Listing of Previous Colloquia
Fall 2007
Statistical Mechanics of Population Coding in the Brain
Eitan Gross, University of Arkansas
September 13, 2007
The response of a single neuron to a sensory stimulus is extremely noisy and only weakly coupled to changes in the stimulus. Consequently, the information carried by a single neuron is very low. The brain overcomes this limitation by distributing the information across a large number of neurons which together carry more accurate information about the stimulus. Population coding is thus a central paradigm for information processing in the brain. This paradigm has evoked numerous studies on the thermodynamic efficiency of population codes. Of particular interest is the way in which the amount of information about the stimulus depends on the size of the neuron population that participates in the response, as well as on the transfer function of the individual neuron. In this project, we developed a computer model of a neuronal population system made of stochastic, statistically independent elements; and studied the mutual information between several types of stimuli and our model system. We analyzed the properties of the mutual information (MI) in the limit of a large system size N, using statistical mechanics. For discrete-valued stimuli, MI saturates exponentially with N. For continuous-valued stimuli, MI increases logarithmically with N and is related to the logarithm of the Fisher information of the system. Furthermore, we found that the exponent of MI saturation scales as the Renyi distance between response probabilities induced by different stimuli. I will also demonstrate how our model can be used to solve for singularities in the binding problem. Our model provides a tractable tool to study brain response mechanisms to neuronal representations of sensory, motor, and cognitive events.
Hawaiian Earrings, Their Homotopy and Homology Groups
Satya Deo, Harish-Chandra Research Institute
September 20, 2007
Hawaiian earrings and their r-dimensional generalizations, r >1, have recently attracted a lot of attention of algebraic topologists for several reasons. These are compact metric spaces which are locally nice everywhere except at one point, and consequently have quite complicated fundamental groups. Their homology groups and homotopy groups are yet not fully computed though several interesting partial results have been obtained. Barrat and Milnor were first to use these spaces to give an example of a space whose homology groups have no respect for the dimension of the space. They also left open several questions which are currently being tackled. The talk will highlight some of the recent results on these problems.
On the non existence of smooth Levi flat real hypersurfaces in the complex projective space
Andrei Iordan, Universite' Paris 6 (France)
October 11, 2007
In 1993 D. Cerveau conjectured the non-existence of smooth Levi-flat real hypersurfaces in in the complex n-dimensional projective space, with n greater then or equal to 2, ie. of real hypersurfaces admitting a local foliation by complex-analytic hypersurfaces. If n is greater than or equal to 3, this problem was solved for real analytic hypersurfaces by A. Lins Neto and for smooth hypersurfaces by Y.-T. Siu . In this lecture we will discuss this problem and we will give an improvement of the regularity in Siu's theorem.
Beyond the Cauchy-Riemann equations
Craig Nolder, Florida State University
October 18, 2007
Identifying Protein Biomarkers From Mass Spectrometry Data with Ordinal Outcomes
Deukwoo Kwon, National Cancer Institute
October 25, 2007
In recent years, there has been an increased interest in using protein mass spectroscopy to identify molecular markers that discriminate diseased from health individuals. Existing methods are tailored towards classifying observations into nominal categories. Sometimes, however, the outcome of interest may be measured on an ordered scale. When we ignore this natural ordering it results in some loss of information. We propose a Bayesian model for the analysis of mass spectrometry data with ordered outcome. The method provides a unified approach for identifying relevant markers and predicting class membership. This is accomplished by building a stochastic search variable selection method within an ordinal outcome model. We apply the methodology to mass spectrometry data on ovarian cancer cases and healthy individuals. We also utilize wavelet-based techniques to remove noise from the mass spectra prior to analysis. We identify protein markers associated with being healthy, having low grade ovarian cancer,or being a high grade case. For comparison, we repeated the analysis using conventional classification procedures and found improved predictive accuracy with our method.
Neuromorphometry and Image-Guided Surgery
John W. Haller, National Institute of Biomedical Imaging and Bioengineering, National Institutes of Health
November 29, 2007
Innovations in biomedical imaging critically depend on the mathematical and statistical sciences. This presentation will focus on the application of mathematics and statistics for post-processing of medical images. Application of patient-specific models for diagnosing disease and guiding interventions (specifically, image-guided surgery) will be described.
This talk will be especially accessible to graduate students and non-experts in the field.
Mathematics and statistics became vital for x-ray computed tomography (CT) and positron emission tomography (PET) imaging in the 1970s. In the 1980s, MRI provided yet another method for exquisitely characterizing soft tissue. A critical problem for medical imaging in the 21st century is moving from what is primarily a qualitative science, where healthcare workers make a subjective determination of the presence or absence of disease, to a quantitative science, where probabilities are assigned, change is quantified, and the quantitative sciences are used to provide greater diagnostic specificity.
To advance to a more quantitative science of medical imaging, computer-based mathematical and statistical methods are being explored in a variety of clinical applications, including real-time, image-guided interventions. An image-guided intervention is defined as a patient encounter where images are used during a minimally-invasive procedure for guidance, navigation and orientation to reach a specified target in the body. Common requirements for all image-guided interventions are a source of images, a real-time interactive display linked to the intervention with a means of target definition in the context of real 3D space of the patient’s anatomy (as distinguished from the virtual image space).
Spring 2007
Mathematics textbooks and state curriculum standards: an analysis of the alignment between the K-8 written and intended curricula
Shannon Dingman, University of Missouri
January 17, 2007
Making Sense of the Infinite: A Study Investigating the Learning and Teaching of Infinite Series
Brian Lindaman, University of Kansas
January 23, 2007
This study used results from a preliminary survey to create and implement a teaching experiment specifically targeting students' understanding of infinite series. The experiment compared computational performance and conceptual understanding of two groups of calculus students. One group received traditional instruction on series; the other group received instruction which included classroom reform strategies such as writing during class, working in pairs, and an emphasis on visualization. Results and conclusions will be shared along with descriptions of classroom assessments and activities related to this project.
