Schedule-at-a-Glance

25 PRIMA 2013 AbstractsPedram HekmatiUniversity of Adelaide, Australiapedram.hekmati@adelaide.edu.auT-duality is a discrete symmetry in string theory that relatestopologically distinct torus fibrations and provides adictionary for translating geometrical structures betweenthem. The duality is mathematically well-understood intype II theories and the purpose of this talk is to explainhow it can be extended to the heterotic setting.The setup naturally involves string structures and reductionof Courant algebroids. This is joint work with DavidBaraglia.A motivic approach to Potts modelsMatilde MarcolliCalifornia Institute of Technology, USAmatilde@caltech.eduThe use of motivic techniques in Quantum Field Theoryhas been widely explored in the past ten years, in relationto the occurrence of periods in the computation ofFeynman integrals. In this lecture, based on joint workwith Aluffi, I will show how some of these techniques canbe extended to a motivic analysis of the partition functionof Potts models in statistical mechanics. An estimateof the complexity of the locus of zeros of the partitionfunction, can be obtained in terms of the classesin the Grothendieck ring of the affine algebraic varietiesdefined by the vanishing of the multivariate Tutte polynomial,based on a deletion-contraction formula for theGrothendieck classes.The Wess-Zumino-Witten model on SL (2; R)David RidoutThe Australian National University, Australiadavid.ridout@anu.edu.auThe prototypical examples of string theories on targetspaces with non-trivial topologies are the Wess-Zumino-Witten (WZW) models for which the target is a compactreductive Lie group. However, the non-compact case isphysically more relevant and is mathematically richer aswell. While the pioneering work of Maldacena and Ooguriproposed string spectra and proved a no-ghost theoremfor the WZW model on SL (2; R), recent work has shownthat the underlying conformal field theory is far richer, atleast for certain levels, and provides an example of a socalledlogarithmic conformal field theory. This talk willreview this recent work and what it suggests for othertheories with non-compact target spaces.M-branes and higher bundlesHisham SatiUniversity of Pittsburgh, USAhsati@pitt.eduWe describe the M-branes in M-theory via higher geometry,including String structures, String bundles with connections,higher (stacky) notions of Chern-Simons theory,and relation to higher WZW models. This is joint workwith Domenico Fiorenza and Urs Schreiber.T-duality for circle bundles via noncommutativegeometryMathai VargheseThe University of Adelaide, Australiavarghese@adelaide.edu.auIt is known that topological T-duality can be extendedto apply not only to principal circle bundles, but also tonon-principal circle bundles. We show that this resultcan also be recovered via the noncommutative geometryapproach which we previously used for principal torusbundles. This work has several interesting byproducts,including a study of the K-theory of crossed products byÕ(2) = Isom(R), the universal cover of O(2), and some interestingfacts about equivariant K-theory for Z/2. Theseresults are then extended to the case of bundles withsingular fibers, or in other words, non-free O(2)-actions.This is joint work with Jonathan Rosenberg.Special Session 13Measurable and Topological DynamicsHeight reducing problemShigeki AkiyamaUniversity of Tsukuba, Japana.h.dooley@bath.ac.ukWe say that an algebraic number α has height reducingproperty (HRP) if there is a positive integer B thatZ[α] = B[α], i.e., every number in Z[α] has an equivalentrepresentation with coefficients in {−B, . . . , B}. Thisproblem is studied for algebraic integers, since it has intimateconnection to the construction of self-affine tilings.In this talk, we consider HRP for general algebraic numbersand obtain some ‘almost’ if and only if conditionfor HRP. The proof relies on a quantitative version ofKronecker’s approximation theorem. This is a joint workwith Toufik Zaimi.Large deviation principle for chaotic dynamicalsystemsYong Moo ChungHiroshima University, Japanchung@amath.hiroshima-u.ac.jpWe will discuss a class of chaotic dynamical systems forwhich the full large deviation principle holds. It containsintermittent maps and quadratic maps on intervals,almost Anosov diffeomorphisms on tori and countableMarkov shifts with return time functions of ’gentle’slopes.Chaotic dynamics of continuous-time topologicalsemiflow on Polish spaceXiongping DaiNanjing University, Chinaxpdai@nju.edu.cnDifferently from Li-Yorke and others in literature, we willintroduce the concept—chaos—for a continuous semiflowf : R + × X → X on a Polish space X without isolatedpoints, which is useful for the theory of ODE and is invariantunder topological equivalence. Our definition isweaker than Devaney’s since here f may have neitherfixed nor periodic elements; but it still implies the sensitivedependence on initial data similar to Devaney’schaos. We will show that f always has a maximal chaoticsubsystem. In addition, we will consider the chaotic behavioron minimal center of attraction of a motion.Random dynamical systemsAnthony DooleyUniversity of Bath, UKa.h.dooley@bath.ac.uk