SIAM Student Chapter Seminar: Difference between revisions

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*'''When:''' Mondays at 4 PM
*'''When:''' Fridays at 1 PM unless noted otherwise
*'''Where:''' See list of talks below
*'''Where:''' 9th floor lounge (we will also broadcast the virtual talks on the 9th floor lounge with refreshments)
*'''Organizers:''' [https://sites.google.com/wisc.edu/evan-sorensen Evan Sorensen]
*'''Organizers:''' Yahui Qu, Peiyi Chen, Shi Chen and Zaidan Wu
*'''Faculty advisers:''' [http://www.math.wisc.edu/~jeanluc/ Jean-Luc Thiffeault], [http://pages.cs.wisc.edu/~swright/ Steve Wright]  
*'''Faculty advisers:''' [http://www.math.wisc.edu/~jeanluc/ Jean-Luc Thiffeault], [http://pages.cs.wisc.edu/~swright/ Steve Wright]  
*'''To join the SIAM Chapter mailing list:''' email [mailto:siam-chapter+join@g-groups.wisc.edu siam-chapter+join@g-groups.wisc.edu].
*'''To join the SIAM Chapter mailing list:''' email [mailto:siam-chapter+join@g-groups.wisc.edu siam-chapter+join@g-groups.wisc.edu].
*'''Zoom link:''' https://uwmadison.zoom.us/j/97976615799?pwd=U2xFSERIcnR6M1Y1czRmTjQ1bTFJQT09
*'''Passcode:  281031'''


<br>
== Spring 2024 ==


==Spring 2022==
{| class="wikitable"
 
|+
{| cellpadding="8"
!Date
!align="left" | date and time
!Location
!align="left" | location
!Speaker
!align="left" | speaker
!Title
!align="left" | title
|-
|-
| Feb 7, 4 PM
|2/2
| LOCATION
|VV911
| [HOMEPAGE | Person ] Department
|Thomas Chandler (UW-Madison)
|''[[#DATE, PERSON |TITLE]]''
|Fluid–body interactions in anisotropic fluids
|-
|-
|3/8
|Ingraham 214
|Danyun He (Harvard)
|Energy-positive soaring using transient turbulent fluctuations
|-
|-
|}
|3/15
== Fall 2021  ==
|VV911&Zoom
 
|Xiaoyu Dong (UMich)
{| cellpadding="8"
|Approximately Hadamard matrices and Riesz bases in frames
!align="left" | date and time
!align="left" | location
!align="left" | speaker
!align="left" | title
|-
| Sept 20, 4 PM
| Ingraham 214
| [https://sites.google.com/view/julialindberg/home/ Julia Lindberg] (Electrical and Computer Engineering)
|''[[#Sept 20, Julia Lindberg |Polynomial system solving in applications]]''
|-
|-
| Sept 27, 4 PM,
| Zoom (refreshments and conference call in 307)
| Wil Cocke (Developer for [https://www.arcyber.army.mil/ ARCYBER])
| ''[[#Sept 27, Wil Cocke |Job talk-Software Development/Data Science]]''
|
|-
|-
| Oct 4, '''2:45 PM'''
| B119 Van Vleck
| [https://sites.google.com/wisc.edu/nair-anjali/home/ Anjali Nair] (Math)
| ''[[#Oct 4, Anjali Nair|Reconstruction of Reflection Coefficients Using the Phonon Transport Equation]]''
|
|-
|-
| Oct 18, 4 PM
| 6104 Social Sciences
| [https://jasonltorchinsky.github.io/ Jason Tochinsky] (Math)
| ''[[#Oct 18, Jason Torchinsky|Improving the Vertical Remapping Algorithm in the Department of Energy’s Energy Exascale Earth Systems Model]]''
|
|-
|-
| Oct 25, 4 PM,
| Zoom (refreshments and conference call in 9th floor lounge)
| [https://www.linkedin.com/in/patricktbardsley/ Patrick Bardsley] (Senior Machine Learning Engineer at [https://www.cirrus.com/ Cirrus Logic])
| ''[[#Oct 25, Patrick Bardsley|Job Talk-Machine Learning]]''
|
|-
|-
|-
| Nov 8, 4 PM,
|3/22
| Zoom (refreshments and conference call in 9th floor lounge)
|VV911&Zoom
| [https://www.linkedin.com/in/libanmohamed496/ Liban Mohamed] (Machine Learning Engineer at [https://www.mitre.org/ MITRE])
|Mengjin Dong (UPenn)
| ''[[#Nov 8, Liban Mohamed|Job Talk-Machine Learning]]''
|Advancing Alzheimer's Disease Research: Insights and Innovations in MRI-Based Progression Tracking
|
|-
|-
|4/5
|VV911
|Sixu Li (UW-Madison)
|TBD
|-
|-
| Nov 15, 4 PM,
|4/12
| Zoom (refreshments and conference call in 9th floor lounge)
|VV911&Zoom
| [https://www.linkedin.com/in/kurt-ehlert-320b8397/ Kurt Ehlert] (Trading Strategy Developer at [https://auros.global/about/ Auros])
|Anjali Nair (UChicago)
| ''[[#Nov 15, Kurt Ehlert|Job Talk-Cryptocurrency Trading]]''
|TBD
|
|-
|-
|4/19
|VV911
|Jingyi Li (UW-Madison)
|TBD
|-
|-
| Nov 29, 4 PM
|5/3
| 9th floor lounge
| [https://people.math.wisc.edu/~boakley/ Bryan Oakley] (Math)
| ''[[#Nov 29, Bryan Oakley|Optimal Spatially Dependent Diffusion]]''
|
|
|-
|Bella Finkel (UW-Madison)
|-
|TBD
| Dec 6, 4 PM
| 9th floor lounge
| [https://sites.google.com/view/hongxuchen/ Hongxu Chen] (Math)
| ''[[#Dec 6, Hongxu Chen|Boltzmann equation with Cercignani-Lampis boundary]]''
|}
|}


