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= GPS Applied Mathematics Seminar =
= Graduate Applied Math Seminar (GAMS) =


The GPS (Graduate Participation Seminar) is a weekly seminar by and for graduate students. If you're interested in presenting a topic or your own research, contact the organizers: Sarah Tumasz, Li Wang, and Zhennan Zhou.
The Graduate Applied Math Seminar is one of the main tools for bringing together applied grad students in the department and building the community. You are encouraged to get involved! It is a weekly seminar run by grad students for grad students. If you have any questions, please contact Martin Guerra (mguerra4 (at) wisc.edu) or Varun Gudibanda (gudibanda (at) wisc.edu).


The seminar schedule can be found here. We meet in Van Vleck B223 from 4:00pm to 5:00pm on Tuesdays.


All seminars are on Mondays from 2:25 to 3:15 in B235 Van Vleck.  Speakers should aim for their talk to last no longer than 45 minutes.
== Fall 2024 ==
{| cellpadding="5"
! align="left" | date
! align="left" | speaker
! align="left" | title
|-
|September 10
|Martin Guerra
|"Introduction to diffusion models: theory and applications"
|-
|September 17
|Borong Zhang
|"Solving the Inverse Scattering Problem: Leveraging Symmetries for Diffusion Models"
|-
|September 24
|Carsen Grote
|"On the motion of bubbles in non-uniform flows"
|-
|October 1
|Hanzhang Mao
|"Geometric Dependence of Curvature-Induced Rigidity"
|-
|October 8
|Jingyi Li
|"Arrested development of active matter in anisotropic fluids"
|-
|October 15
|Bella Finkel
|"Activation thresholds and expressiveness of polynomial neural networks"
|-
|October 22
|Varun Gudibanda
|"Differential Equations with Constraints"
|-
|October 29
|Baihe Duan
|"Global convergence of Cubic Regularization Newton"
|-
|November 5
|Haley Kottler
|"An introduction to latent class analysis"
|-
|November 12
|Elijah Schwab
|"Finite Element Solution for Charge Mediation in Dielectric Breakdown Environment"
|-
|November 19
|Marios Andreou
|"Introduction to Conditional Gaussian Dynamical Systems (and their Online Smoothing and Sampling)"
|-
|''November 26''
|''Thanksgiving''
|''No seminar''
|-
|December 3
|Karan Srivastava
|
|}
 
== Spring 2024 ==
{| cellpadding="5"
! align="left" | date
! align="left" | speaker
! align="left" | title
|-
|January 24
|Karan Srivastava
|"Reinforcement Learning for Generating Isosceles Free Subsets of a Lattice"
|-
|January 31
|Martin Guerra
|"Introduction to Multiresolution Analysis and Wavelets"
|-
|February 7
|John Cobb
|"Missing Data and Likelihood Geometry"
|-
|February 14
|Haley Kottler
|"Reinforcement Learning as a Model for Dog Training"
|-
|February 21
|Yewei Xu
|"What's wrong with NeuralODE Autodifferentiations and How to Correct it"
|-
|February 28
|Jiayin Lu
|"Numerical methods for simulating quasi-static elastoplastic materials"
|-
|March 6
|Peiyi Chen
|"Reconstruction of relaxation time by Boltzmann Transport Equation in the ballistic regime"
|-
|March 13
|William Powell
|"Challenges for reinforcement learning in the average reward setting"
|-
|March 20
|Dionel Jaime
|"On Limitations of Polynomials Interpolation"
|-
|''March 27''
|''Spring break''
|''No seminar''
|-
|April 3
|Sanchita Chakraborty
|"An SEIR Model to Study Stimulant-Use Disorder in College-Age Students"
|-
|April 10
|Varun Gudibanda
|"Coherent Structures in Convection"
|-
|April 17
|Baihe Duan
|"A Newton’s method with low rank approximated Hessian"
|-
|April 24
|Shi Chen
|"Optimization over the space of probability measures: a tutorial via convex optimization"
|-
|May 1
|Sophia Wiedmann
|"A brief introduction to topological data analysis and its applications to the study of climate change"
|}
 
