COLLOQUIUM SCHEDULE
2009
Tuesday, August 11, at 4PM in DM 409A
Speaker: Frank Kutzschebauch, University of Bern, Switzerland
Title:A solution to Gromov's Vaserstein Problem
Any matrix in $Sl_n (\C)$ can (due to the Gauss elimination process)
be written as a product of elementary matrices. If instead of the
complex numbers (a field)
the entries in the matrix are elements of a ring, this becomes a
delicate question. In particular
the rings of maps from a space $X \to \C$ are interesting cases. A
deep result of Suslin gives an affirmative answer for the polynomial
ring in $m$ variables in case the size of the matrix ($n$) is greater
$2$ (for $n=2$ this is not true and has a connection to the Jacobian
conjecture).
In the topological category the problem was solved by Thurston and
Vaserstein. For holomorphic functions on $\C^m$ the problem was posed
by Gromovin the 1980's. We report on a complete solution to Gromov's
problem. A main tool is the Oka-Grauert-Gromov-h-principle in Complex
Analysis.
This is joint work with Björn Ivarsson.
Friday, June 12 at DM409A at 11AM
This week we have our last meeting for the summer of the Geometry seminar. It will be at 11am in DM 409A. The title of the talk is "Linear deformations of foliations into contact strucures on torus bundles over the circle."
and the speaker is P. Rukimbira.
Friday, June 8 at DM409A at 11AM
This week the Geometry seminar will be at 11am in DM 409A. The title of the talk is "Overview of the generalized complex geometry", the speaker is G.Grantcharov.
Wednesday, June 3 at DM409A at 11AM
Ed Dubinsky will visit the dept again next Wed, June 3, from 10:30AM to noon. We will meet in DM 409. I expect an informal meeting of questions and answers, mostly about teaching methods Prof Dubinsky has developed as part of the Algebra Project or Calculus reform.
Friday, May28 at DM409A at 11AM
We continue the Geometry Seminar this Friday at 11am in DM409 with a talk by prof. T. Leness. The title is "Relating the Donaldson and spin invariants of four-manifolds".
Friday, May22 at DM409A at 11AM
We'll have our geometry seminar this Friday at a different time again- at 11.00am. Tedi Draghici will continue with the second part of his talk.
Title: Remarks on bi-K-contact structures
Friday, May15 at DM409A at 12 PM
Speaker: Prof T. Draghici, with the help of Prof P. Rukimbira
Title: Remarks on bi-K-contact structures
Friday, April 3rd at DM409A at 3pm
Speaker: M.Yotov
Title: On the geometry of semi-simple complex compact parallelizable manifolds
In this talk, we are discussing some results on existence of complex curves
in manifolds indicated in the title.
Friday, March 27 , at 9:30 AM in DM 409A
Speaker:Professor Hongtao Yang from UNLV
Financial derivatives are utilized to reduce risk by organizations and
individual investors who are exposed to moves in the world markets. In the
third quarter of 2008, US commercial banks held $175.8 trillion in derivative
contracts such as futures and forwards, swaps, options, and credit
derivatives. It is clearly very important to provide accurate and efficient
numerical methods for valuation of these financial products.
In this talk, our recent work on front-fixing methods for American options on
stocks and calibration of interest rate models will be reported. The elements
of rational option pricing and its history will be introduced in the beginning.
Numerical results will be presented to examine our methods and to compare them
with the other methods. Our current working projects will also be discussed to
conclude the talk.
Tuesday, March 17
Speaker: Xinfeng Liu
Title: Computational studies for turbulent mixing and cell signaling
Abstract:
Many systems in the engineering and biology involve moving interfaces or boundaries. Front tracking method is one of the most accurate and efficient computational approaches for studying such systems. A main challenge of developing front tracking algorithms is to capture the interface topological changes. In this talk I shall introduce an improved three-dimensional front tracking method and consider an application for turbulent mixing driven by Rayleigh-Taylor instability, which shows an excellent agreement with the experiments. For the second part of the talk, I will present a computational analysis of cell signaling in biology and medicine. Scaffold, a class of proteins, plays many important roles in signal transduction. Through studying various models of scaffold, I will show novel regulations induced by its spatial location and switch-like responses due to scaffold. To efficiently compute the models, we introduce a new fast numerical algorithm incorporated with adaptive mesh refinement for solving the stiff systems with spatial dynamics.
