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Abstracts of Colloquim Talks

Cameron Gordon, Utexas,
Abstract: The fundamental group is essentially a complete invariant of
a 3-manifold. We will discuss how the purely algebraic property of this
group being left-orderable is related to the topology of the manifold, and
present evidence for the conjecture that it is equivalent to a property
that is ultimately analytic in nature.

This is joint work with Steve Boyer and Liam Watson.
Jeff Borggaard,
 Reduced-Order Models of Fluids for Fast Simulation.
Abstract:
Reduced-order models based on the proper orthogonal decomposition (POD)
of Navier-Stokes simulations and Galerkin projection are commonly used
as surrogates in design, control, and analysis of fluid systems.  However,
this approach has a number of limitations.  One is that the accuracy of
the reduced-basis may not be adequate when the model is applied at
parameter values different from those used to generate the original
simulation data.  A second is that even mild turbulence can slow the
decay of singular values in the POD and that to achieve a reasonable
model size, a dramatic truncation in the basis is required.  However, the
influence of the discarded modes on the remaining modes must be treated
with additional modeling.

In this talk, we discuss procedures to overcome these limitations.
Computing derivatives of the POD basis with respect to parameters, such
as the Reynolds number, allows us to expand the range of flows that can
be modeled.  This includes at least an order of magnitude in relative
accuracy for nearby parameter variations as well as more effective
prediction of dynamical system properties such as the Strouhal number.
Additionally, we propose models motivated by modern large eddy simulation (LES)
closure models (variational multiscale and dynamic subgridscale models)
along with an efficient two-level implementation to better represent
mildly turbulent 3D flow past a cylinder at Reynolds number 1000.

Finally, we will report on our progress in developing reduced-order
models for the airflow in buildings.  These models may lead to
incorporating airflow considerations earlier in the building control
and design cycle.

This is joint work with Sunil Ahuja, Imran Akhtar, Gene Cliff, Serkan
Gugercin, Alexander Hay, Traian Iliescu, Christopher Jarvis, Zhu Wang,
and Lizette Zietsman.
------------------------------------------------------------------------
Abstract: Friday, 3:15 October 4Long Chen, University of California, Irvine 

Optimal Delanuay Triangulations. 

Abstract.mal Delanuay Triangulations (ODT) are optimal meshes minimizing function in Lp norm.  In this talk we shell present several applications of ODT.

1. Mesh smoothing. Meshes with high quality are obtained by minimizing the interpolation error in a weighted L1 norm.

2. Anisotropic mesh adaptation. Optimal anisotropic interpolation error estimate is obtained by choosing anisotropic functions. The error estimate is used to produce anisotropic mesh adaptation for convection-dominated problems. 

3. Sphere covering and convex polytope approximation. Asymptotic exact and sharp estimate of some constant in these two problems are obtained from ODTs.

4. Quantization. Optimization algorithms based on ODTs are applied to quantizationto speed up the processing. 

When considering a career in Statistics, the hot andexciting fields seem to involve biology or medicalapplications. In recent years, there has been substantialgrowth in the number of statisticians in these

areas. The industrial statistician seems to be something that manypeople regard as yesterdays news, working only on quality tools,such as control charts. With much of U.S. manufacturing movingoverseas and a more global economy, many of the well-known,large industrial statistics groups have been reduced or

eliminated. There have been panel discussions and articleson the future of the industrial statistician (Technometrics,2008). Is there still a place for industrial statisticians in theU.S., and is it a career worth pursuing?

 

 


This presentation will explore some aspects of the use of Statistics in industry, specifically semiconductor 

manufacturing. 

It will provide a brief introduction of semiconductors, the perceptionsand reality of working aan industrial statistician, and illustrate somereal problems encountered when working in the semiconductor industry.

 
 
Friday, 3:15 PM
February 01, 2013
Bernd Sturmfels, UC Berkeley, http://math.berkeley.edu/~bernd/
Title:  Maximum Likelihood for Matrices with Rank Constraints

 Video Link  

 
Abstract: Maximum likelihood estimation is a fundamental computational task in statistics. We discuss this problem for manifolds of low rank matrices.
These represent mixtures of independent distributions of two discrete random variables. This non-convex optimization leads to some beautiful geometry, topology, and combinatorics. We explain how numerical algebraic geometry is used to find the global maximum of the likelihood function.