== Fall 2023 ==
{| cellpadding="5"
! align="left" | date
! align="left" | speaker
! align="left" | title
|-
|September 12
|Martin Guerra
|"Mean-field analysis and swarm optimization methods"
|-
|September 19
|Mohan Ananth
|"Studying the underlying physics of liquid sheet atomization"
|-
|September 26
|Diego Rojas La Luz
|"Chemical Reaction Networks"
|-
|October 3
|Haley Kottler
|"Causal inference and proxy variables"
|-
|October 10
|Zihong Xu
|"Sea Ice Modeling"
|-
|October 17
|Bindesh Tripathi
|"A Tutorial on Modeling Instability-Driven Turbulence"
|-
|October 24
|Shi Chen
|"Accelerating optimization over the space of probability measures"
|-
|October 31
|Praful Gagrani
|"Chemical reaction networks in economics"
|-
|November 7
|William Powell
|"Regularized minimization by incremental surrogate optimization with dependent data"
|-
|November 14
|Carsen Grote
|"Levitation and dynamics of bodies in supersaturated fluids"
|-
|''November 21''
|''Thanksgiving week''
|''No seminar''
|-
|November 28
|Yukun Yue
|"On convergence analysis of an IEQ-based numerical scheme for hydrodynamical Q-tensor model"
|-
|December 5
|Varun Gudibanda
|"A Brief Introduction to Convection"
|}
 
==Spring 2016==


== Spring 2012 ==


{| cellpadding="5"
{| cellpadding="5"
Line 14: Line 199:
!align="left" | title
!align="left" | title
|-
|-
|Feb 6
|February 12
|Zhan Wang
|Jim Brunner
|''Hydroelastic solitary wave and its application in ice problem''
|"Chemical reaction networks"
|-
|February 19
|Xiaoqian Xu
|"Mixing: A brief introduction from the PDE aspect"
|-
|-
|Feb 13
|March 2
|Sarah Tumasz
|Fan Yang
|''What is Topological Mixing?''
|"Berry phase in quantum mechanics"
|-
|-
|Feb 20
|April 1
|Will Mitchell
|"An exercise in asymptotics for finding stagnation points in a Stokes flow"
|}
 
== Abstracts ==
 
Please add your abstracts here.
 
===Friday, Feb 12: Jim Brunner===
"Chemical reaction networks"
 
Abstract: I will present an introduction to Mass Action Kinetic models of biochemical systems. Chemical reaction network theory draws on both the theory of dynamical systems as well as techniques from algebra, algebraic geometry and graph theory, so hopefully I will be able to convince even the more algebraically minded among us that dynamic models are interesting.
 
===Friday, Feb 19: Xiaoqian Xu===
"Mixing: A brief introduction from the PDE aspect"
 
Abstract: I will discuss several definitions and examples of mixing, and introduce an interesting conjecture about mixing, and also talk about the way how we can use them for other complicated situations like social life of bacteria and reproducing of corals.
 
===Friday, April 1: Will Mitchell===
"An exercise in asymptotics for finding stagnation points in a Stokes flow"
 
Abstract: In this two-part talk, I will describe the Stokes flow about a sphere which is held fixed in a background shear flow.  The flow and associated tractions are known exactly.  We wish to find where the tangential component of the traction vanishes.  This leads to some fourth-order polynomial equations which are hard to solve and provides a segue into the second part of the talk, wherein we attempt to solve them approximately using a small parameter argument.
 
== Spring 2014 ==
 
{| cellpadding="5"
!align="left" | date
!align="left" | speaker
!align="left" | title
|-
|February 3
|Jim Brunner
|"Chemical reaction networks"
|-
|February 17
|Peter Mueller
|"Optimal swimming and evolution"
|-
|March 3
|Zhennan Zhou
|Zhennan Zhou
|''Semi-classical analysis of Schrodinger equation with periodic potential''
|-
|-
|Feb 27
|April 7
|Li Wang
|Will Mitchell
|''A Jin-Xin-Glimm scheme for hyperbolic conservation laws''
|"Pade Approximants: How does your machine compute exp(A), with A a matrix?"
|}
 
== Abstracts ==
 
Please add your abstracts here.
 
===Monday, Feb 3: Jim Brunner===
"Chemical reaction networks"
 
Abstract: Jim will be using Jeremy Gunawardena's notes to introduce the topic: http://www.jeremy-gunawardena.com/papers/crnt.pdf and then transition into talking about what Prof. Craciun is looking at.
 
===Monday, Feb 17: Peter Mueller===
"Optimal swimming and evolution"
 
Abstract: We will be going over Christophe Eloy's paper: "On the best results for undulatory swimming" (https://www.irphe.fr/~eloy/PDF/JFM2013a.pdf).
 