A partnership between a middle school mathematics teacher and a university researcher centered on the content
Anthony Fernandes, University of Arizona
January 29, 2007
This talk will outline a case study between a middle school mathematics teacher and a university researcher as we had discussions centered on the mathematics content and teaching. The study seeks to understand the nature of this partnership, how it evolved over time, the constraints on the partners, the benefits to the teacher’s work, and the evolution of the cognitive demand of tasks. In the talk I will share my reasons for doing the study, selected background literature, preliminary results and possible future directions of this research.
A presentation for the automorphisms of the 3-sphere that preserver a genus two Heegard splitting
Erol Akbas, U. of Arkansas
February 08,2007
A spatialy-adjusted Bayesian additive regression tree model to merge two datasets
Song Zhang, University of Texas M.D. Anderson Cancer Center
February 12, 2007
Capturing local spatial behavior and speciation through hybrid Dirichlet Process semi-parametric modeling
Michele Guindani, University of Texas M.D. Anderson Cancer Center
February 22, 2007
Spatial heterogeneity plays an important role in a diverse set of applications. For example, in ecology, heterogeneous environments promote camouflaged prey species and disruptive selection; in economics, local characteristics determine regional policies; in health sciences, histopathological heterogeneity characterizes certain cancer tissues within and among tumor types.
Recent Bayesian modeling of univariate spatial data has considered mixed effect models, where a residual stationary (homogeneous) Gaussian effect is assumed. Arguably, one might prefer the flexibility of a nonstationary, non-Gaussian specification. In a nonparametric setting, this can be accommodated by mixture of Dirichlet process (DP) models. The DP is an example of a species sampling prior, which are typically used to describe diversity of different ecological groups of species under different environmental conditions.
However, a limitation of the mixture of DP models is that the latent factor driving species sampling is globally defined and may fail to account for spatial heterogeneity. In this work, we introduce a novel class of prior distributions, the hybrid Dirichlet Processes (hDP), which generalize the DP and overcome this limitation. In a spatial setting, the hDP are defined as mixtures of Gaussian random fields with spatially varying weights. A crucial feature of this specification is the possibility to model local speciation and hybrid clustering.
We illustrate the procedure by means of a simulated example and an application to the analysis of hippocampal atrophy in brains of patients affected by Alzheimer's disease.
This is joint work with Alan Gelfand (Duke University, USA) and Sonia Petrone (Bocconi University, Italy).
Spatial Panel Data Analysis via Bayesian Hierarchical Modeling
Yanbing Zheng, University of Wisconsin
February 26, 2007
Analysis of spatial panel data is of great importance and interest in spatial econometrics. Here we consider cigarette demand in a spatial panel of 46 states of the US over a 30-year period. We construct a demand equation to examine the elasticity of per pack cigarette price and per capita disposable income. The existing spatial panel models account for both spatial autocorrelation and state-wise heterogeneity, but fail to account for temporal autocorrelation. Thus we propose new spatial panel models and adopt a fully Bayesian approach for model parameter inference and prediction of cigarette demand at future time points using MCMC. We conclude that the spatial panel model that accounts for state-wise heterogeneity, spatial dependence, and temporal dependence clearly outperforms the existing models. Analysis based on the new model suggests a negative cigarette price elasticity but a positive income elasticity. The methodology presented here may be suitable for spatial-temporal lattice data in general.
A Filtering Approach to Abnormal Cluster Identification
Zhengxiao Wu, University of Wisconsin-Madison
March 29, 2007
A series of events $X_1,X_2,\ldots$ occur at times $\tau_1,\tau_2,\ldots$. Each event is either ``normal'' or ``abnormal''. We model the observations as a marked point process with a randomly initiated and growing cluster which represents the ``abnormal'' events. Our goal is to compute the conditional probability that an observed event is abnormal in real time.
Employing filtering techniques, we derive versions of the Zakai and Kushner-Stratonovich equations in our setting. This framework is applied in earthquake occurence modelling. Such filtering model performs well in declustering.
Hawaiian Earrings, their homotopy and homology groups
Satya Deo
April 5, 2007
Hawaiian earrings and their r-dimensional generalizations, r >1, have recently attracted a lot of attention of algebraic topologists for several reasons. These are compact metric spaces which are locally nice everywhere except at one point, and consequently have quite complicated fundamental groups. Their homology groups and homotopy groups are yet not fully computed though several interesting partial results have been obtained. Barrat and Milnor were first to use these spaces to give an example of a space whose homology groups have no respect for the dimension of the space. They also left open several questions which are currently being tackled. The talk will highlight some of the recent results on these problems.
Taking a wavy Euclidian royal road to relativity and quantum theory: Occam’s razors and Evenson’s lasers
Bill Harter
April 12, 2007
A concise, lucid, precise (as well as colorful) derivation of special relativity and quantum theory is possible by Euclidean ruler&compass logic. The trick is to look carefully at the geometry of simple wave interference and apply Occam’s razor to Einstein’s 1905 postulates regarding the speed of light. This shows how light makes its own coordinate frame to position itself in a kind of mini-GPS and then tells us some things about matter.
The Earth Global Positioning System (GPS) is one result of a renaissance in experimental optical precision begun by co-workers of Ken Evenson (1932-2002) who made ultra precise measurements of speed of light: c= 299,792,458m•s-1 in 1972 at the Time and Frequency Section of the Boulder lab of the National Institute of Standards.1 Evenson’s work was honored in the 2005 Nobel Prize in Physics.