== Abstracts ==
==Abstracts==
 
'''February 2, Thomas Chandler (UW-Madison):''' Fluid anisotropy, or direction-dependent response to deformation, can be observed in biofluids like mucus or, at a larger scale, self-aligning swarms of active bacteria. A model fluid used to investigate such environments is a nematic liquid crystal. In this talk, we will use complex variables to analytically solve for the interaction between bodies immersed in liquid crystalline environments. This approach allows for the solution of a wide range of problems, opening the door to studying the role of body geometry, liquid crystal anchoring conditions, and deformability. Shape-dependent forces between bodies, surface tractions, and analogues to classical results in fluid dynamics will also be discussed.
=== Sept 20, Julia Lindberg===
Polynomial systems arise naturally in many applications in engineering and the sciences. This talk will outline classes of homotopy continuation algorithms used to solve them. I will then describe ways in which structures such as irreducibility, symmetry and sparsity can be used to improve computational speed. The efficacy of these algorithms will be demonstrated on systems in power systems engineering, statistics and optimization
 
 
=== Sept 27, Wil Cocke ===
I mostly work as a software developer with an emphasis on data science projects dealing with various Command specific projects. The data science life-cycle is fairly consistent across industries: collect, clean, explore, model, interpret, and repeat with a goal of providing insight to the organization. During my talk, I will share some lessons learned for mathematicians interested in transitioning to software development/ data science.
 
 
=== Oct 4, Anjali Nair ===
The phonon transport equation is used to model heat conduction in solid materials. I will talk about how we use it to solve an inverse problem to reconstruct the thermal reflection coefficient at an interface. This takes the framework of a PDE constrained optimization problem, and I will also mention the stochastic methods used to solve it.
 
 
=== Oct 18, Jason Torchinsky ===
A vertical Lagrangian coordinate has been used in global climate models for nearly two decades and has several advantages over other discretizations, including reducing the dimensionality of the physical problem. As the Lagrangian surfaces deform over time, it is necessary to accurately and conservatively remap the vertical Lagrangian coordinate back to a fixed Eulerian coordinate. A popular choice of remapping algorithm is the piecewise parabolic method, a modified version of which is used in the atmospheric component of the Department of Energy's Energy Exascale Earth System Model. However, this version of the remapping algorithm creates unwanted noise at the model top and planetary surface for several standard test cases. We explore four alternative modifications to the algorithm and show that the most accurate of these eliminates this noise.
 
 
=== Oct 25, Patrick Bardsley ===
During the course of a PhD, students typically enter a proverbial `coal mine’ to extract new information about one or more problems, and in the process become a domain expert in a small niche of the technical and scientific world. Upon leaving the academy, unless one lands a job in their niche domain, much of their problem- and domain-specific knowledge is no longer essential. However, mathematics is broad and general, arguably the most general of all scientific disciplines. This fact alone is a mathematician’s greatest asset and ‘leg-up’ when entering the industrial workforce. In this talk, I will discuss some details of my work, both inside and outside of the academy, with the goal of highlighting the skills and concepts that have been the most general and transferable for me. For example, my academic work on hyperbolic inverse problems helped me learn signal processing concepts I now use daily, while my studies on polycrystalline grain growth pushed me to learn thermodynamics, which translated well to the information theory concepts I now utilize. I will also give you some idea of my current day-to-day responsibilities, and close with my thoughts and suggestions on job searches.
 