===Monday, Mar 3: Zhennan Zhou===
"Efficient computation of the semi-classical limit of the Schrödinger equation"
 
Abstract: After looking at previous techniques, we will try using the Gaussian Wave Packet Transform on the semi-classical Schrödinger equation.
 
== Fall 2013 ==
 
{| cellpadding="5"
!align="left" | date
!align="left" | speaker
!align="left" | title
|-
|September 20
|Peter Mueller
|"Fluid dynamics crash course"
|-
|-
|Mar 5
|September 27
|
|Peter Mueller
|
|"Solutions to Stokes flow"
|-
|October 25
|Zhennan Zhou
|"Numerical approximation of the Schrodinger equation with the electromagnetic field by the
Hagedorn wave packets"
|-
|November 1
|Zhennan Zhou
|Part 2: "Numerical approximation of the Schrodinger equation with the electromagnetic field by the
Hagedorn wave packets"
|-
|November 8
|Will Mitchell
|"How do we make a mesh?  Two fundamental schemes"
|-
|November 22
|David Dynerman
|"Semi-algebraic geometry of common lines"
|}
 
== Abstracts ==
 
Please add your abstracts here.
 
===Friday, Sept 20: Peter Mueller===
"Fluid dynamics crash course"
 
Abstract: Deriving fundamental solutions to Stokes flow and using complex variable tricks to solve two-dimensional problems.
 
===Friday, Sept 27: Peter Mueller===
"Solutions to Stokes flow"
 
Abstract: We will slowly traverse the steps to exactly solve flow past a cylinder (2D) or sphere (3D).
 
===Friday, Oct 25 and Nov 1: Zhennan Zhou===
"Numerical approximation of the Schrodinger equation with the electromagnetic field by the
Hagedorn wave packets"
 
Abstract: In this paper, we approximate the semi-classical Schrodinger equation in the
presence of electromagnetic field by the Hagedorn wave packets approach. By operator
splitting, the Hamiltonian is divided into the modified part and the residual part. The
modified Hamiltonian, which is the main new idea of this paper, is chosen by the fact
that Hagedorn wave packets are localized both in space and momentum so that a crucial
correction term is added to the truncated Hamiltonian, and is treated by evolving the
parameters associated with the Hagedorn wave packets. The residual part is treated by a
Galerkin approximation. We prove that, with the modified Hamiltonian only, the Hagedorn
wave packets dynamics gives the asymptotic solution with error O(eps^{1/2}), where eps  is the the scaled Planck constant. We also prove that, the Galerkin
approximation for the residual Hamiltonian can reduce the approximation error to O(
eps^{k/2}), where k depends on the number of Hagedorn wave packets added to the dynamics.
This approach is easy to implement, and can be naturally extended to the multidimensional
cases. Unlike the high order Gaussian beam method, in which the non-constant cut-off
function is necessary and some extra error is introduced, the Hagedorn wave packets
approach gives a practical way to improve accuracy even when eps is not very small.
 
===Friday, Nov 8: Will Mitchell===
"How do we make a mesh?  Two fundamental schemes"
 
Abstract: Meshing a bounded 2D or 3D region using triangles or tetrahedra is a fundamental problem in numerical mathematics and an area of active research.  In this talk I'll discuss two now-classical (although only 10-year-old) algorithms which can succeed in addressing the challenges of irregular boundaries and variable densities.  For those wishing to read ahead, see:
 
1)  Persson and Strang, "A simple mesh generator in Matlab," SIAM Review, 2004
 
2)  Du et al, "Constrained centroidal Voronoi tesselations for surfaces," SIAM Journal on Scientific Computing, 2003.
 
===Friday, Nov 22: David Dynerman===
"Semi-algebraic geometry of common lines"
 
Abstract: Cryo-electron microscopy (cryo-EM) is a technique for discovering
the 3D structures of small molecules. To perform this 3D reconstruction a
large number of 2D images taken from unknown microscope positions must be
correctly positioned back in 3D space. Although these microscope positions
are unknown, the common lines of intersection of the image planes can be
detected and used in 3D reconstruction. A major difficulty in this process
is large amounts of noise in the common line data.
 
The set of all noiseless common lines forms a semi-algebraic set (a set
defined by polynomial equalities and inequalities). We define and describe
the geometry of this set, and briefly discuss applications.
 