This talk is an attempt to show logical clarity and precision worthy to accompany experimental precision of Evenson metrology, and like his work, exploits wave resonance and spectral properties of light and matter to an uncommon degree.
Carnot-Carath´eodory metrics and viscosity solutions
Frederica Dragoni, Istituto Nazionale d'Alta Matematica (Italy), visiting U. of Pittsburgh
April 19th, 2007
In the first part I’ll give some basic notions about Carnot- Carath´eodory matrics and viscosity solutions. I’m going to show some examples in order to understand why those theories are introduced. Moreover I’ll quote some known results of existence and uniqueness for evolutive Hamilton-Jacobi equations, introducing the Hopf-Lax formula (in the classic setting) and showing an important link to the calculus of variation. In the second part I’ll give an existence result theorem in the context of semicontinuous initial data and H¨ormander-Hamiltonians. The key to prove this result is to solve the associated eikonal equation. In the third part I’ll prove a convergence theorem which generalizes a known result for the usual inf-convolutions to the metric setting. In this part I’ll use a Large Deviation Principle in the hypoelliptic case, got by an easy new proof, using some techniques of mesure theory.
Random walks and groups
Joseph Maher, Oklahoma State
April 20, 2007
We will start from the simplest examples of random walks, which are the nearest neighbour random walks on graphs. After each unit of time, you jump to one of the adjacent verties in the graph with equal probability. The standard examples of random walks on the integer lattice in R, or R^n, are of this form. If we interpret the integer lattice in R^n as the Cayley graph of the abelian group Z^n, we can relate properties of the random walk to algebraic properties of groups. We will mention how random walks have given new information about braid groups and the mapping class groups of surfaces.
A Short Introduction to Cauchy-Riemann Theory
Roman Dwilewicz, University of Missouri-Rolla
April 26, 2007
After a short introduction to the Cauchy-Riemann (CR) theory, some problems of the theory will be presented: holomorphic extensions and approximations of CR functions and, if time allows, d-bar problem in complex fiber bundles and applications to vector bundles over complex tori and relations to theta functions. This all will be done in an elementary way and no prior knowledge of complex analysis will be expected.
Statistical Mechanics of Population Coding in the Brain
Eitan Gross, Dept. of Physics, University of Arkansas
May 1, 2007
The response of a single neuron to a sensory stimulus is extremely noisy and only weakly coupled to changes in the stimulus. Consequently, the information carried by a single neuron is very low. The brain overcomes this limitation by distributing the information across a large number of neurons which together carry more accurate information about the stimulus. Population coding is thus a central paradigm for information processing in the brain. This paradigm has evoked numerous studies on the statistical efficiency of population codes. Of particular interest is the way in which the amount of information about the stimulus depends on the size of the neuron population that participates in the response, as well as on the transfer function of the individual neuron. In this project, we developed a computer model of a neuronal population system made of stochastic, statistically independent elements; and studied the mutual information between several types of stimuli and our model system. We analyzed the properties of the mutual information (MI) in the limit of a large system size N, using statistical mechanics. For discrete-valued stimuli, MI saturates exponentially with N. For continuous-valued stimuli, MI increases logarithmically with N and is related to the logarithm of the Fisher information of the system. Furthermore, we found that the exponent of MI saturation scales as the Renyi distance between response probabilities induced by different stimuli. I will also demonstrate how our model can be used to solve for singularities in the binding problem. Our model provides a tractable tool to study brain response mechanisms to neuronal representations of sensory, motor, and cognitive events.
The geometric structure of the visual cortex
Giovanna Citti, University of Bologna
May 2, 2007
Viscosity Solutions of the p-Laplace Equation
Juan Manfredi, U. Pittsburg
May 3, 2007
Consider the p-Laplacian equation 0 = div(|rv|p-2rv) and its parabolic counterpart @v @t = div(|rv|p-2rv) These equations can be studied as divergence form equations using the notion of weak or distributional solution, and also as non-divergence form equations using the notion of viscosity solution. During the first part of the talk we will discuss the relationships between these two notions of generalized solution, which fortunately agree for bounded functions. During the second part of the talk we will present some recent regularity results for viscosity supersolutions and their spatial gradients. We give a new proof of the existence of rv in Sobolev’s sense and of the validity of the equation ZZ-v @' @t + h|rv|p-2rv, r'idx dt 0 (1) for all test functions ' 0. Here is the underlying domain in Rn+1 and v is a bounded viscosity supersolution in . The first step of our proof is to establish (1) for the so-called infimal convolution va. The function v has the advantage of being differentiable with respect to all its variables x1, x2, · · · , xn, and t, while the original v is merely lower semicontinuous to begin with. The second step is to pass to the limit as ! 0. It is clear that v ! v but it is delicate to establish a sufficiently good convergence of the rv’s. This is joint work with Peter Lindqvist at Trondheim.
Fall 2006
Uniformization results in conformal geometry
Andrea Malchiodi, SISSA (Trieste, Italy)
October 26, 2006
The classical uniformization theorem asserts that every compact surface admits a conformal metric with constant Gauss curvature. This result has a counterpart in dimension greater or equal to three, when one is interested in finding conformal metrics with constant scalar curvature, which is known as the Yamabe problem. I will review these results and discuss some other conformally invariant objects of higher order, the $Q$-curvature and the Paneitz operator, which play a role in the study of four-dimensional manifolds.