Monday, March 16, 1 PM
Speaker: Yulong Xing
Title: New Efficient Sparse Space-Time Algorithms in Numerical Weather
Prediction
Abstract: A major stumbling block in the prediction of weather is the
accurate parameterization of moist convection on microscales. A recent
multi-scale modeling approach, superparameterization (SP), has yielded
promising results and provided a potential solution to this problem. SP is
a large-scale modeling system with explicit representation of small-scale
processes provided by a cloud-resolving model (CRM) embedded in each
column of a large-scale model. In this talk, I will present new efficient
sparse space-time algorithms of SP which solve the small scale model in a
reduced spatially periodic domain with a reduced time interval of
integration. The new algorithms have been applied to a stringent
two-dimensional test suite involving moist convection interacting with
shear. The numerical results are compared with the CRM and original SP. It
is shown that the new efficient algorithms for SP result in a gain of
roughly a factor of 10 in efficiency, and the large scale variables such
as horizontal velocity and specific humidity are captured in a
statistically accurate way.
Friday, March 13Speaker: Tian-Jun Li from University of Minnesota:
12:55pm-2pm, in OE 134
(1) -- "Differential forms and currents on almost complex manifolds"
3:30pm-4:30pm, in DM 409A
(2) -- "Symplectic forms and cohomology decompositions of almost complex 4-manifolds"
The first talk belongs to the joint Math-Physics colloquium series and is meant to be accessible to a wide audience,
the second talk is meant to be more a seminar talk for mathematicians
Friday, March 6, 2009 3:30 - 4:30 PM Room TBA
An Introduction to the No Arbitrage Pricing of
Derivative Securities
Speaker: Dr. Enrique Villamor
Professor, Department of MathematicsWe will present an overview on how to find the "fair price" of any derivative security
under the natural assumption of the absence of arbitrage. We' ll start with the simple binomial
multiperiod models in discrete time, which will naturally lead us to the continuous time models
(Black-Scholes-Merton and others). We will look at the three different ways to approach this
problem: The analytic (solutions of PDE's), the probabilistic (discounted expectations under
the risk neutral probability), and the financial (existence of self financed replicating portfolios);
and show their equivalence using the Feynman-Kac theory, Ito's calculus, and the
martingale representation theorem combined with the existence of the risk neutral probabilities.
Thursday, March5, 330PM GL 132
TITLE: Anisotropic Sparse Grid Stochastic Collocation Techniques for PDEs
with High-Dimensional Random Input DataClayton Webster, Ph.D
Department of Scientific Computing
Florida State UniversityThis talk will propose and analyze a dimension-adaptive (anisotropic) sparse grid stochastic collocation method for solving partial differential equations with random coefficients and forcing terms (input data of the model). These methods have proven to have dramatic impact on several application areas, including statistical mechanics, financial mathematics, bioinformatics, and other fields that must properly predict certain model behaviors. The method consists of a Galerkin approximation in the space variables and a collocation, in probability space, on anisotropic sparse tensor product grids utilizing either Clenshaw-Curtis or Gaussian knots. Even in the presence of nonlinearities, the collocation approach leads to the solution of uncoupled deterministic problems, just as in sampling-based methods, such as Monte Carlo. This talk includes both a priori and a posteriori approaches to adapt the anisotropy of the sparse grids to each given problem. This talk will also provide a rigorous convergence analysis of the fully discrete problem and demonstrate strong error estimates for the solution using L^q norms. In particular, our analysis reveals at least an algebraic convergence with respect to the total number of collocation points. The derived estimates are then used to compare the efficiency of the method with other ensemble-based methods. Real world applications and numerical examples illustrate the theoretical results and are used to compare this approach with several others, including the standard Monte Carlo. In particular, for moderately large dimensional problems, the sparse grid approach with a properly chosen anisotropy is very
effective and superior to all examined methods.
