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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, [http://www.math.wisc.edu/~qinli/ Qin Li] and [http://www.math.wisc.edu/~matz/ Sarah Tumasz].
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 2:25pm to 3:15pm in B211 Van Vleck.
== 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==


== Fall 2011 ==


{| cellpadding="5"
{| cellpadding="5"
Line 14: Line 199:
!align="left" | title
!align="left" | title
|-
|-
|Sept 19
|February 12
|Qin Li
|Jim Brunner
|''AP scheme for multispecies Boltzmann equation''
|"Chemical reaction networks"
|-
|February 19
|Xiaoqian Xu
|"Mixing: A brief introduction from the PDE aspect"
|-
|-
|Sept 26
|March 2
|Sarah Tumasz
|Fan Yang
|''An Introduction to Topological Mixing''
|"Berry phase in quantum mechanics"
|-
|-
|Oct 3
|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
|-
|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 ==
 
{| cellpadding="5"
!align="left" | date
!align="left" | speaker
!align="left" | 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
|Zhennan Zhou
|''Perturbation Theory and Molecular Dynamics''
|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"
|-
|-
|Oct 10
|November 22
|Li Wang
|David Dynerman
|''A class of well balanced scheme for hyperbolic system with source term''
|"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
|-
|-
|Oct 17
|February 1
|E. Alec Johnson
|Bryan Crompton
|''Boundary Integral Positivity Limiters''
|"The surprising math of cities and corporations"
|-
|-
|Oct 24
|February 8
|Bokai Yan
|Peter Mueller
|''An introduction to elliptic flow''
|Mandelbrot's TED talk
|-
|-
|Oct 31
|February 15
|David Seal
|Jim Brunner
|''TBA''
|"Logical Models, Polynomial Dynamical Systems, and Iron Metabolism"
|-
|-
|Nov 7
|February 22
|
|Leland Jefferis
|''No talk this week''
|Video lecture on intro quantum mechanics + The postulates of quantum mechanics + Spin 1/2 systems
|-
|-
|Nov 14
|February 29
|
|Leland Jefferis
|
|Topics in quantum mechanics: Spin 1/2 systems + Uncertainty relations + Quantum harmonic oscillators + ...
|-
|-
|Nov 21
|March 15
|
|Will Mitchell
|
|FEniCS, my favorite finite element software package
|-
|-
|Nov 28
|March 22
|
|
|
|
|-
|-
|Dec 5
|April 5
|
|Bryan Crompton
|
|TBD
|-
|-
|Dec 12
|April 26
|
|Peter Mueller
|
|Stokeslets, flagella, and stresslet swimmers
|}
|}


== Abstracts ==
== Abstracts ==


===Monday, Sept 19: Qin Li===
Please add your abstracts here.
''AP scheme for multispecies Boltzmann equation''
 
It is well-known that the Euler equation and the Navier–Stokes equation are 1st and 2nd order asymptotic limit of the Boltzmann equation when the Knudsen number goes to zero. Numerically the solution to the Boltzmann equation should converge to the Euler limit too. However, when the Knudsen number is small, one has to resolve the mesh to avoid instability, which causes tremendous computational cost. Asymptotic preserving scheme is a type of schemes that only uses coarse mesh but preserves the asymptotic limits of the Boltzmann equation in a discrete setting when Knudsen number vanishes. I'm going to present an AP scheme -- the BGK penalization method to solve the multispecies Boltzmann equation. New difficulties for this multispecies system come from: 1. the accurate definition of BGK term, 2. the different time scaling needed for different species to achieve the equilibrium.
 
