January 15 
Sergey Belyi, Troy UniversityOn system realizations of HerglotzNevanlinna functionsIn this overview talk we discuss realization problems for linear systems of Livsic type (Lsystems) with an unbounded statespace operator. The main object of our study is a class of operatorvalued HerglotzNevanlinna (HN) functions that can be realized as a linearfractional transformation of the transfer function of an Lsystem. We will show how direct and inverse problems for such type of systems are solved and provide a complete description of realizable HN operatorfunctions in a finitedimensional Hilbert space. Various subclasses of the class of realizable HN functions will be described in connection with specific properties of realizing Lsystems. We will also talk about the general realization problem with noncanonical systems. As an important application, we will discuss the realization of certain scalar HN functions by Lsystems that are based on a nonselfadjoint Schrodinger operator in L_{2}[a, +∞).This talk is based on joint work with Yury Arlinskii and Eduard Tsekanovskii
and will survey all the above mentioned developments and connections.

January 22  February 12 
No meetings 
February 19starts at 3:15 
Vrej Zarikian, US Naval AcademyBimodules over Cartan subalgebras, and Mercer's extension theoremThe abstract is here.Also there is a colloquium at 4:30 by Stephen Curran of MIT. 
February 26starts at 3:15 
Craig Kleski, UVaPeaking for operator systemsThe Bishopde Leeuw theorem shows how various notions of peaking for function spaces are related. In this talk, I will discuss progress toward a noncommutative version of this theorem. 
March 5 
Martino Lupini, York UniversityC*algebras and omitting typesI will give an introduction to model theory for operator algebras. I will then explain how many important classes of C*algebras can be characterized by the modeltheoretic notion of omitting types. I will conclude by presenting some applications to the theory of UHF and AF algebras. 
March 12 
SPRING BREAK 
March 19 
David Blecher, University of HoustonGeneralized invertibility and outers in noncommutative Hardy spacesWe review noncommutative H^{p} spaces (Arveson's von Neumann algebraic generalization of the Hardy spaces of the disk), and discuss generalized notions of invertibility and outers, focusing on some work in progress with Labuschagne. Hopefully the seminar will be just a little interactive, with some voluntary input from the audience on the purely function theoretic case. 
March 26 
Chris Ramsey, University of WaterlooTriangular operator algebrasA subalgebra of a C*algebra is triangular if its intersection with its adjoint is a maximal abelian selfadjoint algebra. In a uniformly hyperfinite algebra the closed union of a chain of upper triangular matrix algebras is triangular, this will be the main object for discussion. I will talk about the isometric automorphism groups and dilation theory of these algebras. In particular, we can describe the C*envelope of the semidirect product of one of these algebras by an automorphism. 
April 2 
Rob Martin, University of Cape TownNearly invariant subspaces and symmetric operatorsHere is the abstract. 
April 9 
Stephen Hardy, UVa"Ultra"techniques in Banach space theory IAn introduction to the theory of ultrafilters and ultraproducts along with applications to Banach space theory, based on Stefan Heinrich's 1980 paper "Ultraproducts in Banach space theory". 
April 16 
Stephen Hardy, UVa"Ultra"techniques in Banach space theory IIAdditional applications of ultraproducts to the study of local properties of Banach spaces. Based on Stefan Heinrich's 1980 paper "Ultraproducts in Banach space theory". 
April 23 
Mor Katz, UVaThe boundary Caratheodory–Fejer problemThe Caratheodory–Fejer problem is to determine whether a finite sequence of complex numbers comprises the initial Taylor coefficients of an analytic function in the Pick class about some point x of the domain. In "The boundary Caratheodory–Fejer interpolation problem", Jim Agler, Zinaida A. Lykova and N.J. Young give a new solvability criterion to the situation where x lies on the boundary, and derive a parametrization of all solutions for the real case. We will discuss their work and follow similar steps to derive a parametrization for the "almost real" case. 
April 30 
Mor Katz, UVaEssential normality for a class of composition operatorsA Hilbert space operator is essentially normal if its commutator with its adjoint is compact. Recent work of CowenGallardo and HammondMoorhouseRobbins has produced a pointwise formula for the adjoint of a rationallyinduced composition operator whose constituent parts contain multiplevalued analytic functions which do not individually represent welldefined operators. We show how to work with this formula to produce legitimate operator expressions involving the adjoint and apply this to find a criterion for essential normality of composition operators induced by functions which extend analytically across the boundary of the unit disk. 