Wed March 4, 2009 DM 110 from 4-5
Title: A fast solver for radiative transport equation and applications in
optical imagingSpeaker:Prof. Hongkai Zhao
I will present an efficient forward solver for steady-state or
frequency-domain radiative transfer equation (RTE) on 2D and 3D structured
and unstructured meshes with vacuum boundary condition or reflection
boundary condition. In our algorithm we use a direct angular
discretization and upwind type of spatial discretization that preserves
properties of both scattering and differential operators of RTE. To solve
the large linear system after discretization, we construct an efficient
iterative scheme based on Gauss-Seidel and proper angular dependent
ordering. With this iterative scheme as the relaxation we implement
various multigrid methods in both angular and physical space. Our
algorithm can deal with different scattering regimes efficiently.
Efficiency and accuracy of our algorithm is demonstrated by comparison
with both analytical solutions and Monte Carlo solutions, and various
numerical tests in optical imaging. Based on this algorithm, a multi-level
imaging algorithm is developed for optical tomorgraphy.Feb. 12, 3:30 in GL 132
TITLE: Boundary limits for bounded quasiregular mappings
Speaker: Enrique Villamor
Abstract:
We show the existence of nontangential limits for weighted
A- harmonic functions in the weighted Sobolev space .
These results generalize the ones by Koskela, Manfredi and Villamor, where
the weight was identically equal to one.
We’ll apply these results to improve on results of Koskela, Manfredi and
Villamor, and Martio and Srebro on the existence of radial limits for bounded
quasiregular mappings in the unit ball of Rn with some growth restriction on
their multiplicity function.
A construction by Martio and Srebro shows that our result is sharp.This is joint work with Bao Qin Li and will appear in the Journal of Geometric Analysis.
Thursday, Feb. 5, 2009, from 3:45--4:45 in GL 132
Title: Integrable peakon equations
Speaker: Zhijun Qiao (Dept. of Math, University of Texas-Pan
American)
Abstract: In my talk, I will introduce peakon equations and present a basic approach how to get peakon solutions. Those equations include the well-known Camassa-Holm (CH), the Degasperis-Procesi (DP), and other new peakon equations. Interesting thing is that an integrable equation may have no classical smooth solitons. In the talk, I will illustrate this
feature through two new integrable equations that I found recently. Later, I take the CH case as a typical example to show how we obtain the peaked solitons.
Wednesday, February 4, at 10AM in DM 409A
Meshfree Engineering Analysis With Distances
I. Tsukanov
igor.tsukanov@fiu.edu
I will present a meshfree method of engineering analysis which makes it possible to satisfy all prescribed boundary conditions exactly and to incorporate all a priori known information (singularities, experimental data, etc.) into a solution. The ability to satisfy boundary conditions exactly without using meshes that conform to geometric models as well as a high level of automation of the solution procedure make meshfree method with distances especially attractive for applications that are difficult for traditional engineering analysis methods. Our method represents geometric information by approximate distance functions that can be automatically constructed from most geometric representations including sampled data and biomedical images.
Once approximate distance fields are known, solutions to boundary value problems are represented via generalized Taylor series in terms of powers of the distance field. All boundary conditions are interpolated transfinitely via inverse weighting distance method, and the remainder term may be chosen to approximate differential or integral constraints – usually on a non-conforming grid of suitable shape functions, such as B-splines. Furthermore, the approximate distance fields are usually parameterized, and changes in the parameters are reflected not only in the distance fields but also in the resulting solutions to the boundary value problems. This makes our approach highly suitable for modeling and solving problems in time-varying geometric domains and for shape optimization.
I will overview the basic theoretical foundations of the meshfree method with distance fields, its computational infrastructure and steps in a typical solution procedure as well as demonstrate a working computer system for meshfree analysis. I will discuss the ongoing research activity and future directions towards further development of our meshfree computational technology.
Tuesday January 20, 330-430PM in DM 409A
Title: A multi-resolution method for climate system modeling:
Application of spherical centroidal Voronoi tessellationsSpeaker: Max Gunzburger
Departments of Scientific Computing and Mathematics
Florida State UniversityAbstract: During the next decade and beyond, climate system models will
be challenged to resolve scales and processes that are far beyond
their current scope. Each climate system component has its
prototypical example of an unresolved process that may strongly
influence the global climate system, ranging from eddy activity within
ocean models, to ice streams within ice sheet models, to surface
hydrological processes within land system models, to cloud processes
within atmosphere models. These new demands will almost certainly
result in the develop of multi-resolution schemes that are able, at
least regional, to faithfully simulate these fine-scale processes.