On Hardy type inequalities
Alexander Balinsky, University of Cardiff (United Kingdom)
November 2, 2006
The aim of this talk is to present some recent results on Hardy and Sobolev type inequalities for magnetic Dirichlet forms with multiple singularities in dimension d=2. Our approach is based on the conformal invariance of magnetic Dirichlet forms with Aharonov-Bohm potentials. The strategy is first to establish Hardy-type inequalities for doubly connected domains using uniformization, and second to use Morse theory to decompose R2 into doubly connected domains with explicit uniformizations.
On Hermitian geometry of complex surfaces
Massimiliano Pontecorvo, University of Rome 3, Italy
November 6, 2006
We present some recent results on anti-self-dual Hermitian metrics and relate them to more general questions on the geometry of compact complex surfaces.
Spectral analysis of Laplacians on the Heisenberg group
Fulvio Ricci, Scuola Normale (Pisa, Italy)
November 14, 2006
The Heisenberg group $H_n$ is a non-commutative Lie group, and Fourier analysis on it in principle requires tools from representation theory that make it hard to handle in many instances. However, if attention is restricted to functions or operators that are invariant under unitary transformations of $H_n$, the Fourier analysis becomes essentially commutative, and various aspects of classical analysis on $R^n$ can be recovered. This applies to functional calculus on left-invariant differential operators that commute with unitary transformations, namely the central derivative, the sub-Laplacian and polynomials in these two operators. Recently these methods have been pushed forward so to cover other operators, including Hodge Laplacians acting on differential forms.
Tunnel number 1 knots and the disk complex
Darryl McCollough, University of Oklahoma
November 20th, 2006
A knot K in the 3-sphere is said to be a tunnel number 1 knot when there exists an arc meeting K in its endpoints so that a neighborhood of the union of K and the arc, necessarily a genus-2 handlebody, can be moved to the standard (unknotted) position. The tunnel number 1 knots are an interesting and well-studied class, which includes all 2-bridge knots and torus knots. In this talk, we present the basic ideas of a new theory which describes all the tunnels of tunnel number 1 knots using a tree derived from the collection of all disks in the standard genus-2 handlebody. The theory makes fundamental use of recent results of M. Scharlemann and E. Akbas.
A Presentation For The Automorphisms Of The $3$-Sphere That Preserve A Genus Two Heegaard Splitting
Erol Akbas
November 30, 2006
Scharlemann constructed a connected simplicial 2-complex $\Gamma$ with an action by the group ${\mathcal H_{2}}$ of isotopy classes of orientation preserving homeomorphisms of $S3$ that preserve the isotopy class of an unknotted genus $2$ handlebody $V$. We prove that the 2-complex $\Gamma$ is contractible. Therefore we get a finite presentation of ${\mathcal H_{2}}$.
Spring 2006
Fourier Series: Past, Present and Future
M. Lacey, Georgia Tech.
January 26, 2006
Yang-Baxter Equations and Their Super Solutions
Gizem Karaali, University of California, Santa Barbara
February 9, 2006
Complex Symmetric Operators
Stephen Garcia, University of California, Santa Barbara
February 10, 2006
Motion of Surfaces by Curvature
Gieri Simonett, Vanderbilt University
February 16, 2006
What wavelets are and do
Guido Weiss, Washington University (St. Louis)
February 23, 2006
A meta-analysis of effects of standards-based curricula on student's achievement in mathematics classes
Xiaobao Li, Texas A&M University
March 1, 2006
Boundedness of Fourier integral operators on Hardy spaces
Marco Peloso, Politecnico di Torino, U. Missouri-Columbia and Washington University (St Louis)
March 9, 2006
Circle Packing and the Experimental Imperative (illustration)
Ken Stephenson, U. Tennessee
March 30, 2006
Local Isometric embedding of surfaces in 3-space
Qing Han, Notre Dame
April 11, 2006
Quasiconformal geometry of fractals
Mario Bonk, University of Michigan
April 27, 2006
Finding global minimizers of segmentation and denoising functionals
Selim Esedoglu, University of Michigan
May 2nd, 2006
Fall 2005
Visualizing one dimensional Teichmuller space
Yasushi Yamashita
November 8, 2005
On square-free monomial ideals
Tai Huy Ha, Tulane University
November 10, 2005
3:30pm, SCEN 322
A closer look at certain strongly Cohen-Macaulay ideals and residual intersections
Christine Cumming, Tulane University
November 11, 2005
3:30pm
Some Zero-Sum Problems
Francesco Pappalardi, Universita Rome III
November 17, 2005
Spring 2005
Heat Operator on Some Noncompact Spaces
Thalia Jeffres, Wichita State University
Thursday April 28, 2005 Abstract
Uniqueness in the inverse conductivity problem and regularity of the conductivity
Russell Brown, University of Kentucky
Thursday April 21, 2005
