Seminar Calendar
for Analysis Seminar events the next 12 months of Friday, August 1, 2008.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery. 
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Thursday, September 4, 2008

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, September 4, 2008
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Submitted by fboca.
Leonid Vainerman (Universite de Caen)
Subfactors, quantum groupoids, and fusion categories
Abstract: We explain that every finite index and finite depth subfactor canonically generate a specific algebraic structure called a finite quantum groupoid (or a weak Hopf algebra). In its turn, the category of representations of this structure verifies all conditions of so-called fusion category and can be reconstructed out of such a category. We discuss relations between these notions as well as concrete examples.

Tuesday, September 9, 2008

Analysis Seminar
2:00 pm   in 241 Altgeld Hall,  Tuesday, September 9, 2008
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Submitted by fboca.
Edward Effros (UCLA)
Matrix convexity, the Lieb inequalities, and the problem of smoothness in operator spaces
Abstract: The notion of matrix convexity is an obvious generalization of classical convexity. Furthermore the matrix analogues of the Jensen inequality formulated by Hansen and Pedersen can be given very straightforward proofs. Nevertheless, these simple ideas provide a very powerful approach to some of the more difficult results in quantum statistical mechanics, including the Lieb inequalities. We also explore the notions of smoothness for matrix convex functions.

Thursday, September 11, 2008

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, September 11, 2008
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Submitted by aimo.
Aimo Hinkkanen (Department of Mathematics, University of Illinois)
Majorization of analytic functions
Abstract: We sketch the proof of a majorization result for analytic functions in open sets in the complex plane in terms of upper bounds for differences of the function on the boundary.

Thursday, September 18, 2008

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, September 18, 2008
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Submitted by aimo.
Ken Stolarsky (Department of Mathematics, University of Illinois)
Analytic and algebraic properties of Chebyshev-like polynomials
Abstract: We shall survey various analytic and functional properties of Chebyshev polynomials and see how they extend to wider classes of polynomials. Some particular attention will be paid to the discriminants and zero distributions of such polynomials. If time permits, some open problems and connections with number theory will be given. Please note that there will be substantial overlap with the talk given on Tuesday in the number theory seminar.

Thursday, September 25, 2008

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, September 25, 2008
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Submitted by aimo.
Aimo Hinkkanen (Department of Mathematics, University of Illinois)
Majorization of analytic functions II
Abstract: We sketch the proof of a majorization result for analytic functions in open sets in the complex plane in terms of upper bounds for differences of the function on the boundary.

Thursday, October 2, 2008

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, October 2, 2008
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Submitted by aimo.
Aimo Hinkkanen (Department of Mathematics, University of Illinois)
Majorization of analytic functions III
Abstract: We sketch the proof of a majorization result for analytic functions in open sets in the complex plane in terms of upper bounds for differences of the function on the boundary.

Thursday, October 9, 2008

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, October 9, 2008
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Submitted by aimo.
Kevin Pilgrim (Indiana University)
The conformal dimension of a dynamical system
Abstract: Bowditch gave a purely topological characterization of the action of a hyperbolic group on its boundary. Since the boundary of such a group carries a (class of) metrics in which the dynamics acts nicely (by uniformly quasi-Möbius maps), one may interpret his result as saying that associated to a topological dynamical system, there is a preferred class of metrics with respect to which the dynamics is geometrically optimal. A similar result holds for certain non-invertible topological dynamical systems. As a consequence, the vast theory of analysis on metric spaces may be brought to bear, yielding new numerical invariants. I will outline the construction of these metrics and discuss their properties. This is joint work with Peter Haissinsky.