== Spring 2013 ==
 
{| cellpadding="5"
!align="left" | date
!align="left" | speaker
!align="left" | title
|-
|-
|Mar 12
|February 1
|
|Bryan Crompton
|
|"The surprising math of cities and corporations"
|-
|-
|Mar 19
|February 8
|
|Peter Mueller
|
|Mandelbrot's TED talk
|-
|-
|Mar 26
|February 15
|
|Jim Brunner
|
|"Logical Models, Polynomial Dynamical Systems, and Iron Metabolism"
|-
|-
|Apr 2
|February 22
|
|Leland Jefferis
|
|Video lecture on intro quantum mechanics + The postulates of quantum mechanics + Spin 1/2 systems
|-
|-
|Apr 9
|February 29
|
|Leland Jefferis
|
|Topics in quantum mechanics: Spin 1/2 systems + Uncertainty relations + Quantum harmonic oscillators + ...
|-
|-
|Apr 16
|March 15
|
|Will Mitchell
|
|FEniCS, my favorite finite element software package
|-
|-
|Apr 23
|March 22
|
|
|
|
|-
|-
|Apr 30
|April 5
|
|Bryan Crompton
|
|TBD
|-
|-
|May 7
|April 26
|
|Peter Mueller
|
|Stokeslets, flagella, and stresslet swimmers
|}
|}


== Abstracts ==
== Abstracts ==


Please add your abstracts here.
===Friday, Feb 1: Bryan Cromtpon===
"The surprising math of cities and corporations"
Abstract: We'll watch Geoffrey West's TED talk and discuss some of the math in his papers.
===Friday, Feb 15: Jim Brunner===
"Logical Models, Polynomial Dynamical Systems, and Iron Metabolism"
Abstract: I will introduce logical models and polynomial dynamical systems in the context of a model of iron metabolism in an epithelial cell.
===Friday, Feb 22 & Feb 29: Leland Jefferis===
"Topics in Quantum Mechanics"
Abstract: I will introduce the key ideas of quantum mechanics and expose the fascinating mathematical framework behind the theory.


===Monday, February 6: Zhan Wang===
===Friday, Mar 15: Will Mitchell===
''Hydroelastic solitary wave and its application in ice problem''
"FEniCS, my favorite finite element software"


The study of deformation of a floating ice sheet has applications in polar
Abstract: The finite element method is mathematically elegant but can be thorny to code from scratch.  The free, open-source FEniCS software takes care of the worst implementation details without constraining the freedom of the user to specify methods.  I'll review the finite element method and then give some examples of FEniCS code.
regions where ice cover is used for roads or runways and there is an interesting on the  
safe use of these transport links. We use the full potential model to study the forced
and unforced dynamics of hydroelastic waves near the minimum phase speed in deep water.
This is a joint work with Paul Milewski and J.-M. Vanden-Broeck.


===Monday, February 13: Sarah Tumasz===
===Friday, Apr 6: Bryan Crompton===
''What is Topological Mixing?''
"Fractional Calculus and the Fractional Diffusion Wave Equation"


In this talk, I hope to provide an answer to the question 'What is Topological Mixing?'  This will be a very introductory level talk, and I'll attempt to give intuitive, rather than technical, definitions. I'll discuss the basics of mixing, topology, and braids (as they apply) and then give some examples of applications.
Abstract: I'll talk about the equivalent formulations, the Grundwald-Letnikov and Riemann-Liouville, of fractional calculus. I will give some examples of fractional derivatives (and integrals) and then discuss the fundamental solutions to the fractional diffusion wave equation. Derivations will be done non-rigorously.


===Monday, February 20: Zhennan Zhou===
===Friday, Apr 26: Peter Mueller===
''Semi-classical analysis of Schrodinger equation with periodic potential''
"Stokeslets, flagella, and stresslet swimmers"


abstract
Abstract: I will be discussing time-dependent swimmers involving stokeslets as an approximation to flagella. We will then approximate the far-field by an oscillating stresslet and discuss some questionable results.
In this talk, I plan to (at least try to) convince you that for Schrodinger equations, we
need more analytic insight to build up reliable numerical schemes. I will introduce basic
asymptotic methods for semiclassical limits, and explain why the situation changes
dramatically for highly oscillatory potentials.  