Two and Three D modeling, analysis of Navier-Stokes Equations
Kumud Altmeyer, University of Arkansas Pine Bluff
Wednesday April 20, 2005
When are 3 dimensions not 3-dimensional? Understanding the topology of 3-manifolds
Ryan Derby-Talbot, University of Texas
Tuesday April 12, 2005 Abstract
TBA
Tao Li, Oklahoma State University
Friday April 8, 2005 @ 2:30 pm
Approximation and Geometric Function Theory in Complex and Hypercomplex Variables
Sorin Gal, University of Oradea, Romania
Thursday April 7, 2005 @ 2:30 pm
Equilibrium distribution of a charge in presence of an external field
Igor Pritsker, Oklahoma State University
Thursday March 31, 2005 Abstract
Space-Time Analysis of Extreme Values
Gabriel Huerta, University of New M
Friday March 18, 2005 @ 2:30 pm Abstract
Bayesian Multivariate Spatial Models for Roadway Traffic Crashing Mapping
Joon Jin Song, University of Massachusetts
Thursday March 17, 2005 @ 2:30 pm Abstract
On the Geometrical Structure of the Visual Cortex
Professor Giovanna Citti, Universita' di Bologna, Italy
Wednesday March 16, 2005 @ 2:30 pm
Clifford Analysis on Dirac Bundles and Applications
Mircea Martin, Baker University, Kansas
Thursday March 3, 2005 Abstract
Extremal Problems in Hardy and Bergman Spaces
Catherine Beneteau, Seton Hall University
Tuesday March 1, 2005
Largest Circuits and Cocircuits in Matroids
Nolan McMurray, University of North Carolina at Wilmington
Thursday February 24, 2005
A Glimpse into Cofiniteness and Local Cohomology
Janet Vassilev, University of Arkansas
Tuesday February 22, 2005 Abstract
A generalization of Gram-Schmidt orthogonalization generating all Parseval frames
Gitta Kutyniok, University of Giessen, Germany
Thursday February 17, 2005 Abstract
Multivariate Lattice Models for Areal Data with Application to Multiple Disease Mapping
Xiaoping Jin, University of Minnesota
Thursday January 27, 2005 Abstract
Empirical Bayesian Analysis for High-Dimensional Computer Output
Dorin Drignei, Iowa State University
Monday January 24, 2005 Abstract
Robust transmission/disequilibrium test for incomplete family genotypes
Gulhan Alpargu, University of Massachusetts
Thursday January 20, 2005
Fall 2004
G-compactness of elliptic systems
Leonid Kovalev, Washington University
Thursday September 30, 2004 Abstract
The theorem of Busemann-Feller-Alexandrov for convex functions in Carnot groups
Nicola Garofalo, Purdue University
Thursday November 18, 2004
Schrodinger equations with time dependent potentials
Virginia Naibo, University of Kansas
Thursday December 2, 2004
Intersection Multiplicity
Izuru Mori, SUNY, Brockport
Friday December 3, 2004
Spring 2004
Benchmark Estimation for Markov Chain Monte Carlo Samples
Subharup Guha, Department of Statistics, The Ohio State University
Monday, February 16, 2004
Discrimination Measures for Locally Stationary Time Series Using the Excess Mass Functional
Gabriel Chandler, Department of Statistics, University of California, Davis
Friday, February 20, 2004
Invertible substitutions on the line and the projection method
Edmund Harris, Imperial College, London UK
Thursday, February 26, 2004
How far can a convex function stretch the unit disk from being a disk?
Roger Barnard, Texas Tech University
Thursday, March 4, 2004
Conjugate functions and semi-conformal mappings
Michael Eastwood, University of Adelaide, Australia
Tuesday, March 23, 2004 Abstract
Linear Regression With Multiple Changepoints: An Application to Monthly Mean United States Temperature trends
Qi Qi Lu, Department of Statistics, University of Georgia
Wednesday, March 24, 2004 Abstract
Efficient Parameterization and Estimation of Spatio-Temporal Dynamic Models
(Bill) Ke Xu, Department of Statistics, University of Missouri - Columbia
Monday, March 29, 2004 Abstract
Integrable field theories, meromorphic loops and the Riemann-Hilbert problem
Edwin Beggs, University College of Wales, Swansea, UK
Tuesday, March 30, 2004
Slepian functions as the solution of energy concentration problem: A brief history and new development
Xiaping Shen, University of Ohio
Thursday, April 1, 2004 Abstract
Dense surface groups in Lie groups
Juan Souto, Mathematisches Institut Rheinische Friedrich-Wilhelms-Universitdt Bonn, Germany
Tuesday, April 6, 2004 Abstract
The Radon transform in texture analysis
Swanhild Bernstein, University of Mining and Technology, Freiberg, Germany
Thursday, April 8, 2004
Sparse Fourier representations via sampling
Martin Strauss, AT&T Labs and the University of Michigan
Tuesday, April 20, 2004
Fall 2003
Configurations of Lines
Javier Bracho, UNAM, Mexico
Thursday, October 23, 2003
Extending bounded holomorphic functions
John McCarthy, Washington University
Thursday, November 6, 2003 Abstract
Complex-valued planar harmonic functions and regions of constant valence
Genevra Neuman, Kansas State University
Thursday, November 13, 2003 Abstract
Why is the isotropic correlation model so popular in spatial statistics?
