Schedule-at-a-Glance

31 PRIMA 2013 AbstractsRapoport-Zink spaces are certain moduli spaces of quasiisogeniesof p-divisible groups with additional structures,and can be regarded as local analogues of Shimura varieties.It is conjectured that the l-adic cohomology ofRapoport-Zink spaces can be precisely decribed by meansof the local Langlands correspondence for general reductivegroups. In this talk, I will give results on relationshipbetween the l-adic cohomology of Rapoport-Zink spacesand the Zelevinsky involution. I will also explain someapplications to compute the l-adic cohomology.Geometrizing characters of toriDavid RoeUniversity of Calgary, Canadaroed.math@gmail.comThe passage from functions to sheaves has proven a valuabletool in the geometric Langlands program. In thistalk I’ll describe a “geometric avatar” for the group ofcharacters of T (K), where T is an algebraic torus over alocal field K. I will then give some potential applicationsto the classical Langlands correspondence. This is jointwork with Clifton Cunningham.Twisted Bhargava cubesGordan SavinUniversity of Utah, USAsavin@math.utah.eduLet G be a reductive group and P = MN a maximalparabolic subgroup. The group M acts, by conjugation,on N/[N, N]. It is well known that, over an algebraicallyclosed field, the group M acts transitively on a Zariskiopen set. However, over a general field, the structure oforbits may be quite non-trivial. A description my involveunexpected invariants. A notable example is when G isa split, simply connected group of type D 4 , and P is themaximal parabolic corresponding to the branching pointof the Dynkin diagram. The space N/[N, N] is also knownas the Bhargava cube, and it was the starting point of hisinvestigations of prehomogeneous spaces. We consider aversion of this problem for the triality D 4 . This is a jointwork with Wee Teck Gan.Stability and sign changes in p-adic harmonicanalysisLoren SpiceTexas Christian University, USAl.spice@tcu.eduReeder has described a conjectural candidate for thepartition of certain supercuspidal representations constructedby Yu (the so called toral, unramified supercuspidals)into L-packets, and verified that it satisfies most ofthe necessary properties. However, the problem of stabilityof the appropriate character sums remained outstanding.In this talk, I will discuss joint work with DeBackerthat shows the necessary stability. A key ingredient isthe study of a sign associated to combinatorial data involvingGalois orbits on a root system, which we computeunconditionally in the unramified case.Conservation relations for local theta correspondenceBinyong SunAcademy of Mathematics and Systems Science, CAS,Chinasun@math.ac.cnI will introduce Kudla-Rallis conjecture on first occurrencesof local theta correspondence, and explain the ideaof its proof. This is a report of a joint work with Chen-BoZhu.L-functions and theta correspondenceShunsuke YamanaKyushu University, Japanyamana@math.kyushu-u.ac.jpThe doubling method of Piatetski-Shapiro and Rallis appliesin the local situation to define local factors of representationsof classical groups. On the one hand, theL-factor is defined as a g.c.d. of the local zeta integralsfor all good sections. On the other hand, it is definedfrom the gamma factor by using the Langlands classification.In this talk I develop a theory of the zeta integraland prove that the two candidates of the L-factor agree.Applications include a characterization of nonvanishing ofglobal theta liftings in terms of the analytic properties ofthe complete L-functions and the occurrence in the localtheta correspondence.Special Session 16Operator Algebras and Harmonic AnalysisUncertainty principles for infinite abeliangroupsLiming Ge, Jingsong Wu, Wenming Wu & Wei YuanUniversity of New Hampshire, USAliming@unh.eduIn this paper, we shall revisit uncertainty principle onfinite abelian groups and determine the functions thatgive Tao’s lower bound in above inequality. Our mainfocus then moves to the additive integer group Z. Itsdual is identified with R/Z (= [0, 1)). Since there is nocountably additive invariant (probability) measure on Z,we shall use von Neumann’s invariant mean which is afinitely additive for any disjoint subsets. With respectto a given mean on Z and Lebesgue measure on R/Z,we show that there is a subset S of Z with mean 1 sothat any square summable functions f supported on Shave “full” supported Fourier transform in the sense thatthe closure of supp(f) is equal to [0, 1]. Symmetrical, weshow that there is subset G of Z with mean 0 so that, forany x ∈ [0, 1] and any ɛ > 0, all functions supported onG together with those f with supp( ˆf) ⊂ [x, x + ɛ] spana dense subset of l 2 (Z), the Hilbert space of all squaresummable functions.Operator theoretic analogue for Lehmer’sproblemKunyu GuoFudan Unversity, Chinakyguo@fudan.edu.cnIn this talk, we will establish a fascinating connectionbetween Lehmer’s problem and operator theory. This isa joint work with Jiayang Yu.Convolution algebras associated with locallycompact quantum groupsZhiguo HuUniversity of Windsor, Canadazhiguohu@uwindsor.caWe consider the convolution algebras L 1 (G) andT (L 2 (G)) associated with a locally compact quantum