Thursday, October 16, 2008

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, October 16, 2008
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Submitted by aimo.
Madgalena Musat (University of Southern Denmark, Odense)
Grothendieck inequalities--from classical to non-commutative
Abstract: In 1956 Grothendieck published his celebrated ”Résumé”, containing a general theory of tensor norms on tensor products of Banach spaces, describing several operations to generate new norms from known ones, and studying the duality theory between these norms. The highlight of the paper is the result now called Grothendieck’s Theorem (inequality). The non-commutative version of Grothendieck’s inequality (conjectured in the ”Résumé”) was first proved by Pisier under some approximability assumption, and obtained in full generality by Haagerup. In 1991 Effros and Ruan conjectured that a certain Grothendieck-type inequality for a bilinear form on C∗ -algebras holds if (and only if) the bilinear form is jointly completely bounded. In 2002 Pisier and Shlyakhtenko proved that this inequality holds in the more general setting of operator spaces, provided that the operator spaces in question are exact. Moreover, they proved that the conjecture of Effros and Ruan holds for pairs of C∗ -algebras, of which at least one is exact. In recent joint work with Uffe Haagerup we prove that the Effros-Ruan conjecture holds for general C∗ -algebras, with constant one. More precisely, we show that for every jointly completely bounded (for short, j.c.b.) bilinear form on C∗ -algebras A and B , there exist states f_1 , f_2 on A and g_1 , g_2 on B such that for all a in A and b in B, |u(a,b)| ≤ ||u||_{jcb} (f_1(aa*)^{1/2} g_1(b*b)^{1/2} + f_2(a*a)^{1/2} g_2(bb*)^{1/2}). While the approach by Pisier and Shlyakhtenko relies on free probability techniques, our proof uses more classical operator algebra theory, namely, Tomita-Takesaki theory and special properties of the Powers factors of type III_λ , 0 < λ < 1.

Tuesday, October 21, 2008

Probabilty Seminar/Stochastic and Non-linear Analysis seminar
2:00 pm   in 345 Altgeld Hall,  Tuesday, October 21, 2008
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Submitted by rsong.
Prof. Joseph Conlon (University of Michigan)
The Becker-Doering (B-D) and Lifschitz-Slyozov-Wagner (LSW) Equations
Abstract: The B-D equations describe a mean field approximation for a many body system in relaxation to equilibrium. The two B-D equations determine the time evolution of the density c(L,t) of particles with mass L, L=1,2,... One of the equations is a discretized linear diffusion equation for c(L,t), and the other is a non-local constraint equivalent to mass conservation. Existence and uniqueness for the B-D system was established in the 1980's by Ball, Carr and Penrose. Research in the past decade has concentrated on understanding the large time behavior of solutions to the B-D system. This behavior is characterized by the phenomenon of "coarsening", whereby excess density is concentrated in large particles with mass increasing at a definite rate. An important conjecture in the field is that the coarsening rate can be obtained from a particular self- similar solution of the simpler LSW system. In this talk we shall discuss the B-D and LSW equations, and some recent progress by the speaker and others towards the resolution of this conjecture.

Thursday, October 23, 2008

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, October 23, 2008
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Submitted by aimo.
Caleb Eckhardt (Department of Mathematics, University of Illinois)
Operator Spaces and C*-algebras
Abstract: We discuss an operator space invariant for C*-algebras. Then connections between the range of the invariant and the open question "Is every nuclear stably finite C* algebra quasidiagonal?" Definitions, examples and motivations will all be provided.

Thursday, October 30, 2008

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, October 30, 2008
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Submitted by aimo.
Laura DeMarco (University of Illinois at Chicago)
Escape combinatorics for polynomial dynamics
Abstract: I will describe a new combinatorial approach to studying dynamics of complex polynomials. The method can be used to distinguish topological conjugacy classes of polynomials, to study global structure of the moduli space of polynomials, or to generalize the statement that the Mandelbrot set is connected. I will not assume any background in the subject.

Thursday, November 6, 2008

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, November 6, 2008
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Submitted by aimo.
Enrico Le Donne (Yale University)
Bi-Lipschitz homogeneous geodesic surfaces
Abstract: In this talk, we present general metric properties of spaces which have a transitive group of bi-Lipschitz homeomorphisms. We will mostly focus on the case of geodesic surfaces, i.e., path metric spaces that are topologically equivalent to 2 dimensional manifolds. In particular, we will exhibit the fact that such bi-Lipschitz homogeneous geodesic surfaces are locally doubling. If there is time, I would discuss the fact that there exists a special doubling measure that behaves like the Haar measure for locally compact groups. By the fact that such properties hold, one can start to apply the general theory of Analysis on Metric Spaces to further study such objects.