===Monday, Sept 26: Sarah Tumasz===
''An Introduction to Topological Mixing''


What does topology have to do with mixing fluids?  I will give an introduction to topological mixing from the bottom up.  The talk will include a description of the basic theory, and demonstration of how to apply the techniques to a specific system.  No prior knowledge of topology is needed!
===Friday, Feb 1: Bryan Cromtpon===
"The surprising math of cities and corporations"


===Monday, Oct 3: Zhennan Zhou===
Abstract: We'll watch Geoffrey West's TED talk and discuss some of the math in his papers.
''Perturbation Theory and Molecular Dynamics''


I would like to give a brief introduction to quantum molecular dynamics  with the method
===Friday, Feb 15: Jim Brunner===
of adiabatic perturbation theory.In the framework of Quantum Mechanics, the dynamics of a
"Logical Models, Polynomial Dynamical Systems, and Iron Metabolism"
molecule is governed by the (time-dependent) Schr\"odinger equation, involving nuclei and
electrons coupled through electromagnetic interactions. In recent years, Born-Oppenheimer
approximation with many applications in mathematics, physics and chemistry, turns out to
be a very successful approximation scheme, which is a prototypical example of adiabatic
decoupling, and plays a fundamental role in the understanding of complex molecular
systems.


===Monday, Oct 10: Li Wang===
Abstract: I will introduce logical models and polynomial dynamical systems in the context of a model of iron metabolism in an epithelial cell.
''A class of well balanced scheme for hyperbolic system with source term''


In many physical problems one encounters source terms that are balanced by internal
===Friday, Feb 22 & Feb 29: Leland Jefferis===
forces, and this kind of problem can be described by a hyperbolic system with source
"Topics in Quantum Mechanics"
term. In comparison with the homogeneous system, a significant difference is that this
system encounters non-constant stationary sloutions. So people want to preserve the steay
state solutions, or some discrete versions at least, with enough accuracy. This is the
so called well balanced scheme. I will give some basic idea of the scheme through a
typical example, the Saint-Venant system for shallow water flows with nonuniform bottom.
This talk is based on the paper [E.Audusse, etc SIAM J. Sci. Comput. 2004].


===Monday, Oct 17: E. Alec Johnson===
Abstract: I will introduce the key ideas of quantum mechanics and expose the fascinating mathematical framework behind the theory.
''Boundary Integral Positivity Limiting''


We consider positivity-preserving discontinuous Galerkin (DG)
===Friday, Mar 15: Will Mitchell===
schemes for hyperbolic PDEs. For simplicity we focus on scalar
"FEniCS, my favorite finite element software"
PDEs with flux functions that may be spatially varying. We assume
that physical solutions maintain positivity of the solution.


The DG method evolves a piecewise polynomial representation.
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.
Specifically, the representation is typically discontinuous at
mesh cell interfaces and when restricted to a mesh cell is a
polynomial. The coefficients of the representation are evolved
using an ODE solver, which for simplicity we take to be the
explicit Euler method.


Positivity limiters maintain positivity of the cell average by
===Friday, Apr 6: Bryan Crompton===
after each time step damping the deviation from the cell average
"Fractional Calculus and the Fractional Diffusion Wave Equation"
just enough so that a cell positivity condition is satisfied.


The question we consider is how the cell positivity condition
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.
ought to be defined. The positivity condition should at least
require positivity at the boundary nodes (where Riemann problems
must be solved) and should at most require positivity everywhere
in the cell (lest order of accuracy be violated).


Testing whether a higher-order polynomial with extremum
===Friday, Apr 26: Peter Mueller===
arbitrarily close to zero is everywhere positive is NP-hard. We
"Stokeslets, flagella, and stresslet swimmers"
therefore seek a less stringent positivity indicator which is
inexpensive to compute.


The time until an Euler step violates positivity of the cell
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.
average is the ratio of the amount of stuff in the cell to the
rate at which it is flowing out of the boundary. This immediately
suggests a simple positivity indicator which we call the boundary
integral positivity indicator. Enforcing positivity of the
boundary integral positivity indicator is computationally no
more expensive than enforcing positivity at a single point
and guarantees the same positivity-preserving time step as if
positivity were enforced everywhere in the mesh cell.


This is joint work with James Rossmanith.
== Archived semesters ==
*[[Applied/GPS/Fall2012|Fall 2012]]
*[[Applied/GPS/Spring2012|Spring 2012]]
*[[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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