Chunsheng Ma, Wichita State University
Thursday, November 20, 2003 Abstract
Spring 2003
Density of wavelet frames
Gitta Kutyniok, University of Paderborn, Germany
Thursday, January 23, 2003 Abstract
Step functions, harmonic measure, and planar domains
Lesley Ward, Harvey Mudd College
Monday, February 24, 2003 Abstract
The inverse mapping theorem on stratified groups
Valentino Magnani, Scuola Normale Superiore, Pisa, Italy
Tuesday, March 4, 2003
Extremal Problems in Hardy and Bergman Spaces
Catherine Beneteau, Seton Hall University, New Jersey
Thursday, March 13, 2003
An inversive approach to the Cauchy integral
Michael Bolt, University of Michigan, Ann Arbor
Thursday, March 27, 2003 Abstract
Reproducing Kernels and Invariant Subspaces
Stefan Richter, University of Tennessee
Thursday, April 24, 2003 Abstract
Application of Bayesian Methods to Spatial Econometrics
James P. LeSage, University of Toledo, Ohio
Thursday, May 1, 2003
Fall 2002
The strange but true history of the Poincare Conjecture
Mark Brittenham, University of Nebraska, Lincoln
Thursday September 26, 2002 Abstract
Electromagnetic wavelets and conformal spacetime transformations
Gerald Kaiser, Virginia Center for Signals and Waves
Thursday October 10, 2002
Function theory on the Unit Sphere in C2
John Wermer, Brown University
Thursday October 17, 2002
Some Applications of Wavelets in Statistics
Marina Vannucci, Texas A&M
Thursday October 31, 2002
Geometry of nilpotent Lie groups
Michael Cowling, University of New South Wales
Tuesday November 19, 2002
On projective duality and osculating spaces
Sergey Lvovskiy, Independent University of Moscow
Thursday November 21, 2002 Abstract
Distortion of dimension by quasisymmetric maps
Jeremy Tyson, University of Illinois, Urbana Champaign
Thursday December 5, 2002
Spring 2002
Viscosity Solutions on Grushin type Planes
Tom Bieske, University of Michigan, Ann Arbor
Thursday February 7, 2002
Complex cobordisms and the embeddability of CR-manifolds
Bruno De Oliveira, University of Pennsylvania
Tuesday February 12, 2002
A history of primary decomposition
Tom Marley, University of Nebraska, Lincoln
Thursday February 14, 2002
Aspects of Liaison theory
Uwe Nagel, University of Paderborn, Germany
Monday February 18, 2002 Abstract
On the partial derivatives of the fundamental solution of the Euclidean Cauchy-Riemann operator in R^{n+1} and their associated Eisenstein series in Clifford Analysis
Soeren Krausshar, Ghent State University, Belgium
Thursday February 21, 2002
Factorization of almost periodic matrix functions and its applications
Ilya Spitkovsky, William and Mary College
Friday March 1, 2002 Abstract
Minimal area problems in conformal mapping
Alex Solynin, Texas Tech University
Thursday March 7, 2002 Abstract
Recent Advances on Function Spaces, Harmonic Analysis and Boundary Value Problems
Osvaldo Mendez, University of Texas, El Paso
Tuesday March 12, 2002
Multiplicities in Local Algebras
C.-Y. Jean Chan, Purdue University
Monday March 25, 2002 Abstract
Some remarks concerning integrals of curvature for curves and surfaces
Stephen Semmes, Rice University
Thursday March 28, 2002
The geometry of modules over a complete intersection
David Jorgensen, University of Texas, Arlington
Monday April 1, 2002 Abstract
On the conformal Martin boundaries
Nageswari Shanmugalingam, University of Texas, Austin
Thursday April 4, 2002 Abstract
Zeros of hypergeometric functions
Peter Duren, University of Michigan, Ann Arbor
Tuesday April 16, 2002
Inverse Eigenvalue problems for quadratic matrix and operator pencils
Biswa Nath Datta, Northern Illinois University
Thursday April 18, 2002
Analytic capacity and Calderon-Zygmund Theory
Joan Verdera, Universitat Autonoma de Barcelona/UCLA
Tuesday April 23, 2002
The space of monogenic BMO-functions on the unit sphere
Swanhild Bernstein, Bauhaus University, Weiman, Germany
Monday May 27, 2002
Analysis of spherical symmetries in Clifford analysis
Yakov Krasnov, Bar-Ilan University , Israel
Tuesday May 28, 2002
Fall 2001
Nonparametric Minimal Surfaces in the Heisenberg Group
Scott Pauls, Dartmouth College
Thursday, September 13, 2001 at 2:30 p.m.
Fixed points of holomorphic mappings
Steven Krantz, Washington University
Thursday, September 20, 2001
Torsion in the group of homeomorphisms of the long line
Satya Deo, R.D. University Jabalpur, India
Thursday October 4, 2001
Subelliptic harmonic maps from Carnot groups
Changyou Wang, University of Kentacky
Thursday, October 11, 2001
Potential theory of the furthest-point distance function
Igor Pritsker, Oklahoma State University
Friday, October 26, 2001
Null Lagrangians
Tadeusz Iwaniec, Syracuse University
Thursday November 8, 2001
On algebras of two dimentional singular integral operators with homogeneous discontinuities in symbols
Alexey Karapetyants, University of Arkansas
Thursday November 15, 2001
Bayesian unit root tests in Stochastic volatility models
Sujit Ghosh, North Carolina State University
Thursday November 29, 2001
How hard is it to decide whether a collection of polynomials has a common zero?
Carlos Berenstein, University of Maryland
Friday December 7, 2001
Spring 2001
Bergman's Coordinates at Corners
David Barrett, University of Michigan
Thursday, May 3, 2001 at 3:30 p.m.
Meromorphic functions and Picard's Theorem
Elias Saleeby, University of Arkansas
Thursday, April 26, 2001 at 3:30 p.m.
Recent Progress on the Bethe-Sommerfeld Conjecture
Zhongwei Shen, University of Kentucky
Wednesday, April 25, 2001 at 3:30 p.m.
Lee Form on Quaternionic Kaehler Manifolds
Loius Pernas, University of Picardie, France
Thursday, April 19, 2001 at 3:30 p.m.
One-dimensional symmetry of entire solutions of non-uniformly elliptic equations arising in geometry and in phase transitions
Nicola Garofalo, Johns Hopkins/Purdue University
Thursday, April 12, 2001 at 3:30 p.m.
The Harmonic Analysis for \box_b Operators
Lihe Wang, University of Iowa
Thursday, April 5, 2001 at 3:30 p.m.
On the Motion of the Interface Between Two Fluids
Sijue Wu, University of Maryland
Wednesday, March 28, 2001 at 3:30 p.m.
Mathematical Uncertainty Principles: Old and New
Joe Lakey, New Mexico State University
Tuesday, March 27, 2001 at 3:30 p.m.
An Elementary Approach to Symmetric Spaces of Rank One
Adam Koranyi, Lehman College, New York
Thursday, March 8, 2001 at 3:30 p.m.