 
=== Nov 8, Liban Mohamed ===
I work as a researcher at MITRE, a company that manages R&D contracts (FFRDCs) with federal agencies. I am nominally a machine learning engineer, but my department supports a diverse array of initiatives with the IRS. In this talk I'll give an overview of the FFRDC space, give a sketch of what I work on and how I spend my time, and share my thoughts about navigating the transition from academia to industry.
 
 
=== Nov 15, Kurt Ehlert ===
After graduating from the UW, I ventured into the world of trading. My first job was at Virtu, a high-frequency market-maker, and currently I work at Auros, which is a high-frequency trading firm that focuses on cryptocurrencies. During the talk, I will give an overview of the industry, job market, and interview process from the perspective of a "quant". Then I will describe the day-to-day work and give a high-level description of typical projects.  


'''March 8, Danyun He (Harvard University):''' The ability of birds to soar in the atmosphere is a fascinating scientific problem. It relies on an interplay between the physical processes governing atmospheric flows, and the capacity of birds to process cues from their environment and learn complex navigational strategies. Previous models for soaring have primarily taken advantage of thermals of ascending hot air to gain energy. Yet, it remains unclear whether energy loss due to drag can be overcome by extracting work from transient turbulent fluctuations. In this talk, I will present a recent work that we look at the alternative scenario of a glider navigating in an idealized model of a turbulent fluid where no thermals are present. First, I will show the numerical simulations of gliders navigating in a kinematic model that captures the spatio-temporal correlations of atmospheric turbulence. Energy extraction is enabled by an adaptive algorithm based on Monte Carlo tree search that dynamically filters acquired information about the flow to plan future paths. Then, I will demonstrate that for realistic parameter choices, a glider can navigate to gain height and extract energy from flow. Glider paths reflect patterns of foraging, where exploration of the flow is interspersed with bouts of energy extraction through localized spirals. As such, this work broadens our understanding of soaring, and extends the range of scenarios where soaring is known to be possible.


=== Nov 29, Bryan Oakley ===
'''March 15, Xiaoyu Dong (University of Michigan, Ann Arbor):''' An $n \times n$ matrix with $\pm 1$ entries which acts on $\R^n$ as a scaled isometry is called Hadamard. Such matrices exist in some, but not all dimensions. Combining number-theoretic and probabilistic tools we construct matrices with $\pm 1$ entries which act as approximate scaled isometries in $\R^n$ for all $n \in \N$. More precisely, the matrices we construct have condition numbers bounded by a constant independent of $n$.
The solution to the diffusion equation is known to converge exponentially to its steady state, and the rate is given by the spectral gap of the elliptic operator. Using variational techniques, we will maximize the spectral gap over choices of spatially dependent diffusion functions. Using this characterization, we can obtain bounds on the optimal rate of convergence.


=== Dec 6, Hongxu Chen ===
Using this construction, we establish a phase transition for the probability that a random frame contains a Riesz basis. Namely, we show that a random frame in $\R^n$ formed by $N$ vectors with  independent identically distributed coordinate having a non-degenerate symmetric distribution contains many Riesz bases with high probability provided that $N \ge \exp(Cn)$. On the other hand, we prove that if the entries are subgaussian, then a random frame fails to contain a Riesz basis with probability close to $1$ whenever $N \le \exp(cn)$, where $c<C$ are constants depending on the distribution of the entries.
Boltzmann equation is a fundamental kinetic equation that describes the dynamics of dilute gas. In this talk I will focus on the boundary value problem of the Boltzmann equation and introduce the Cercignani-Lampis boundary, which is a physical boundary that describes the intermediate reflection law between diffuse reflection and specular reflection.  




'''March 22, Mengjin Dong (University of  Pennsylvania)''': Alzheimer’s disease (AD) is a progressive neurodegenerative disorder characterized by memory loss, cognitive decline, and behavioral changes primarily in the elderly population. As the most prevalent form of dementia, it impacts millions of families globally. The pathological hallmarks of AD, such as abnormal protein build-up in the brain, can manifest decades before the onset of clinical symptoms. Neuroimaging modalities such as positron emission tomography (PET) and magnetic resonance imaging (MRI) play pivotal roles in studying disease progression and elucidating its underlying mechanisms.


<br>
In this presentation, I will commence with an overview of AD fundamentals and recent research advancements. Subsequently, I will delve into my research, which utilizes deep learning techniques to longitudinally monitor and localize AD progression using MRI data.


