SIAM Student Chapter Seminar: Difference between revisions

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*'''When:''' Fridays at 1 PM unless noted otherwise
*'''When:''' Fridays at 1:30 PM unless noted otherwise
*'''Where:''' 9th floor lounge (we will also broadcast the virtual talks on the 9th floor lounge with refreshments)
*'''Where:''' 9th floor lounge (we will also broadcast the virtual talks on the 9th floor lounge with refreshments)
*'''Organizers:''' Yahui Qu, Peiyi Chen, Shi Chen and Zaidan Wu
*'''Organizers:''' Yahui Qu, Peiyi 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].
Line 9: Line 9:
*'''Passcode:  281031'''
*'''Passcode:  281031'''


== Spring 2024 ==
== Spring 2025 ==


{| class="wikitable"
{| class="wikitable"
|+
|+
!Date
|Date
!Location
|Location
!Speaker
|Speaker
!Title
|Title
|-
|-
|2/2
|03/07
|VV911
|9th floor
|Thomas Chandler (UW-Madison)
|Ang Li
|Fluid–body interactions in anisotropic fluids
|Applying for postdocs and different industry jobs ... at the
same time
|-
|-
|3/8
|04/04
|Ingraham 214
|9th floor
|Danyun He (Harvard)
|Borong Zhang
|Energy-positive soaring using transient turbulent fluctuations
|Stochastic Multigrid Minimization for Ptychographic Phase Retrieval
|-
|-
|3/15
|04/11
|VV911&Zoom
|903
|Xiaoyu Dong (UMich)
|Ian McPherson
|Approximately Hadamard matrices and Riesz bases in frames
|Convergence Rates for Riemannian Proximal Bundle Methods
|-
|-
|3/22
|04/18
|VV911&Zoom
|9th floor
|Mengjin Dong (UPenn)
|Weidong Ma
|Advancing Alzheimer's Disease Research: Insights and Innovations in MRI-Based Progression Tracking
|A topic in kernel based indepedence testing
|-
|4/5
|VV911
|Sixu Li (UW-Madison)
|A Good Score Does not Lead to A Good Generative Model
|-
|4/12
|VV911&Zoom
|Anjali Nair (UChicago)
|Some scaling limits for long distance wave propagation in random media
|-
|4/19
|VV911
|Jingyi Li (UW-Madison)
|Arrested development of active suspensions in anisotropic fluids
|-
|5/2 (Thursday!)
|VV911
|David Keating(UW-Madison)
|A tour of domino tilings
|}
|}


==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.
'''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.
'''April 5, Sixu Li (UW-Madison):''' Score-based Generative Models (SGMs) is one leading method in generative modeling, renowned for their ability to generate high-quality samples from complex, high-dimensional data distributions. The method enjoys empirical success and is supported by rigorous theoretical convergence properties. In particular, it has been shown that SGMs can generate samples from a distribution that is close to the ground-truth if the underlying score function is learned well, suggesting the success of SGM as a generative model. We provide a counter-example in this paper. Through the sample complexity argument, we provide one specific setting where the score function is learned well. Yet, SGMs in this setting can only output samples that are Gaussian blurring of training data points, mimicking the effects of kernel density estimation. The finding resonates a series of recent finding that reveal that SGMs can demonstrate strong memorization effect and fail to generate.
This is a joint work with Shi Chen and Qin Li.
'''April 12, Anjali Nair (UChicago):''' Wave propagation in random media is a rather interesting and complex phenomenon owing to the interplay of multiple scales. While a complete understanding of wave fields propagating in reasonably arbitrary random media remains essentially out of reach, much progress has been made in the setting of paraxial beam propagation. The paraxial approximation aims at considering high-frequency waves propagating over long distances along a privileged direction with negligible backscattering. In particular, I will discuss the so-called white noise paraxial scaling, where different asymptotic regimes lead to very different statistical limits for the wave field.
'''April 19, Jingyi Li (UW-Madison):''' Active suspensions in anisotropic, viscoelastic fluids experience competing stresses on their orientational alignment. The orientational order of extensile-stress-generating particles is hydrodynamically unstable to a bend instability, but the elasticity of the fluid drives the system towards alignment. To study these competing effects, we examine a dilute suspension of active particles in an Ericksen-Leslie model nematic liquid crystal. Our first observation is that, a bifurcation emerges uniform alignment with no flow, to a steady flowing state of arrested development, as the particle activity cross a critical threshold. And a secondary instability to transverse perturbations is observed at larger activity, leading to arrested, flowing states with features emerging at smaller wavelengths. Finally, if the system is motile, the arrested states become traveling wave solutions of coupled nonlinear advection-diffusion equations with spatially varying particle concentration and orientation.
'''May 2, David Keating (UW-Madison):'''A classic problem asks whether or not an 8x8 checkerboard can be tiled by dominos where each domino takes up covers two adjacent squares of the checkerboard and we do not allow the dominos to overlap. It is easy to see that this is possible (construct a tiling yourself!) but it is much harder to count the number of possible tilings. In this talk, we will discuss this and related questions about domino tilings of checkerboard regions. We will focus on two main topics.
Enumeration: is it possible to tile a region by dominos, and how many possible tilings are there?