Bayesian Methods for Change-Point Detection in Long-Range Dependent Processes
Bonnie Ray, New Jersey Institute of Technology
Thursday, February 8, 2001 at 3:30 p.m.
On the Set of Solutions to Some Nonlinear Equations
Dimiter Vassilev, University of Arkansas
Thursday, January 18, 2001 at 3:30 p.m.
Fall 2000
The Inverse Conductivity Problem with Less Regular Conductivities
Russell Brown, University of Kentucky
Thursday, November 10, 2000 at 3:30 p.m.
Pretzel, a Proof by Computer Animation
Professor Eric Sedgwick, DePaul University
Thursday, November 3, 2000 at 3:30 p.m.
The Homeomorphism Problem and Triangulation
William Jaco, Oklahoma State University
Thursday, October 26, 2000 at 3:30 p.m.
A Class of Differential Equations with Singular PerturbationsM
Qing Han, Notre Dame University
Thursday, October 12, 2000 at 3:30 p.m.
Test Ideals in One Dimensional Domains
Professor Janet Vassilev, University of Arkansas
Thursday, October 5, 2000 at 3:30 p.m.
Spring 2000
Reversible Cellular Automata
Jarkko Kari, University of Iowa
Thursday, February 3, 2000 at 3:30 p.m.
Topology of Cyclic Configuration Spaces and Periodic Trajectories of Multi-Dimensional Billiards
Michael Farber, Tel Aviv University, Israel
Thursday, February 10, 2000 at 3:30 p.m.
Variation of the Spectrum
Thomas Ransford, University of Laval, Quebec, Canada
Thursday, February 17, 2000 at 3:30 p.m.
Hardy Spaces in Non-Smooth Domains: Recent Progress
Marius Mitrea, University of Missouri at Columbia
Wednesday, March 1, 2000 at 3:30 p.m.
Interactions between Several Complex Variables and Clifford Analysis
Swanhild Berstein, Bauhaus University, Weimar, Germany
Tuesday, March 7, 2000 at 3:30 p.m.
Circles, Triangles and Billiards
Eugene Gutkin, University of Southern California
Thursday, March 9, 2000 at 3:30 p.m.
Spectral Properties of Elliptic Layer Potentials on Curvilinear Polygons
Irena Mitrea, University of Minnesota
Friday, April 14, 2000 at 3:30 p.m.
NSF: Program, Funding in Mathematical Sciences and the Future
Joe Jenkins, Program Director for Mathematical Analysis, National Science Foundation, Washington DC
Thursday, April 27, 2000 at 3:30 p.m.
A Notion of Rectifiability Modeled on Carnot Groups
Scott Paul, Rice University
Thursday, May 4, 2000 at 3:30 p.m.
Fall 1999
Bounded Point Evaluations and Polynomial Approximation
Jim Thomsen, Indiana University
Thursday, September 16, 1999 at 2:30 p.m.
Unknotting knots: new codes and the Dynnikov algebra
Alexei Sossinsky, Independent University of Moscow
Thursday, September 23, 1999 at 3:30 p.m.
Stability of Sobolev spaces with zero boundary values
Lars Hedberg, Linkoping University, Sweden
Monday, October 4, 1999 at 3:30 p.m.
Clifford analysis techniques in multidimensional operator theory
Mircea Martin, Baker University
Thursday, October 14, 1999 at 3:30 p.m.
Equations with critical growth on Carnot groups suggested by problems in CR geometry
Nicola Garofalo, Purdue University
Thursday, October 28, 1999
Lipschitz extensions on the Heisenberg group
Thomas Bieske, Visiting Assistant Professor, University of Arkansas
Thursday, November 11, 1999
Koenig's map of analytic self maps of the disc
Pietro Poggi-Carradini, Kansas State University
Thursday, November 18, 1999
Spring 1999
Systems of Analytic Functions that are Simultaneously Orthogonal over Two Domains
Harold S.Shapiro, Royal Institute of Technology, Stockholm
Thursday, January 28, 1999
A Singular Perturbation Approach to a Two Phase Parabolic Free Boundary Problem Arising In Flame Prapagation
Donatella Danielli, Purdue University
Monday, February 15, 1999
Boundary behavior of harmonic functions and conformal geometry of sub-Laplacians
Nicola Garofalo, Purdue University
Monday, February 22, 1999
Squares of Vector Lattices
Gerard Buskes, University of Mississippi
Thursday, February 25, 1999
Calculus Reform: Trickle Up and Trickle Down
Janet Woodland, University of Arkansas
Tuesday, March 2, 1999
Duality in Complex Analysis
Lev Aizenberg, Bar-Ilan University, Israel
Thursday, March 4, 1999
Exact Bootstrap Moments of an L-estimator
Michael Ernst, Division of Statistics, University of Florida
Friday, March 5, 1999
Nonparametric Bqyesian Modeling of Long Memory Time Processes
Giovanni Petris, Department of Statistics, Carnegie Mellon University
Monday, March 8, 1999
Topology and Three-Dimensional Magnetic Fields: From Gauss and Maxwell to Modern Computational Electromagnetics
P. Robert Kotiuga, Boston University
Thursday, March 11, 1999
Estimating a Life Distribution Based on Ages and Ages of Departure
Mark Rothmann, Department of Statistics, University of Iowa
Friday, March 12, 1999
The story of a pentagonal tiling and a "pentagonal" number
Ken Stephenson, University of Tennessee
Thursday, March 25, 1999
The invariant subspace problem for positive operators
Yuri Abramovich, IUPUI
Friday, April 2, 1999
The role of genetic catastrophesin the origin of species: reconstruction of evolutionary history of mammals by analysis of the genetic texts
Andrei Gudkov, Professor of Biological Sciences, University of lllinois at Chicago
Thursday, April 8, 1999
Minimal Area Problems with Side Conditions
Dov Aharonov, Technion, Haifa