== Archived semesters ==
== Archived semesters ==
*[[Applied/GPS/Fall2012|Fall 2012]]
*[[Applied/GPS/Spring2012|Spring 2012]]
*[[Applied/GPS/Fall2011|Fall 2011]]
*[[Applied/GPS/Fall2011|Fall 2011]]

Latest revision as of 06:01, 14 November 2024

Graduate Applied Math Seminar (GAMS)

The Graduate Applied Math Seminar is one of the main tools for bringing together applied grad students in the department and building the community. You are encouraged to get involved! It is a weekly seminar run by grad students for grad students. If you have any questions, please contact Martin Guerra (mguerra4 (at) wisc.edu) or Varun Gudibanda (gudibanda (at) wisc.edu).

The seminar schedule can be found here. We meet in Van Vleck B223 from 4:00pm to 5:00pm on Tuesdays.

Fall 2024

date speaker title
September 10 Martin Guerra "Introduction to diffusion models: theory and applications"
September 17 Borong Zhang "Solving the Inverse Scattering Problem: Leveraging Symmetries for Diffusion Models"
September 24 Carsen Grote "On the motion of bubbles in non-uniform flows"
October 1 Hanzhang Mao "Geometric Dependence of Curvature-Induced Rigidity"
October 8 Jingyi Li "Arrested development of active matter in anisotropic fluids"
October 15 Bella Finkel "Activation thresholds and expressiveness of polynomial neural networks"
October 22 Varun Gudibanda "Differential Equations with Constraints"
October 29 Baihe Duan "Global convergence of Cubic Regularization Newton"
November 5 Haley Kottler "An introduction to latent class analysis"
November 12 Elijah Schwab "Finite Element Solution for Charge Mediation in Dielectric Breakdown Environment"
November 19 Marios Andreou "Introduction to Conditional Gaussian Dynamical Systems (and their Online Smoothing and Sampling)"
November 26 Thanksgiving No seminar
December 3 Karan Srivastava

Spring 2024

date speaker title
January 24 Karan Srivastava "Reinforcement Learning for Generating Isosceles Free Subsets of a Lattice"
January 31 Martin Guerra "Introduction to Multiresolution Analysis and Wavelets"
February 7 John Cobb "Missing Data and Likelihood Geometry"
February 14 Haley Kottler "Reinforcement Learning as a Model for Dog Training"
February 21 Yewei Xu "What's wrong with NeuralODE Autodifferentiations and How to Correct it"
February 28 Jiayin Lu "Numerical methods for simulating quasi-static elastoplastic materials"
March 6 Peiyi Chen "Reconstruction of relaxation time by Boltzmann Transport Equation in the ballistic regime"
March 13 William Powell "Challenges for reinforcement learning in the average reward setting"
March 20 Dionel Jaime "On Limitations of Polynomials Interpolation"
March 27 Spring break No seminar
April 3 Sanchita Chakraborty "An SEIR Model to Study Stimulant-Use Disorder in College-Age Students"
April 10 Varun Gudibanda "Coherent Structures in Convection"
April 17 Baihe Duan "A Newton’s method with low rank approximated Hessian"
April 24 Shi Chen "Optimization over the space of probability measures: a tutorial via convex optimization"
May 1 Sophia Wiedmann "A brief introduction to topological data analysis and its applications to the study of climate change"

Fall 2023

date speaker title
September 12 Martin Guerra "Mean-field analysis and swarm optimization methods"
September 19 Mohan Ananth "Studying the underlying physics of liquid sheet atomization"
September 26 Diego Rojas La Luz "Chemical Reaction Networks"
October 3 Haley Kottler "Causal inference and proxy variables"
October 10 Zihong Xu "Sea Ice Modeling"
October 17 Bindesh Tripathi "A Tutorial on Modeling Instability-Driven Turbulence"
October 24 Shi Chen "Accelerating optimization over the space of probability measures"
October 31 Praful Gagrani "Chemical reaction networks in economics"
November 7 William Powell "Regularized minimization by incremental surrogate optimization with dependent data"
November 14 Carsen Grote "Levitation and dynamics of bodies in supersaturated fluids"
November 21 Thanksgiving week No seminar
November 28 Yukun Yue "On convergence analysis of an IEQ-based numerical scheme for hydrodynamical Q-tensor model"
December 5 Varun Gudibanda "A Brief Introduction to Convection"

Spring 2016

date speaker title
February 12 Jim Brunner "Chemical reaction networks"
February 19 Xiaoqian Xu "Mixing: A brief introduction from the PDE aspect"
March 2 Fan Yang "Berry phase in quantum mechanics"
April 1 Will Mitchell "An exercise in asymptotics for finding stagnation points in a Stokes flow"

Abstracts

Please add your abstracts here.