 Video Link  

Friday, 3:15 PM
February 08 2013
Kristyn Maschhoff, Cray Inc.

Title: Designing a Supercomputer

 Video Link  

 
 

> Abstract:

> I will present  my experience working in Cray, what it is like to be on an engineering team designing a supercomputer, and the types of skills we look for at Cray for both internships and recent graduates looking to work in industry.  Most recently I worked as Technical Project Lead on the recently completed Defense Advanced Research Project Agency's (DARPA) High Productivity Computing Systems program where I was responsible for the performance analysis component (Benchmarking/Applications). This program helped fund our development of the next-generation Cray supercomputer code-named "Cascade".

> Time permitting, I will walk through some of the innovations of this new architecture.

 Friday 3:15 PM,
  February 22.
Neuberger Hall, rm. 454
 

Ginger McKee,

Mathematica in Education and Research
3:15-4:15, Including Q & A

 
This is a free one hour talk that illustrates capabilities in Mathematica 9 that are
directly applicable for use in teaching and research on campus. Topics
of this technical talk include:

* 2D and 3D visualization
* Free form input & predictive interface capabilities
* Dynamic interactivity
* On-demand scientific data
* Example-driven course materials
* Wolfram Alpha integration
* Symbolic interface construction
* Practical and theoretical applications

Prior knowledge of Mathematica is not required.


 

Friday, 3:15 PM
March 01 2013
Arash Yavari, Georgia Institute of Technology
Title:

Riemann-Cartan Geometry and the Nonlinear Mechanics of

Distributed Dislocations    

 

 

 
 Abstract: In  this  seminar  we  will   show  that  the  nonlinear mechanics of  solids  with distributed  dislocations  canbe formulated  as a nonlinear  elasticity  problem provided that the material manifold   where the body is stress-free− is chosen appropriately.  Choosing a Weitzenböckmanifold  (a manifold  with  a flat  and metric-compatible  affine  connection  that  has  torsion)   with   torsion  tensor identified with the given dislocation density tensorthe body would be stress-free in the material manifold byconstruction. For classical nonlinear elastic solids in order to  calculate stresses one needs to  know  the  changesof  the  relative distances, i.e. a metric  in  the  material manifold  is  needed. For  distributed dislocations   this  metric   is  the  metric   compatible   with   the Weitzenböck connection. We will  present exact solutionsfor the residual stress field of several distributed dislocation problems in incompressible nonlinear elasticsolids using Cartan's method of moving frames. We will also discuss zero-stress dislocation distributions innonlinear dislocation mechanics.
 
 
Friday, 3:15 PM
March 08, 2013
Irina Kogan, North Carolina State University.
Object-Image Correspondence for Algebraic Curves Under Projections
 

 Video Link  

 
 Abstract:

I will present a novel algorithm for deciding whether a given planar curve is an image of a given spatial curve, obtained by a central or a parallel projection with unknown parameters. The motivation comes from the problem of establishing a correspondence between an object and an image, taken by a camera with unknown position and parameters.  A straightforward approach to this problem consists of setting up a system of conditions on the projection parameters and then checking whether or not this system has a solution. The computational advantage of the algorithm presented here, in comparison to algorithms based on the straightforward approach, lies in a significant reduction of a number of real parameters that need to be eliminated in order to establish existence or non-existence of a projection that maps a given spatial curve to a given planar curve. Our algorithm is based on projection criteria that reduce the projection problem to a certain modification of the equivalence problem of planar curves under affine and projective transformations.  To solve the latter  problem we make an algebraic adaptation of signature construction that has been used to solve the equivalence problems for smooth curves. We introduce a notion of a classifying  set of rational differential invariants and produce explicit formulas for such invariants for  the actions of the projective and the affine groups on the plane. This is a joint work with Joseph Burdis and Hoon Hong.

 

 

 
 
 
 
Friday, 3:15 PM
April 05, 2013
Fadil Santosa, IMA, University of Minnesota
"The mathematics behind bar codes"
Video Link

 Video lhttp://echo360.pdx.edu/ess/echo/presentation/eeac6b9c-2fa7-41df-bf00-811...   