Tuesday, April 13, 1999
Robin Capacity
Peter Duren, University of Michigan at Ann Arbor
Thursday, April 22, 1999
Fall 1998
Nonlinear Singular Integral equations Involving the Hilbert Transform in Clifford Analysis
Swanhild Bernstein, University of Arkansas
Thursday, October 29, 1998
Fluid Flows with Moving Boundary, Integrals of Motion and Algebraic Geometry
Pavel Etingof, Harvard University
Thursday, November 5th, 1998
Stein-Weiss Operators, Spectra and Ellipticity
Tom Branson, University of Iowa
Thursday, November 12th, 1998
Dual Varieties, Local Differential Geometry, and a Classical Problem in Linear Algebra
Joseph Landsberg, Paul Sabatier University, Toulouse
Thursday, November 19th, 1998
Spring 1998
Partial Differential equations in Carnot Caratheodory spaces
Luca Capogna, Courant Institute
Thursday, January 15
Construction of high order general linear methods for ordering differential equations
Zdzislaw Jackiewicz, Arizona State University
Thursday, February 12
The $bar\partial$ and $bar\partial_b$ problems on nonsmooth domains
Mei-Chi Shaw, University of Notre Dame
Thursday, March 5
On regular hypercomplex elementary functions and boundary value problems
Wolfgang Sproessig, Technical University of Freiberg, Germany
Tuesday, March 10, 4:30pm
Legendrian tangles
Lisa Traynor, Bryn Mawr College
Thursday, March 12
Approximation of Cauchy type integrals by rational functions with prescribed poles
Genrik Tumarkin, LA
Wednesday, March 25
The minmax sphere eversion
John Sullivan, University of Illinois, Champagne-Urbana
Friday, March 27th
Nevanlinna-Pick kernels
John McCarthy, Washington University
Thursday, April 9
Congruences of lines in 3-space
Serge Lvovsky, Moscow Independent University, Russia
Tuesday, April 21st
Tight closure, or why characteristic p>0 can be better
Ian Aberbach, University of Missouri, Columbia
Thursday, April 23rd, 2:30 pm
Fall 1997
Hypergeometric functions and geometry of Grassmanians
Vladimir Retakh, University of Arkansas
Thursday, October 2
Modeling and control issues concerning magnetostrictive materials
Ralph Smith, Iowa State University
Friday, October 17
Some theorems on strictly ordered but aperiodic structures in euclidean space
Ludwig Danzer, University of Dortmund, Germany
Friday, October 24
Weil classes on abelian varieties
Yuri Zahrin, Pennsylvania State University
Thursday, November 6, 2:30 pm
Spectral theory and harmonic analysis
Alan McIntosh, Macquarie University, Australia
Friday, November 21
Spring 1997
The Favard class for a nonlinear parabolic problem
Gisele Goldstein, University of Memphis
Friday, January 24th, 12:30pm
Semilinear semigroups and the KdV equation
Jerry Goldstein, University of Memphis
Friday, January 24th, 3:30pm
Decidable Theories
Matthew Valeriote, McMaster University, Canada
Thursday, February 13
Zoo of primative Vassilev knot invariants
Serge Chmutov, Russian Academy of Sciences and Fields Institute, Canada
Thursday, February 20
Finite type invariants of 3-manifolds
Thang Le, SUNY at Buffalo
Thursday, April 3
Derivations into Banach modules
Garth Dales, University of Leeds, U. K.
Wednesday, April 16
Interpolation by bounded analytic functions
John Wermer, Brown University
Thursday, April 17 in SE 109
Fall 1996
Quantitative Approximation Theory
Stephen Fisher, Northwestern University
Thursday, September 5
On self dual locally compact abelian groups
Karl Hofmann, Darmstadt, Germany and Tulane
Friday, September 20
Invariant subspaces of spaces of analytic functions
Dinesh Singh, University of Delhi
Wednesday, October 2
Aperiodic tilings with n-fold symmetry
Ludwig Danzer, Dortmund, Germany
Thursday, October 3rd
Singular integrals on star shaped Lipschitz surfaces and generalisations
Tao Qian, University of New England, Armidale, Australia
Thursday, October 24th
Compact composition operators of some Moebius invariant Banach spaces
Maria Tjani, University of Arkansas, Fayetteville
Thursday, November 7th
Billiard dynamics: a survey
Eugene Gutkin, University of Southern California
Tuesday, November 12th
Hyperbolic n-manifolds via Clifford algebras
Peter Waterman, University of Northern Illinois, DeKalb
Thursday, November 14th, 4:30pm
On damping in elastic systems: myths, models and mathematics
John Burns, VPISU
Tuesday, November 19th, 3:30pm
Spring 1996
Wavelets - The Angle between Past and Future
Sasha Volberg, Michigan State University
Thursday, January 20
Symbolic Powers and Cohen-Macauley Rees Algebras
Susan Morey, University of Texas, Austin
Thursday, February 15
On the Projective Dimension of the Cauchy Fueter System and Applications to the Theory of Regular Functions in Several Quaternionic Variables
Daniele Struppa, George Mason University, Virginia
Thursday, February 22
Statistical Analysis of Mixtures and the Empirical Probability Measure
Philippe Barbe, CNRS, Toulouse, France
Wednesday, March 13
Hardy Spaces on Lipschitz Domains, Clifford Algebras and Compensated Compactness
Marius Mitrea, University of Minnesota, Minneapolis
Thursday, March 14
Joint Seminormality
Norberto Salinas, University of Kansas
Thursday, March 28
To Be Announced
Peter Ebenfelt, University of California, San Diego
April 18