Spherical Centroidal Voronoi Tessellations (SCVTs) offer one potential
path toward the development of robust, multi-resolution climate system
component models. SCVTs allow for the generation of high quality
Voronoi diagrams and Delaunay triangulations through the use of an
intuitive, user-defined density function. In each of the examples
provided, this method results in high-quality meshes where the quality
measures are guaranteed to improve as the number of nodes is increased.
Real-world examples are developed for the Greenland ice sheet and the
North Atlantic ocean. Idealized examples are developed for ocean-ice
shelf interaction and for regional atmospheric modeling. In addition to
defining, developing and exhibiting SCVTs, we pair this mesh generation
technique with a previously developed finite-volume method. Our
numerical example is based on the nonlinear shallow-water equations
spanning the entire surface of the sphere. This example is used to
elucidate both the potential benefits of this multi-resolution method
and the challenges ahead. (This is joint work with Lili Ju of the
University of South Carolina and Todd Ringler of the Los Alamos
National Laboratory.)Thursday Jan 15, 3:30pm in DM 409A
We will start our department seminar this Thursday at
3:30pm in DM 409A. Baoqin will be our first speaker.Title: Study on L-functions
Abstract: L-functions, with the Riemann-zeta function as a prototype, are important objects in number theory. I will discuss some of my recent work on this subject and the proof of a conjecture on unicity of the Rimann-zeta funtion.2008
Thurs, 11 Dec 2008
Title: Riesz bases of exponentials and their applications
Speaker: Sergei Avdonin, University of Alaska Fairbanks
Abstract: We present some old and new results concerning properties of exponential
families $\{e^{i\lambda_n t}\}$ in $L2(0,T)$ and vector exponential
families $\{a_n e^{i\lambda_n t}\}$ in $L2(0,T;H).$ Several applications
to control theory and signal processing will also be discussed.
Tues, 9 Dec 2008
Mon, 21 Apr 2008
On Monday we will be holding two talks, both by Phil Kutzko of
University of Iowa. He is running a successful special program for
minority graduate students there, and one of his talks will be on
this. He is being brought down as a consultant for our PhD program
for this reason.In addition, Kutzko is a representation theorist with a good record
(publications in Annals, Duke, Am.J. Math), and he has agreed to give a
colloquium.On Wednesday, Pablo Olivares from University of Toronto will be speaking
at 2PM in DM 409A.
Wed, 12 Mar 2008
Next Wednesday, 10-11AM in DM 409A, Prof. Weining Kang will give our talk. Title and abstract below.
Title: Semimartingale Property of a Class of Reflected Brownian Motions
via an Extended Skorokhod ProblemAbstract: Reflected Brownian motions are a class of multidimensional
diffusion processes that arise as approximate models of queueing
networks. Motivated from a generalized processor sharing model, we
consider a class of reflected Brownian motions defined via an Extended
Skorokhod problem. We show that this class of reflected Brownian motions
are not semimartingales, i.e., they can not be decomposed as sums of
martingales and processes with finite variations on finite time
intervals. On the other hand, They actually belong to another class of
processes, called Dirichlet processes. In the end of the talk I will
discuss some extensions of these two results and some future work.
Fri, 29 Feb 2008 HU
Title: Modeling Shrimp Biomass and Viral Infection for Production of
Biological CountermeasuresAbstract: A hybrid model of shrimp biomass and vaccine production system
was developed for the production of large quantities of biological
countermeasures, where the output of biomass production model for the
healthy shrimp is served as input to the vaccine production model for
shrimp that have been infected with a recombinant viral vector expressing
a foreign antigen. The biomass production model has size as the only
structure variable, and the vaccine production model entails both size and
class age structure. Sensitivity of size-structured population model with
respect to growth and mortality rates is one important factor in
optimizing the entire biomass production system. A rigorous derivation of
the partial differential equations for the sensitivities of the population
density with respect to initial conditions, growth, mortality and
fecundity rates was established via the method of characteristics. A
reassuring aspect of our investigations is that they reveal that the
correct sensitivity equations can be formally obtained by simply
differentiating the population equation of interest with respect to the
interested functions.