Thursday, November 13, 2008

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, November 13, 2008
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Submitted by aimo.
Sergei Merenkov (Department of Mathematics, University of Illinois)
Conformality of quasisymmetric maps between relative Schottky sets
Abstract: A relative Schottky set in a domain D contained in the standard n-sphere is obtained by removing a collection of disjoint open balls from D so that no interior is left. Quasisymmetries form a natural class of maps between such spaces. In a recent work with M. Bonk and B. Kleiner we proved that if n is at least 3, every quasisymmetric map between zero measure relative Schottky sets (satisfying mild geometric assumptions) is the restriction of a Moebius transformation. The situation is much less rigid when n=2. In this talk I will discuss local and infinitesimal properties of quasisymmetric maps between planar relative Schottky sets. The main result states that every quasisymmetric map between zero measure relative Schottky sets (satisfying mild geometric assumptions) in Jordan domains is conformal and locally bi-Lipschitz.

Tuesday, November 18, 2008

Analysis Seminar
2:00 pm   in 347 Altgeld Hall,  Tuesday, November 18, 2008
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Submitted by aimo.
Analysis tenure-track hiring meeting

Thursday, November 20, 2008

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, November 20, 2008
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Submitted by aimo.
Analysis tenure-track hiring meeting

Thursday, December 4, 2008

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, December 4, 2008
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Submitted by aimo.
Vladimir Eiderman (visiting Purdue University)
Cartan type estimates for Riesz transforms
Abstract: This is a joint work with F. Nazarov and A. Volberg. For given real numbers v_1,... ,v_N, points y_1,...,y_N in R^d, d ≥ 1, and s > 0 we define the set Z (ν, P ) = {x ∈ R^d : | \sum_{j=1}^N (x-y_j) |x-y_j|^{-s-1} v_j | > P }, P>0. Our goal is to give sharp upper bounds for the size of Z (ν, P ). This size will be measured by the Hausdorff content M_h with various gauge functions h. Among other things, we shall characterize all h for which the estimates do not blow up as N → ∞. In this case routine limiting arguments allow us to extend our bounds to s-Riesz transforms of all finite Borel measures. As an application of obtained results we establish geometrical properties of the capacity generated by the Riesz transform, as well as the relation of this capacity with non-linear capacities of Maz’ya-Havin and Hedberg.

Monday, December 8, 2008

Analysis Seminar
2:00 pm   in 1 Illini Hall,  Monday, December 8, 2008
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Submitted by aimo.
Analysis postdoc hiring meeting

Thursday, December 11, 2008

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, December 11, 2008
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Submitted by aimo.
Hrant Hakobyan (University of Toronto)
Modulus of measures and conformal dimension
Abstract: The conformal dimension of a metric space X is the infimum of the Hausdorff dimensions of all spaces quasisymmetric to X. This is one of the main quasisymmetric invariants of a space. Tyson proved that a family of curves in X of positive modulus gives a lower bound for the conformal dimension. We will show that a family of certain one-dimensional measures, supported on minimal Cantor sets, of positive Fuglede modulus also gives a lower bound. As an application we obtain new lower bounds for the conformal dimension of many self-affine spaces in terms of the Hausdorff dimensions of certain cross-sections.

Thursday, January 29, 2009

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, January 29, 2009
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Submitted by aimo.
Pierre Fima (Department of Mathematics, University of Illinois)
Property T for discrete quantum groups
Abstract: We give a simple definition of property T for discrete quantum groups. We prove the basic expected properties: discrete quantum groups with property T are finitely generated and unimodular. Moreover we show that, for ``I.C.C.'' discrete quantum groups, property T is equivalent to Connes' property T for the dual von Neumann algebra. This allows us to give the first example of a property T discrete quantum group which is not a group using the twisting construction.

Thursday, February 19, 2009

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, February 19, 2009
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Submitted by berdogan.
Alex Iosevich (University of Missouri Columbia)
Geometric configurations in vector spaces over finite fields
Abstract: We are going to see in a variety of situations that a sufficiently large subset of a $d$-dimensional vector space over a finite field contains a copy of a given geometric configuration. Fourier analytic viewpoint and number theoretic obstructions are emphasized throughout.