== Past Semesters ==
==Past Semesters==
*[[SIAM Fall 2023]]
*[[SIAM Spring 2023]]
*[[SIAM Seminar Fall 2022|Fall 2022]]
*[[Spring 2022 SIAM|Spring 2022]]
*[[SIAM Student Chapter Seminar/Fall2021|Fall 2021]]
*[[SIAM_Student_Chapter_Seminar/Fall2020|Fall 2020]]
*[[SIAM_Student_Chapter_Seminar/Fall2020|Fall 2020]]
*[[SIAM_Student_Chapter_Seminar/Spring2020|Spring 2020]]
*[[SIAM_Student_Chapter_Seminar/Spring2020|Spring 2020]]

Latest revision as of 19:28, 18 March 2024


Spring 2024

Date Location Speaker Title
2/2 VV911 Thomas Chandler (UW-Madison) Fluid–body interactions in anisotropic fluids
3/8 Ingraham 214 Danyun He (Harvard) Energy-positive soaring using transient turbulent fluctuations
3/15 VV911&Zoom Xiaoyu Dong (UMich) Approximately Hadamard matrices and Riesz bases in frames
3/22 VV911&Zoom Mengjin Dong (UPenn) Advancing Alzheimer's Disease Research: Insights and Innovations in MRI-Based Progression Tracking
4/5 VV911 Sixu Li (UW-Madison) TBD
4/12 VV911&Zoom Anjali Nair (UChicago) TBD
4/19 VV911 Jingyi Li (UW-Madison) TBD
5/3 Bella Finkel (UW-Madison) TBD

Abstracts

February 2, Thomas Chandler (UW-Madison): Fluid anisotropy, or direction-dependent response to deformation, can be observed in biofluids like mucus or, at a larger scale, self-aligning swarms of active bacteria. A model fluid used to investigate such environments is a nematic liquid crystal. In this talk, we will use complex variables to analytically solve for the interaction between bodies immersed in liquid crystalline environments. This approach allows for the solution of a wide range of problems, opening the door to studying the role of body geometry, liquid crystal anchoring conditions, and deformability. Shape-dependent forces between bodies, surface tractions, and analogues to classical results in fluid dynamics will also be discussed.

March 8, Danyun He (Harvard University): The ability of birds to soar in the atmosphere is a fascinating scientific problem. It relies on an interplay between the physical processes governing atmospheric flows, and the capacity of birds to process cues from their environment and learn complex navigational strategies. Previous models for soaring have primarily taken advantage of thermals of ascending hot air to gain energy. Yet, it remains unclear whether energy loss due to drag can be overcome by extracting work from transient turbulent fluctuations. In this talk, I will present a recent work that we look at the alternative scenario of a glider navigating in an idealized model of a turbulent fluid where no thermals are present. First, I will show the numerical simulations of gliders navigating in a kinematic model that captures the spatio-temporal correlations of atmospheric turbulence. Energy extraction is enabled by an adaptive algorithm based on Monte Carlo tree search that dynamically filters acquired information about the flow to plan future paths. Then, I will demonstrate that for realistic parameter choices, a glider can navigate to gain height and extract energy from flow. Glider paths reflect patterns of foraging, where exploration of the flow is interspersed with bouts of energy extraction through localized spirals. As such, this work broadens our understanding of soaring, and extends the range of scenarios where soaring is known to be possible.

March 15, Xiaoyu Dong (University of Michigan, Ann Arbor): An $n \times n$ matrix with $\pm 1$ entries which acts on $\R^n$ as a scaled isometry is called Hadamard. Such matrices exist in some, but not all dimensions. Combining number-theoretic and probabilistic tools we construct matrices with $\pm 1$ entries which act as approximate scaled isometries in $\R^n$ for all $n \in \N$. More precisely, the matrices we construct have condition numbers bounded by a constant independent of $n$.

Using this construction, we establish a phase transition for the probability that a random frame contains a Riesz basis. Namely, we show that a random frame in $\R^n$ formed by $N$ vectors with  independent identically distributed coordinate having a non-degenerate symmetric distribution contains many Riesz bases with high probability provided that $N \ge \exp(Cn)$. On the other hand, we prove that if the entries are subgaussian, then a random frame fails to contain a Riesz basis with probability close to $1$ whenever $N \le \exp(cn)$, where $c<C$ are constants depending on the distribution of the entries.


March 22, Mengjin Dong (University of Pennsylvania): Alzheimer’s disease (AD) is a progressive neurodegenerative disorder characterized by memory loss, cognitive decline, and behavioral changes primarily in the elderly population. As the most prevalent form of dementia, it impacts millions of families globally. The pathological hallmarks of AD, such as abnormal protein build-up in the brain, can manifest decades before the onset of clinical symptoms. Neuroimaging modalities such as positron emission tomography (PET) and magnetic resonance imaging (MRI) play pivotal roles in studying disease progression and elucidating its underlying mechanisms.

In this presentation, I will commence with an overview of AD fundamentals and recent research advancements. Subsequently, I will delve into my research, which utilizes deep learning techniques to longitudinally monitor and localize AD progression using MRI data.

Past Semesters