Tues, 15 Jan 2008
At Tuesday, 11AM in DM 409A, Prof. Rajamani Narayanan from the Physics
department will give a talk titled
"Gauge Field Topology on a Lattice"
SPRING 2007
Wednesday, January 24, 2007 at 9:30 AM in DM 409A
Speaker: Professor Huseyin Yuce (New York City College of Technology, CUNY)
Title: Perturbation Methods for Biharmonic Equations and Their Applications
Abstract: The biharmonic eigenvalue problem has a general analytical solution in a circular domain given by linear combinations of the Bessel functions.
However, the difficulty in finding solutions arises when the domain is no longer circular. For rectangular domains Navier's double series solution and Levy's single series solution for certain boundary conditions are known.
Biharmonic equations find applications in fluid dynamics, buckling and vibration of plates which has extensive applications in civil, mechanical, aerospace, and material engineering as well as vibration of piezoelectric and acoustic devices.
The lack of analytical solutions for several other domains with various boundary conditions led many researchers to use numerical methods. The Rayleigh-Ritz method, the finite element method, and the Galerkin's method are among such numerical methods. However, in some cases, the numerical methods often encounter the problem of singularity, scaling, and sensitivity to the boundary conditions. Some singularities for annular plates are pointed out in recent work of C.Y. Wang and C.M. Wang. In joint work with C.Y. Wang, we developed a special formulation of perturbation method to improve accuracy and reliability of the fundamental frequency.
The purpose of the present work is to provide approximate analytical formulation of the fundamental frequency for clamped plates with circularly periodic boundaries, especially plates with a core where singularities arise. We develop a boundary perturbation method to extract the fundamental eigenvalue of the biharmonic boundary value problem on circularly periodic domains.
Wednesday, March 14, 2007 at 5:00 PM in RB140
Speaker: Professor Luis Seco (University of Toronto)
Title: Spectral gaps in electricity markets
Abstract: Electricity price modeling continues to be an elusive topic, and is perhaps the hardest mathematical challenge these days amongst price modeling in capital markets. This talk will give some background information on why, and will focus on some models that exist; at the mathematical level, one interesting difficulty that arises is the existence of spectral gaps for a class of non-self-adjoint differential operators.
FALL 2006
Friday, September 29, 2006 at 2:00 PM in DM 409A
Speaker: Professor Nikolaos Tsoukias (Department of Biomedical Engineering , FIU)
Title: Modeling Nitric Oxide and Oxygen BiotransportAbstract: Nitric oxide (NO) plays a key role in a number of physiological functions including neurotransmission, host defense response, platelet aggregation, angiogenesis, apoptosis, as well as in the regulation of vascular tone and blood flow. According to the Nitric Oxide Society "from diabetes to hypertension, cancer to drug addiction, stroke to intestinal motility, memory and learning disorders to septic shock, sunburn to anorexia, male impotence to tuberculosis, there is probably no pathological condition where nitric oxide does not play an important role". The interest about the biomedical role of NO is relatively resent, but it has grown exponentially over he last few years. The significance of this field was highlighted in 1998 when Drs. Furchgott, Murad and Ignarro were awarded the Nobel Prize of Medicine for their discoveries a decade earlier concerning "nitric oxide as a signaling molecule in the cardiovascular system". Despite significant scientific contributions over the last few years, fundamental questions about basic physiological functions of NO remain unanswered, which hinders current therapeutic strategies and the development of new products and treatments that will act on the NO signaling pathway. Mathematical modeling offers a systematic approach for system analysis and can assist in this effort both as a tool for data analysis and for guiding new experimental studies.
Monday, November 13, 2006 at 11:30 AM in GC 273A
Speaker: Professor Lotfi Hermi (University of Arizona)
Title: On Riesz Means of Vibrating Membranes
Abstract: Over the past decade, Laptev, Weidl (and co-authors) have promoted the idea that the route to prove the P\'olya conjecture for the eigenvalues of the fixed membrane problem is to view it in Riesz means terms. In any case, this view has led to many fruitful discoveries and beautiful connections. The P\'olya conjecture is the statement that the Weyl asymptotics for the eigenvalues (which give estimates for the high frequencies of a vibrating membrane in terms of the volume of the underlying domain) is always trapped between the eigenvalues of the fixed and free membrane problems. This conjecture was proved by P\'olya for tiling domains, but is still open in general. The talk will trace some known inequalities and feature some new results for the Riesz means of these frequencies in terms of the fundamental one in the case of the fixed membrane problem.