 Abstract:

Bar codes are ubiquitous -- they are used to identify products in stores, parts in a warehouse, and books in a library, etc.  In this talk, the speaker will describe how information is encoded in a bar code and how it is read by a scanner.  The presentation will go over how the decoding process, from scanner signal to coded information, can be formulated as an inverse problem.  The inverse problem involves finding the "word" hidden in the signal.  What makes this inverse problem, and the approach to solve it, somewhat unusual is that the unknown has a finite number of states.

Short bio:
Fadil Santosa received his PhD in Theoretical and Applied Mechanics from the University of Illinois in 1980.  He held positions at Cornell University and University of Delaware before joining the faculty of the School of Mathematics as Professor in 1995.  He currently serves as the director of the Institute for Mathematics and its Applications.  His research interests are in inverse problems, optimal design, and optics.

Friday, 3:15 PM
May 03, 2013
Maochao Xu, Department of Mathematics, Illinois State University
Optimal Capital Allocation: Mean-Variants Model

 

 
 
Friday, 3:15 PM
May 17, 2013
Location:  URBN rm.204
 Speaker: Louis H. Kauffman, University of Illinois at Chicago
Title: Knot Logic and Topological Quantum Computing with Majorana Fermions
 
 
 Abstract: This talk is an introduction to relationships between quantum
topology and quantum computing. We show how knots are related not just to braiding and quantum operators, but to quantum set theoretical foundations and algebras of fermions.
     We show how the operation of negation in logic, seen as both a value and an operator, can generate the fusion algebra for a Majorana fermion, a particle that is its own anti-particle and interacts with itself either to annihilate itself or to produce itself.
      We call negation in this mode the Mark, as it
operates on itself to change from marked to unmarked states. The Mark
viewed recursively as a simplest discrete dynamical system
generates the fermion algebra, the quaternions and the braid group
representations related to Majorana fermions.
     The talk begins with these fundmentals. They provide a conceptual key to many of the models that appear later. In particular, the Fibonacci model for topological quantum computing is seen to be based on the fusion rules for a Majorana fermion.
    All these models have their roots in unitary representations of the Artin braid group to the quaternions
 
 
 
 
Friday, 3:15 PM-4:15
May 31, 2013
Amanda Jansen, University of Delaware
Engagement in School Mathematics: Listening to Student's Voices. 

 Video link

 
 Abstract:

What do students talk about when they talk about their school mathematics experiences? Students often talk about social aspects of engaging in mathematics in school, because when they have opportunities to learn about mathematics content, they also learn how to bemathematics learners (Boaler, 2000). Students learn about what it means to participate in doing mathematics and who they are (and can be) when learning and doing mathematics. In my research on social aspects of mathematics classrooms, I have examined students’ voices about participating in whole class discussions (Jansen, 2006, 2008, & 2009), small group discussions (Jansen, 2012), transitioning from middle school to high school mathematics (Star, Smith, & Jansen, 2008; Jansen, Herbel-Eisenmann, & Smith, 2012), and caring teacher-student relationships in mathematics classrooms (Jansen & Bartell, in press). During this talk, I will share highlights of findings from this body of work, including how students’ engagement is shaped by their interpretations of the purposes of what they are asked to do in mathematics classrooms. Listening to students’ voices provides insights into how to provide opportunities for more students to engage in and benefit from school mathematics instruction.

 
 

Friday, 3:15 October 4Long Chen, University of California, Irvine 

Optimal Delanuay Triangulations. 

Abstract.mal Delanuay Triangulations (ODT) are optimal meshes minimizing function in Lp norm.  In this talk we shell present several applications of ODT.

1. Mesh smoothing. Meshes with high quality are obtained by minimizing the interpolation error in a weighted L1 norm.

2. Anisotropic mesh adaptation. Optimal anisotropic interpolation error estimate is obtained by choosing anisotropic functions. The error estimate is used to produce anisotropic mesh adaptation for convection-dominated problems. 

3. Sphere covering and convex polytope approximation. Asymptotic exact and sharp estimate of some constant in these two problems are obtained from ODTs.

4. Quantization. Optimization algorithms based on ODTs are applied to quantizationto speed up the processing. 

Friday, 3:15PM
October 18 
 Jeff Borggaard, Virginia Tech.
TBA
 October 25
Gordon Cameron, UTexas.

 

Friday, 3:15PM-4:15PM

November 15

Peter Monk,  University of Delaware

TBA

 January 24  Shari Moskow, Drexel University