Schedule-at-a-Glance

49 PRIMA 2013 Abstractsthe end of 20th century (named after Chinese mathematicianLuogeng Hua). We will first give a brief introductionto Hua domains, and then give a complete description oftheir automorphism groups.Weighted harmonic spacesLuis Manuel Tovar Sánchez ∗ , Lino Feliciano Reséndis∗ National Polytechnic Institute, Mexicotovar@esfm.ipn.mxIn 1994, R. Aulaskari and Peter Lappan introduced theQ p spaces p > 0, of analytic functions defined in theunit disk of the complex plane. Considering that analyticfunctions f(z) = u(x, y) + iv(x, y) consist of a pairof harmonic conjugate functions, in this paper we considerweighted harmonic spaces, consisting of real harmonicfunctions defined in the unit disk of the plane. Westudy their basic properties and relationships with someother weighted function spaces.Variable equation of state for a dark energymodel with linearly varying deceleration parameterMing ShenFuzhou University, Chinashenming0516@fzu.edu.cnWe present a dark energy model in an inhomogeneousplane symmetric space-time by considering a linearlyvarying deceleration parameter. In the model, the equationof state (EoS) parameter ω is found to be time dependent.For different cosmic times, we obtain quintessence,vacuum energy and phantom fluid dominated universe.The universe we described has finite lifetime and endswith a big-rip which is a result consistent with recentcosmological observations.Diversities and the geometry of hypergraphsPaul Tupper, David BryantSimon Fraser University, Canadapft3@sfu.caThere are well-known connections between certain combinatorialoptimization problems and the geometry of metricembeddings of graphs. Instead of metrics, we considerdiversities, which are a generalization of the conceptof metrics to functions of finite sets of points, ratherthan just pairs of points. We show that analogous to therelation between flow problems and combinatorial optimizationin graphs, there are intimate relations betweendiversities and a different set of flow problems, includingfractional Steiner tree packing and optimal flows in hypergraphs.We discuss polynomial approximation algorithmsthat would result from a effective theory of embedding diversitiesinto l 1 .On the potential function of gradient steadyRicci solitonsPeng WuCornell University, USAwupenguin@math.cornell.eduWe prove that the infimum of the potential function ofa gradient steady Ricci soliton decays linearly. As consequences,a gradient steady Ricci soliton with bounded potentialfunction must be Ricci-flat, and no gradient steadyRicci soliton admits uniformly positive scalar curvature.New heat kernel estimates on manifolds withnegative Ricci curvature lower boundXiangjin XuBinghamton University, USAxxu@math.binghamton.eduApply the new Li-Yau type Harnack estimates for theheat equations on manifolds with Ric(M) ≥ −K, K ≥ 0,which established by Junfang Li and the author [Advancein Mathematics 226(5) (2011), 4456-4491], I prove a newupper bound estimate for the heat kernel H(x, y, t) ofmanifolds with Ric(M) ≥ −K,H(x, y, t) ≤ A K (t)Vx −1/2 (δ(t))Vy−1/2 (δ(t))[]· exp − d2 (x, y)+ [1 + d 2 (x, y)]B K (t) ,4twhere A K (t), B K (t) : [0, ∞) → [0, ∞) are bounded functions,and δ(t) ∼ t as t → 0 and δ(t) ∼ 1 as t → ∞.While in the seminal work of Li-Yau [Acta Math. 156(1986) 153-201.], the heat kernel upper bound estimateshad δ-loss:H(x, y, t) ≤C(δ, n)Vx −1/2 ( √ t)Vy −1/2 ( √ t)[]· exp − d2 (x, y)(4 + δ)t + C 1δKt ,[ ]cwhere constant C(δ, n) ∼ exp 1δ as δ → 0, due thatthere was non-sharp Harnack estimates on manifolds withRic(M) ≥ −K.Contributed Talks Group 2Algebra and Number TheoryUniversal objects for free G-spacesNatella AntonyanMonterrey Institute of Technology, Mexiconantonya@itesm.mxThroughout G is assumed to be a compact Lie group.A G-space U is called universal for a given class of G-spaces G-P, if U ∈ G-P and U contains as a G-subspacea G-homeomorphic copy of any G-space X from the classG-P.In this talk we shall present universal G-spaces in the classof all paracompact (respectively, metrizable, and separablemetrizable) free G-spaces. Recall that for a G-spaceX and a point x ∈ X the stabilizer (or stationary subgroup)of x is defined by G x = {g ∈ G | gx = x}. IfG x = {e} for all x ∈ X then we say that the action ofG is free and X is a free G-space. Denote by Cone Gthe cone over G endowed with the natural action of G inducedby left translations. Let J ∞(G) be the infinite joinG ∗ G ∗ . . . ; it is just the subset of the countable product(Cone G) ∞ consisting of all those points (t 1 g 1 , t 2 g 2 , . . . )for which only a finite number of t i ≠ 0 and ∑ ∞i=1 t i = 1.We let G act coordinate-wise on J ∞(G). Denote by Ithe unit interval [0, 1] and by I τ the Tychonoff cube of agiven infinite weight τ endowed with the trivial action ofG.We prove that for every infinite cardinal number τ, theproduct J ∞(G) × I τ is universal in the class of all paracompactfree G-spaces of weight ≤ τ. A similar result formetrizable free G-spaces of weight ≤ τ is also obtained.Categorification in topology, geometry andcombinatorics