Friday, December 8, 2006 at 11:00 AM in DM 409A
Speaker: Professor Franz-Viktor Kuhlmann (University of Saskatchewan)
Title: Bad Places, Resolution of Singularities, and the Model Theory of Valued Fields
Abstract: Want to prove local uniformization (a local form of resolution of singularities) or deal with the model theory of valued fields in positive characteristic? Then meet your enemy! There are bad places and valuations, and they are the main obstruction in the above mentioned projects. We show how the defect, a phenomenon only appearing for valuations of positive residue characteristic, affects the structure theory of valued function fields, which in turn is crucial for local
uniformization and model theoretic questions about valued fields. We have been able to produce lots of defects and construct very complicated bad
places on very simple fields, namely rational function fields. But not only in positive characteristic, bad places on rational function fields are interesting. They can give rise to bad orderings. This shows that field arithmetic structure on fields as "simple" as rational function fields can be very complicated.
SPRING 2006
Friday, February 3, 2006 at 2:00 PM in DM 409A
Speaker: Professor David Russell (Virginia Tech)
Title: Harmonic Wavelets
Abstract: T. Morita, following earlier work of D. E. Newland, has shown how to construct a system of harmonic wavelets via
a particular ``re-orthogonalization" of the standard Fourier basis for the space $L^2[-\pi,\pi]$. His wavelets, in real form, are based on two
distinct types of scaling functions. In this talk we consider different, but related, re-orthogonalizations leading to wavelet systems which, in
real form, are based on translations of a single type of scaling function and, in addition, have very attractive properties
from the viewpoint of trigonometric interpolation at $n$ evenly spaced points. The cases $n$ even and $n$ odd lead to distinctly different
scaling functions and related trigonometric interpolation formulae.
Friday, March 10, 2006 at 2:00 PM in DM 409A
Speaker: Professor Vilmos Komornik (Strasbourg, France)
Title: Semi-discrete Ingham Type Inequalities
Abstract: This is a joint work with P. Loreti. One of the general methods in linear control theory is based on harmonic and non-harmonic Fourier series. The key of this approach is the establishment of various suitable adaptations and generalizations of the classical Parseval equality. A new and systematic
approach was begun in our papers in collaboration with C. Baiocchi. Although these works were concentrated on continuous models, in
connection with numerical simulations a natural question is whether these results admit useful discrete versions, too. The purpose of this
paper is to establish discrete versions of various Ingham type theorems by using our approach. They imply the earlier continuous results by a simple limit process.
Friday, March 31, 2006 at 2:00 PM in DM 409A
Speaker: Professor Aron Simis (Universidade Federal de Pernambuco, Brazil)
Title: Algebraic Description and Effective Computation of Certain Structures in Algebraic Geometry
Abstract: We will first swiftly digress on classical constructions of the geometry of projective varieties (correspondences, incidence varieties,
joins, secants, etc). Then we introduce the appropriate algebraic language to deal with these constructions, finally we explain how to effectively
compute the algebraic version.
Friday, March 31, 2006 at 3:00 PM in DM 409A
Speaker: Professor David Blair (Michigan State University)
Title: Conformally flat contact metric manifolds, the bad news and the good news!
Thursday, May 18, 2006 at 11:00 AM in DM 409A
Speaker: Professor Luis Seco (University of Toronto)
Title: Mathematics and Finance: past, present and future
Abstract: With minor exceptions, the relationship between mathematics and finance started in the decade of the seventies with the explosion of the derivative markets. The decade of the eighties signified the birth of the risk management, specially in the market risk area, and credit risk management ruled the decade of the the nineties. A theme has been common to that history: advanced, sophisticated mathematics and professional mathematicians have played a key role in its development. This talk will survey the fundamentals of that relationship, focusing on some key problems and opportunities, both from the mathematical as well as from the business standpoint.
