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 and Zaidan Wu
*'''Organizers:''' Yahui Qu, Peiyi Chen and Zaidan Wu
Line 9: Line 9:
*'''Passcode:  281031'''
*'''Passcode:  281031'''


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


{| class="wikitable"
{| class="wikitable"
|+
|+
!Date
|Date
!Location
|Location
!Speaker
|Speaker
!Title
|Title
|-
|-
|10 AM 10/4
|03/07
|Birge 346
|9th floor
|Federica Ferrarese (University of Ferrara, Italy)
|Ang Li
|Control plasma instabilities via an external magnetic field: deterministic and uncertain approaches
|Applying for postdocs and different industry jobs ... at the
same time
|-
|-
|11 AM 10/18
|04/04
|9th floor
|9th floor
|Martin Guerra (UW-Madison)
|Borong Zhang
|Swarm-Based Gradient Descent Meets Simulated Annealing
|Stochastic Multigrid Minimization for Ptychographic Phase Retrieval
|-
|-
|12:30 PM 10/31
|04/11
|VV 901
|903
|Chuanqi Zhang (University of Technology Sydney)
|Ian McPherson
|Faster isomorphism testing of p-groups of Frattini class-2
|Convergence Rates for Riemannian Proximal Bundle Methods
|-
|-
|11/8
|04/18
|9th floor
|9th floor
|Borong Zhang (UW-Madison)
|Weidong Ma
|
|A topic in kernel based indepedence testing
|-
|
|
|
|
|-
|
|
|
|
|-
|
|
|
|
|-
|
|
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|}
|}


==Abstracts==
==Abstracts==
'''October 4th, Federica Ferrarese (University of Ferrara, Italy)''': The study of the problem of plasma confinement in huge devices, such as for example Tokamaks and Stellarators, has attracted a lot of attention in recent years. Strong magnetic fields in these systems can lead to instabilities, resulting in vortex formation. Due to the extremely high temperatures in plasma fusion, physical materials cannot be used for confinement, necessitating the use of external magnetic fields to control plasma density. This approach involves studying the evolution of plasma, made up of numerous particles, using the Vlasov-Poisson equations. In the first part of the talk, the case without uncertainty is explored. Particle dynamics are simulated using the Particle-in-Cell (PIC) method, known for its ability to capture kinetic effects and self-consistent interactions. The goal is to derive an instantaneous feedback control that forces the plasma density to achieve a desired distribution. Various numerical experiments are presented to validate the results. In the second part, uncertainty is introduced into the system, leading to the development of a different control strategy. This method is designed to steer the plasma towards a desired configuration even in the presence of uncertainty. The presentation concludes with a comparison of the two control strategies, supported by various numerical experiments.


'''October 18th, Martin Guerra (UW-Madison)''': In generic non-convex optimization, one needs to be able to pull samples out of local optimal points to achieve global optimization. Two common strategies are deployed: adding stochasticity to samples such as Brownian motion, as is done in simulated annealing (SA), and employing a swarm of samples to explore the whole landscape, as is done in Swarm-Based Gradient Descent (SBGD). The two strategies have severe drawbacks but complement each other on their strengths. SA fails in the accuracy sense, i.e., finding the exact optimal point, but succeeds in always being able to get close, while SBGD fails in the probability sense, i.e., it has non-trivial probability to fail, but if succeeds, can find the exact optimal point. We propose to combine the strength of the two and develop a swarm-based stochastic gradient method with samples automatically adjusting their annealing. Using mean-field analysis and long-time behavior PDE tools, we can prove the method to succeed in both the accuracy sense and the probability sense. Numerical examples verify these theoretical findings.
'''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.


'''October 31st, Chuanqi Zhang''' (University of Technology Sydney): The finite group isomorphism problem asks to decide whether two finite groups of order N are isomorphic. Improving the classical $N^{O(\log N)}$-time algorithm for group isomorphism is a long-standing open problem. It is generally regarded that p-groups of class 2 and exponent p form a bottleneck case for group isomorphism in general. The recent breakthrough by Sun (STOC '23) presents an $N^{O((\log N)^{5/6})}$-time algorithm for this group class. Our work sharpens the key technical ingredients in Sun's algorithm and further improves Sun's result by presenting an $N^{\tilde O((\log N)^{1/2})}$-time algorithm for this group class. Besides, we also extend the result to the more general p-groups of Frattini class-2, which includes non-abelian 2-groups. In this talk, I will present the problem background and our main algorithm in detail, and introduce some connections with other research topics. For example, one intriguing connection is with the maximal and non-commutative ranks of matrix spaces, which have recently received considerable attention in algebraic complexity and computational invariant theory. Results from the theory of Tensor Isomorphism complexity class (Grochow--Qiao, SIAM J. Comput. '23) are utilized to simplify the algorithm and achieve the extension to p-groups of Frattini class-2.  
'''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 Seminar Fall 2024|Fall 2024]]
*[https://wiki.math.wisc.edu/index.php/SIAM_Spring_2024 Spring 2024]
*[https://wiki.math.wisc.edu/index.php/SIAM_Spring_2024 Spring 2024]
*[[SIAM Fall 2023|Fall 2023]]
*[[SIAM Fall 2023|Fall 2023]]

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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