Friday, Feb 12: Jim Brunner

"Chemical reaction networks"

Abstract: I will present an introduction to Mass Action Kinetic models of biochemical systems. Chemical reaction network theory draws on both the theory of dynamical systems as well as techniques from algebra, algebraic geometry and graph theory, so hopefully I will be able to convince even the more algebraically minded among us that dynamic models are interesting.

Friday, Feb 19: Xiaoqian Xu

"Mixing: A brief introduction from the PDE aspect"

Abstract: I will discuss several definitions and examples of mixing, and introduce an interesting conjecture about mixing, and also talk about the way how we can use them for other complicated situations like social life of bacteria and reproducing of corals.

Friday, April 1: Will Mitchell

"An exercise in asymptotics for finding stagnation points in a Stokes flow"

Abstract: In this two-part talk, I will describe the Stokes flow about a sphere which is held fixed in a background shear flow. The flow and associated tractions are known exactly. We wish to find where the tangential component of the traction vanishes. This leads to some fourth-order polynomial equations which are hard to solve and provides a segue into the second part of the talk, wherein we attempt to solve them approximately using a small parameter argument.

Spring 2014

date speaker title
February 3 Jim Brunner "Chemical reaction networks"
February 17 Peter Mueller "Optimal swimming and evolution"
March 3 Zhennan Zhou
April 7 Will Mitchell "Pade Approximants: How does your machine compute exp(A), with A a matrix?"

Abstracts

Please add your abstracts here.

Monday, Feb 3: Jim Brunner

"Chemical reaction networks"

Abstract: Jim will be using Jeremy Gunawardena's notes to introduce the topic: http://www.jeremy-gunawardena.com/papers/crnt.pdf and then transition into talking about what Prof. Craciun is looking at.

Monday, Feb 17: Peter Mueller

"Optimal swimming and evolution"

Abstract: We will be going over Christophe Eloy's paper: "On the best results for undulatory swimming" (https://www.irphe.fr/~eloy/PDF/JFM2013a.pdf).

Monday, Mar 3: Zhennan Zhou

"Efficient computation of the semi-classical limit of the Schrödinger equation"

Abstract: After looking at previous techniques, we will try using the Gaussian Wave Packet Transform on the semi-classical Schrödinger equation.

Fall 2013

date speaker title
September 20 Peter Mueller "Fluid dynamics crash course"
September 27 Peter Mueller "Solutions to Stokes flow"
October 25 Zhennan Zhou "Numerical approximation of the Schrodinger equation with the electromagnetic field by the

Hagedorn wave packets"

November 1 Zhennan Zhou Part 2: "Numerical approximation of the Schrodinger equation with the electromagnetic field by the

Hagedorn wave packets"

November 8 Will Mitchell "How do we make a mesh? Two fundamental schemes"
November 22 David Dynerman "Semi-algebraic geometry of common lines"

Abstracts

Please add your abstracts here.

Friday, Sept 20: Peter Mueller

"Fluid dynamics crash course"

Abstract: Deriving fundamental solutions to Stokes flow and using complex variable tricks to solve two-dimensional problems.

Friday, Sept 27: Peter Mueller

"Solutions to Stokes flow"

Abstract: We will slowly traverse the steps to exactly solve flow past a cylinder (2D) or sphere (3D).

Friday, Oct 25 and Nov 1: Zhennan Zhou

"Numerical approximation of the Schrodinger equation with the electromagnetic field by the Hagedorn wave packets"

Abstract: In this paper, we approximate the semi-classical Schrodinger equation in the presence of electromagnetic field by the Hagedorn wave packets approach. By operator splitting, the Hamiltonian is divided into the modified part and the residual part. The modified Hamiltonian, which is the main new idea of this paper, is chosen by the fact that Hagedorn wave packets are localized both in space and momentum so that a crucial correction term is added to the truncated Hamiltonian, and is treated by evolving the parameters associated with the Hagedorn wave packets. The residual part is treated by a Galerkin approximation. We prove that, with the modified Hamiltonian only, the Hagedorn wave packets dynamics gives the asymptotic solution with error O(eps^{1/2}), where eps is the the scaled Planck constant. We also prove that, the Galerkin approximation for the residual Hamiltonian can reduce the approximation error to O( eps^{k/2}), where k depends on the number of Hagedorn wave packets added to the dynamics. This approach is easy to implement, and can be naturally extended to the multidimensional cases. Unlike the high order Gaussian beam method, in which the non-constant cut-off function is necessary and some extra error is introduced, the Hagedorn wave packets approach gives a practical way to improve accuracy even when eps is not very small.