Thursday, March 5, 2009

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, March 5, 2009
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Submitted by aimo.
John Mackay (Department of Mathematics, University of Illinois)
Existence of Quasi-arcs
Abstract: It is a standard topological fact that a complete metric space which is locally connected, connected and locally compact is arc-wise connected. Tukia (1996) showed that an analogous geometric statement is true: if a complete metric space is linearly connected and doubling, then it is connected by quasi-arcs. I will describe a new proof of this fact, which is constructive and much more straightforward. Pictures will be drawn.

Tuesday, March 10, 2009

Analysis Seminar
3:00 pm   in 447 Altgeld Hall,  Tuesday, March 10, 2009
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Submitted by jmmackay.
Kevin Wildrick (University of Jyväskylä)
Space filling with derivatives in a Lorentz space
Abstract: Recent work of Hajlasz and Tyson updated the classical construction of a continuous surjection from the unit cube onto an arbitrary metric space to include Sobolev regularity. We give a similar construction where the desired regularity is measured by the finer Lorentz scale. A sharp picture arises from a complementary result stating that sufficiently regular mappings, as measured by the Lorentz scale, must send sets of measure zero to sets of measure zero. (Joint work with Thomas Zuercher, University of Bern.)

Thursday, March 12, 2009

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, March 12, 2009
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Submitted by aimo.
Pierre Fima (Department of Mathematics, University of Illinois)
Haagerup Property for Discrete Quantum Groups
Abstract: We will discuss the notion of positive definite functions on discrete quantum groups and introduce the Haagerup property. We will show some basic expected results about Haagerup property. We will also show the equivalence between Haagerup property for discrete Kac algebra and Haagerup property for the dual von Neumann algebra. This last result allows us to show that the Haagerup property is preserved by twisting.

Thursday, March 19, 2009

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, March 19, 2009
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Submitted by aimo.
Robert Kaufman (Department of Mathematics, University of Illinois)
Renorming in Banach spaces, nearest points and analytic sets
Abstract: Let X be a separable Banach space, Y a closed nonreflexive subspace, and N the set of points in X that have a nearest point in Y. Then N is analytic (Suslin) and has some obvious geometric properties (and depends on the norm in X). Theorem: Any analytic set of this type is the set N for a suitable norm in X. Main tools are the following: Bartle-Graves selectors; nonshrinking basic sequence; LUR norms; discontinuous functions in metric spaces.

Friday, March 27, 2009

Illinois/Missouri Applied Harmonic Analysis Seminar
9:00 am   in Coordinated Science Lab, room B02,  Friday, March 27, 2009
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Submitted by laugesen.
John Benedetto, Emmanuel Candes and Yoram Bresler (Maryland, Caltech, Illinois)
To Be Announced
Abstract: This mini-conference is open to all. Please contact Richard Laugesen if you plan to attend. See http://www.math.uiuc.edu/~laugesen/imaha05/imaha05.html for more information.

Tuesday, March 31, 2009

Analysis Seminar
3:00 pm   in 447 Altgeld Hall,  Tuesday, March 31, 2009
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Submitted by tyson.
Mario Bonk (University of Michigan)
Function spaces and hyperbolic fillings

Wednesday, April 1, 2009

Analysis Seminar
3:00 pm   in 141 Altgeld Hall,  Wednesday, April 1, 2009
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Submitted by aimo.
Ilpo Laine (University of Joensuu, Finland)
Value distribution theory of shifts of meromorphic functions
Abstract: The abstract is available at http://www.math.uiuc.edu/~aimo/Urbanaabs2.pdf

Thursday, April 2, 2009

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, April 2, 2009
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Submitted by aimo.
Pekka Pankka (University of Michigan)
From quasiregularity to finite distortion on quasiregularly elliptic manifolds
Abstract: Riemannian manifolds admitting quasiregular mappings from the Euclidean space form a special class of non-hyperbolic manifolds, so called quasiregularly elliptic manifolds. I will discuss results on the topology of quasiregularly elliptic manifolds and counterparts for these results for manifolds receiving more general geometrically controlled branched covering mappings.

Thursday, April 30, 2009

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, April 30, 2009
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Submitted by aimo.
Caleb Eckhardt (Department of Mathematics, University of Illinois)
Noncommutative Gauss Map
Abstract: In this preliminary report we will focus on importing the Gauss map that appears in the continued fraction algorithm to the noncommutative setting. This noncommutative map will act on an AF algebra in the same way the (adjoint of the) Gauss map acts on [0,1].