Updated on Feb. 8, 2010
Dr. Dechao Zheng
Vanderbilt UniversityTitle to be Announced
Dr. Edward Burger
Williams CollegeTitle to be Announced
Dr. David Blecher
University of HoustonTitle to be Announced
Dr. Nikolai Vasilevski
CINVESTAV del I.P.N., MexicoTitle to be Announced
Mr. Joshua Isralowitz
University at Buffalo, State University of New YorkTitle to be Announced
Dr. David Kerr
Texas A&M UniversityTopological entropy for actions of sofic groups
Abstract: Recently Lewis Bowen introduced a notion of entropy for measure-preserving actions of sofic groups which he used to solve the Bernoulli shift isomorphism problem for a large class of nonamenable groups. I will show that by taking an operator-algebraic viewpoint one can define a topological version of Bowen’s measure entropy and then discuss how the two are related via a variational principle.
Dr.William Menasco
University at Buffalo, State University of New YorkMorton-Franks-Williams inequality and related problems
Dr. Hanfeng Li
University at Buffalo, State University of New YorkEntropy and Fuglede-Kadison determinant- Part II
Dr. David Hemmer
University at Buffalo, State University of New YorkMathematics of the Rubik’s Magic Cube
Dr. Hanfeng Li
University at Buffalo, State University of New YorkEntropy and Fuglede-Kadison determinant- Part I
Abstract: For any discrete group G and any element f in the integral group ring ZG of G, one may consider the algebraic action of G associated to f, i.e., the shift action of G on the Pontryagin dual of ZG/ZGf. When G is amenable, the entropy is defined for actions of G. I will discuss the relation between the entropy of the above algebraic action and the Fugelde-Kadison determinant of f in the von Neumann algebra of G.
Dr. Diane Henderson
Penn State UniversityThe Benjamin-Feir Instability and Propagation of Swell Across the Pacific
Abstract: About forty years ago, oceanographers (Snodgrass et al, 1966) tracked swell propagating from storms in the Antarctic to the beaches of Alaska. At about the same time, it was shown that such waves are unstable to modulational perturbations [the Benjamin-Feir (1967) instability]. In light of this instability, why did the waves travel coherently across the Pacific ocean? More recently, Segur et al (2005) re=-examined the Benjamin-Feir instability to account for linear damping. They found that any amount of damping stabilizes the instability and that their predictions were in good agreement with laboratory experiments.
In this talk, we consider the effects of linear damping on the Benjamin-Feir instability in waves with one- or two-dimensional surface patterns and apply the results to the ocean data from Snodgrass et al (1966).
Dr. Wen Huang
University of Science and Technology of ChinaStable sets and unstable sets in positive entropy systems
Abstract: Stable sets and unstable sets of a dynamical system with positive entropy are investigated. It is shown that in any invertible system with positive entropy, there is a measure-theoretically “rather big” set such that for any point from the set, the intersection of the closure of the stable set and the closure of the unstable set of the point has positive entropy. Moreover, for several kinds of specific systems, the lower bound of Hausdorff dimension of these sets is estimated. Particularly the lower bound of the Hausdorff dimension of such sets appearing in a positive entropy diffeomorphism on a smooth Riemannian manifold is given in terms of the metric entropy and of Lyapunov exponent.
Dr. Daniel Groves
University of Illinois at ChicagoParametrizing surface bundles
Abstract: Let S be an orientable surface of finite type (not a torus or a sphere) and B a reasonable space (CW complex or manifold). The the set of S-bundles over B is naturally parametrised by the set Hom(π1(B), Mod(S))/~ of conjugacy classes of homomorphisms from the fundamental group of B to the mapping class group of S.
I will discuss some recent work (still being written) which provides a description of this set of homomorphisms whenever π1(B) is finitely generated.
Dr. Bernard Deconinck
University of WashingtonThe stability of periodic finite-gap solutions of the KdV equation
Abstract: The periodic finite-gap solutions of the KdV equation are the largest class of periodic solutions of the KdV equation whose functional form is known explicitly. The one-gap solutions are stationary, and their stability has been a topic of much discussion in their literature. Recently, it was settled that they are (nonlinearly) orbitally stable with respect to perturbations that are periodic with periodic equal to an integer multiple of the one-gap solutions period. In this talk, I will show how one proceeds to show that this orbital stability results holds for all periodic finite-gap solutions.
Dr. Byung-Jay Kahng
Canisius CollegeSome remarks on duality in the locally compact quantum group setting
Abstract: In abstract harmonic analysis, among the most important result is the Pontryagin duality, wheich holds at the level of locally compact abelian (LCA) groups. Also, at the LCA group level, the notion of Fourier transform is defined. For further generalization, we consider the category of quantum groups, where Pontryagin-type, self-duality holds. Our quantum groups are locally compact quantum groups, in the C*-algebra or von Neumann algebra framework.
By using the notion of the multiplicative unitary operators and the generalized Fourier transform, we can enhance our understanding of the duality picture at the quantum group level. In particular, we will consider a case of a certain coalgebra deformation of the quantum double, and its dual counterpart.
Dr. Bulent Tosun
Georgia Institute of TechnologyOn the Legendrian and transverse classification of cabled knot types
Abstract: In 3-dimensional contact topology one of the main problems is classifying Legendrian (transverse) knots in certain knot type up to Legendrian (transverse) isotopy. In particular we want to decide if two (one in the case of transverse knots) classical invarients of this knot are complete set of invariants. If it is, then we call this knot type Legendrian (transversely) simple knot type otherwise it is called Legendrian (transversely) non-simple. In this talk, by tracing the techniques developed by Etnyre and Honda, we will present some results concerning the complete Legendrian and transverse classification of certain cabled knots in the standard tight contact 3-sphere. Moreover we will provide an infinite family of Legendrian and transversely non-simple prime knots.
Dr. Adam Glesser
Suffolk UniversitySparse fusion systems
Abstract: Classical results on fusion in finite groups from Frobenius to Alperin to Glauberman and Thompson played a major role in the classification of finite simple groups. A modern treatment of fusion takes place in the category of fusion systems, a relatively new object that allows results to extend from groups to blocks as well as making a connection to algebraic topology via the classifying space of a finite group. In this talk, we discuss how certain minimal nontrivial elements in the lattice of subfusion systems of a system (called sparse fusion systems) are used to simplify several recent proofs of fusion results and how, in the case of a theorem of Navarro, fusion systems naturally lead to a stronger result about groups than was not previously known.
Dr. Jingbo Xia
University at Buffalo, State University of New YorkDefect Operators Associated with Submodules of the Hardy Module