Friday, Nov 8: Will Mitchell

"How do we make a mesh? Two fundamental schemes"

Abstract: Meshing a bounded 2D or 3D region using triangles or tetrahedra is a fundamental problem in numerical mathematics and an area of active research. In this talk I'll discuss two now-classical (although only 10-year-old) algorithms which can succeed in addressing the challenges of irregular boundaries and variable densities. For those wishing to read ahead, see:

1) Persson and Strang, "A simple mesh generator in Matlab," SIAM Review, 2004

2) Du et al, "Constrained centroidal Voronoi tesselations for surfaces," SIAM Journal on Scientific Computing, 2003.

Friday, Nov 22: David Dynerman

"Semi-algebraic geometry of common lines"

Abstract: Cryo-electron microscopy (cryo-EM) is a technique for discovering the 3D structures of small molecules. To perform this 3D reconstruction a large number of 2D images taken from unknown microscope positions must be correctly positioned back in 3D space. Although these microscope positions are unknown, the common lines of intersection of the image planes can be detected and used in 3D reconstruction. A major difficulty in this process is large amounts of noise in the common line data.

The set of all noiseless common lines forms a semi-algebraic set (a set defined by polynomial equalities and inequalities). We define and describe the geometry of this set, and briefly discuss applications.

Spring 2013

date speaker title
February 1 Bryan Crompton "The surprising math of cities and corporations"
February 8 Peter Mueller Mandelbrot's TED talk
February 15 Jim Brunner "Logical Models, Polynomial Dynamical Systems, and Iron Metabolism"
February 22 Leland Jefferis Video lecture on intro quantum mechanics + The postulates of quantum mechanics + Spin 1/2 systems
February 29 Leland Jefferis Topics in quantum mechanics: Spin 1/2 systems + Uncertainty relations + Quantum harmonic oscillators + ...
March 15 Will Mitchell FEniCS, my favorite finite element software package
March 22
April 5 Bryan Crompton TBD
April 26 Peter Mueller Stokeslets, flagella, and stresslet swimmers

Abstracts

Please add your abstracts here.

Friday, Feb 1: Bryan Cromtpon

"The surprising math of cities and corporations"

Abstract: We'll watch Geoffrey West's TED talk and discuss some of the math in his papers.

Friday, Feb 15: Jim Brunner

"Logical Models, Polynomial Dynamical Systems, and Iron Metabolism"

Abstract: I will introduce logical models and polynomial dynamical systems in the context of a model of iron metabolism in an epithelial cell.

Friday, Feb 22 & Feb 29: Leland Jefferis

"Topics in Quantum Mechanics"

Abstract: I will introduce the key ideas of quantum mechanics and expose the fascinating mathematical framework behind the theory.

Friday, Mar 15: Will Mitchell

"FEniCS, my favorite finite element software"

Abstract: The finite element method is mathematically elegant but can be thorny to code from scratch. The free, open-source FEniCS software takes care of the worst implementation details without constraining the freedom of the user to specify methods. I'll review the finite element method and then give some examples of FEniCS code.

Friday, Apr 6: Bryan Crompton

"Fractional Calculus and the Fractional Diffusion Wave Equation"

Abstract: I'll talk about the equivalent formulations, the Grundwald-Letnikov and Riemann-Liouville, of fractional calculus. I will give some examples of fractional derivatives (and integrals) and then discuss the fundamental solutions to the fractional diffusion wave equation. Derivations will be done non-rigorously.

Friday, Apr 26: Peter Mueller

"Stokeslets, flagella, and stresslet swimmers"

Abstract: I will be discussing time-dependent swimmers involving stokeslets as an approximation to flagella. We will then approximate the far-field by an oscillating stresslet and discuss some questionable results.

Archived semesters

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