methods for Zimmer’s Conjecture
2017/12/20
The purpose of this workshop is to bring focused attention on a recent breakthrough by Brown, Fisher and ZIM2018_imageHurtado on Zimmer’s Conjecture. The conjecture concerns low dimensional actions of...
THE PUZZLE CONJECTURE FOR THE COHOMOLOGY OF TWO-STEP FLAG MANIFOLDS
PUZZLE CONJECTURE TWO-STEP FLAG MANIFOLDS
2015/12/17
We prove a conjecture of Knutson asserting that the Schubert
structure constants of the cohomology ring of a two-step flag variety are equal
to the number of puzzles with specified borde...
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 ...
We prove the Noether-Lefschetz conjecture on the moduli space of quasi-polarized K3 surfaces. This is deduced as a particular case of a general theorem that states that low degree cohomology classes o...
We show that a certain class of varieties with origin in Physics,
generates (additively) the Denef-Loeser ring of Motives. In particular, this
disproves a conjecture of Kontsevich on the number of p...
BOWEN’S ENTROPY-CONJUGACY CONJECTURE IS TRUE UP TO FINITE INDEX
BOWEN’S ENTROPY CONJUGACY CONJECTURE FINITE INDEX
2015/9/29
For a topological dynamical system (X, f), consisting of a continuous map f : X → X, and a (not necessarily compact) set Z ⊂ X, Bowen [2] defined a dimension-like version of entropy,hX(f, Z). In...