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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...
AN ERGODIC ACTION OF THE OUTER AUTOMORPHISM GROUP OF A FREE GROUP     OUTER AUTOMORPHISM  ERGODIC ACTION       font style='font-size:12px;'> 2015/9/29
For n > 2, the action of the outer automorphism group of the rank n free group Fn on Hom(Fn, SU(2))/SU(2) is ergodic with respect to the Lebesgue measure class.
Let G denote a connected reductive group, de ned and split over Z, and let M  G denote a Levi subgroup. In this paper we study varieties of geodesic triangles with xed vector-valued side-lengths ...
Diameters of Cayley Graphs of Chevalley Groups     Chevalley Groups  Cayley       font style='font-size:12px;'> 2015/8/26
We show that for integers k > 1 and n > 2, the diameter of the Cayley graph of SLn(Z/kZ) with respect to a standard two-element generating set, is at most a constant times n2 ln k. This answers a ques...
HIGHER-LEVEL CANONICAL SUBGROUPS IN ABELIAN VARIETIES     ABELIAN VARIETIES  CANONICAL SUBGROUPS       font style='font-size:12px;'> 2015/7/6
An abeloid space over a rigid space S over a non-archimedean field k is a proper smooth S-group A → S with connected fibers. Relative ampleness (in the sense of [C3]) gives a good notion ...
REDUCTIVE GROUP SCHEMES     GROUP SCHEMES  reductive group       font style='font-size:12px;'> 2015/7/6
We develop the relative theory of reductive group schemes, using dynamic techniques and algebraic spaces to streamline the original development in SGA3.
For metaplectic covers of these groups, the Whittaker models may or may not be unique. Gelbart and Piatetski-Shapiro considered the representations of the double cover of SL2 that have unique Whitta...
Speci cally, two distinct versions of the Gelfand-Tsetlin de nition were given. It is not apparent that they are equal. Either of these de nitions is purely local in that it speci es the p-part of t...
Conditional Optimal Composite Design     Conditional Optimal  Composite Design       font style='font-size:12px;'> 2015/3/20
Conditional Optimal Composite Design.
Wh ile D-O p tim al exp er im ental d es ign s ar e u s ed w ith gr eat f r equ en cy in s u r f ace r es p on s e an alys is th ey als o offer a m ech an is m to s cr een f actor s an d f actor inte...
通过随机矩阵方法识别、消除极端或非无关抽样样本, 提高Markowitz 模型的参数估计精度, 改进应用Markowitz 模型的效果;同时, 针对抽样不足的情况, 使用Bootstrap 方法较好地解决了该问题.
Large stars with few colors     Ramsey numbers  Edge coloring  Combinatorics       font style='font-size:12px;'> 2012/7/11
A recent question in generalized Ramsey theory is that for fixed positive integers $s\leq t$, at least how many vertices can be covered by the vertices of no more than $s$ monochromatic members of the...
Let $\J$ and $\K$ be convex sets in $\R^{n}$ whose affine spans intersect at a single rational point in $\J \cap \K$, and let $\J \oplus \K = \conv(\J \cup \K)$. We give expressions for the generating...
Extremal values on the eccentric distance sum of trees     Eccentric distance sum  Domination number  Leaves  Bipartition       font style='font-size:12px;'> 2012/7/11
Let $G=(V_G, E_G)$ be a simple connected graph. The eccentric distance sum of $G$ is defined as $\xi^{d}(G) = \sum_{v\in V_G}\varepsilon_{G}(v)D_{G}(v)$, where $\varepsilon_G(v)$ is the eccentricity o...
Let $D=(V(D), A(D))$ be a digraph and $k \ge 2$ an integer. We say that $D$ is $k$-quasi-transitive if for every directed path $(v_0, v_1,..., v_k)$ in $D$, then $(v_0, v_k) \in A(D)$ or $(v_k, v_0) \...

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