Randomness: how can one chose a tiling uniformly at random from the set of all possible tilings, and what does such a tiling look like?
'''March 7th, Ang Li (UW-Madison)''': I will share my experience with postdoc and industry job applications. This talk might be helpful for those who haven’t decided between academia and industry or are considering different paths within industry since I made my own decision quite late.


A region that will be of particular interest to us is known as the Aztec diamond.  Random tilings of very large Aztec diamonds exhibit what is known as the limit shape phenomenon, a kind of law of large numbers in which random tilings exhibit interesting geometric features.  We will see examples of these limit shapes and mention connections to other areas in probability.
'''April 4th, Borong Zhang (UW-Madison)''': In this talk, we introduce a novel stochastic multigrid minimization method designed for ptychographic phase retrieval. By reformulating the inverse problem as the iterative minimization of a quadratic surrogate that majorizes the original objective function, our approach unifies a range of iterative algorithms, including first-order methods and the well-known Ptychographic Iterative Engine (PIE). By efficiently solving the surrogate problem using a multigrid method, our method delivers significant improvements in both convergence speed and reconstruction quality compared to conventional PIE techniques.


'''April 11th, Ian McPherson (Johns-Hopkins):''' Nonsmooth convex optimization is a classically studied regime with a plethora of different optimization algorithms being developed in order to solve them. Of these methods, proximal bundle methods have been created and used within the Euclidean setting for decades - attempting to mimic the dynamics of the proximal point method. While practitioners have enjoyed very robust convergence results with respect to choice of parameters, it was not until the late 2020s that we have had theoretical results giving non-asymptotic guarantees - recovering optimal convergence rates. Within the past few years, the first Riemannian Proximal Bundle Methods have been proposed, again lacking non-asymptotic guarantees. Within this talk, we discuss how we are able to both generalize proposed methods and lift the non-asymptotic rates to the Riemannian setting. Moreover, we will do so without access to exponential maps or parallel transports. In addition, to our knowledge these are the first theoretical guarantees for non-smooth geodesically convex optimization in the Riemannian setting, without access to either exponential maps and parallel transports. The work presented is joint work with Mateo Diaz and Benjamin Grimmer.
'''April 18th, Weidong Ma (Univeristy of Pennsylvania)''':
==Past Semesters==
==Past Semesters==
*[[SIAM Fall 2023]]
*[[SIAM Seminar Fall 2024|Fall 2024]]
*[[SIAM Spring 2023]]
*[https://wiki.math.wisc.edu/index.php/SIAM_Spring_2024 Spring 2024]
*[[SIAM Fall 2023|Fall 2023]]
*[[SIAM Spring 2023|Spring 2023]]
*[[SIAM Seminar Fall 2022|Fall 2022]]
*[[SIAM Seminar Fall 2022|Fall 2022]]
*[[Spring 2022 SIAM|Spring 2022]]
*[[Spring 2022 SIAM|Spring 2022]]

Latest revision as of 16:23, 4 April 2025


Spring 2025

Date Location Speaker Title
03/07 9th floor Ang Li Applying for postdocs and different industry jobs ... at the

same time

04/04 9th floor Borong Zhang Stochastic Multigrid Minimization for Ptychographic Phase Retrieval
04/11 903 Ian McPherson Convergence Rates for Riemannian Proximal Bundle Methods
04/18 9th floor Weidong Ma A topic in kernel based indepedence testing


Abstracts

March 7th, Ang Li (UW-Madison): I will share my experience with postdoc and industry job applications. This talk might be helpful for those who haven’t decided between academia and industry or are considering different paths within industry since I made my own decision quite late.

April 4th, Borong Zhang (UW-Madison): In this talk, we introduce a novel stochastic multigrid minimization method designed for ptychographic phase retrieval. By reformulating the inverse problem as the iterative minimization of a quadratic surrogate that majorizes the original objective function, our approach unifies a range of iterative algorithms, including first-order methods and the well-known Ptychographic Iterative Engine (PIE). By efficiently solving the surrogate problem using a multigrid method, our method delivers significant improvements in both convergence speed and reconstruction quality compared to conventional PIE techniques.

April 11th, Ian McPherson (Johns-Hopkins): Nonsmooth convex optimization is a classically studied regime with a plethora of different optimization algorithms being developed in order to solve them. Of these methods, proximal bundle methods have been created and used within the Euclidean setting for decades - attempting to mimic the dynamics of the proximal point method. While practitioners have enjoyed very robust convergence results with respect to choice of parameters, it was not until the late 2020s that we have had theoretical results giving non-asymptotic guarantees - recovering optimal convergence rates. Within the past few years, the first Riemannian Proximal Bundle Methods have been proposed, again lacking non-asymptotic guarantees. Within this talk, we discuss how we are able to both generalize proposed methods and lift the non-asymptotic rates to the Riemannian setting. Moreover, we will do so without access to exponential maps or parallel transports. In addition, to our knowledge these are the first theoretical guarantees for non-smooth geodesically convex optimization in the Riemannian setting, without access to either exponential maps and parallel transports. The work presented is joint work with Mateo Diaz and Benjamin Grimmer. April 18th, Weidong Ma (Univeristy of Pennsylvania):

Past Semesters

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