swat math/stat research
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Swat Math/Stat ResearchSummer 2022
How to use this document: Faculty members in the math/stat department who may have Summer 2022 research projects have each made a slide or two to give you a short overview of their work and potential ideas for what students could work on. Some have also included further reading and next steps for potential research assistants.
Take a look at the following slides, check out the linked resources, and reach out to any professors that you might be interested in working with!
(Note: demand for math/stat summer research far exceeds the supply of positions available, and most funding will be through the college’s funding application, which happens in February or later)
Hyperbolic Geometry -- Tom CrawfordI like working with objects/shapes I can visualize, so my research is in Hyperbolic Geometry and in Knot Theory.
Currently I study 3 dimensional shapes called Hyperbolic 3-Manifolds. These shapes typically bend onto themselves in ways that make them tricky to visualize, but a newly defined system can let us rephrase various questions about the Manifolds as questions about functions in the complex plane. As such, much of the structure of the Manifold can be seen to develop as a fractal pattern. One project involves investigating the behavior of classes of these functions.
Hyperbolic Geometry -- Tom CrawfordEach of these images were generated by my somewhat rudimentary python scripts. Another (related) project is to generalize these procedures.
Required background: At least one proof intensive class.
Preferred: Math 67, some programming ability/experience
Please reach out with any questions. If interested, please include a brief statement about your background.
[email protected] images/gifs
Geometric Combinatorics -- Prof. Michael DoughertyMy research comes from the areas of group theory, combinatorics, and topology. I am primarily interested in braids and other related objects, including partitions, permutations, graphs, and polytopes. A lot of my work involves finding useful connections from one type of object to another.
Geometric Combinatorics -- Prof. Michael DoughertyPotential projects might involve the following objects:
● Parking functions and noncrossing partitions (article)● Determinant identities for complex polynomials (article)● Braids (wikipedia)● Associahedra and cyclohedra (blog post)
I am planning to mentor research this summer.
Ideal background: Math 67 (combinatorics, topology, or programming experience a plus)
If you’re interested, send me an email ([email protected]) with some information on your background and interests.
(some noncrossing partitions)
Algebraic Combinatorics and/or Algebraic Geometry -- Prof. Linda Chen
My research is at the interface of algebraic geometry, algebraic combinatorics, and representation theory:
● the translation of problems in geometry to problems in algebra and combinatorics,
● combinatorial structures such as partitions and permutations,● families of symmetric polynomials.
I might supervise undergraduate research this summer. If interested: email [email protected] with a paragraph about your background and potential interest.
Ideal background: at least two of Math 65/Math 67/Math 69/Math 105. Bonus background: programming experience, any math seminar (Math 102/103/104).
Quick reference and video.
Number Theory -- Prof. Ian WhiteheadI am an analytic number theorist interested in symmetry. Some key objects in my work include L-functions, automorphic forms, and infinite-dimensional Lie groups. The reason why I love these esoteric objects is because they are powerful tools to help understand some of the oldest and most mysterious sets of integers:
● The prime numbers● The numbers of solutions to polynomial equations mod p● The numbers appearing in Apollonian circle packings
The set of integers appearing in an Apollonian circle packing is the focus of my current project.
To work with me, you need some background experience reading and writing proofs, at the level of Math 63 or Math 67. Programming experience is often helpful, but not required. If you are interested, please contact me and please sign up for Math 53 in the spring semester.
Number Theory -- Prof. Ian WhiteheadThe image at left is an Apollonian circle packing. Each new circle is tangent to three circles surrounding it. Each circle is labeled with one over its radius. Interesting questions about these numbers include:
● Given a (large) integer X, how many numbers less than X appear in the picture?● Given a (large) integer X, can you predict whether X appears without searching for it?
My own research uses analysis techniques to study these questions. I discovered that certain power series converge in domains closely related to Apollonian packings: see the image at right. My students have explored generalizations of these packings. Last summer, we computed the fractal dimensions of many circle packings, and in the process, discovered new types of packings. This summer, we’ll explore the properties of these new packing types and of sphere and torus packings.References here and here. Last summer’s project here.
Mathematical neuroscience and nonlinear dynamics -- Prof. Josh Goldwyn
I use mathematical modeling and mathematical theory to understand signal processing in the brain. I often study cells and circuits in the brain that are highly specialized to represent temporal information in sound signals (the auditory system).
Possible research this summer would focus on modeling the activity of neurons whose activity helps us determine where sounds come from in space.
Mathematical topics you would learn and use:Differential equations modeling, numerical simulations, analysis of nonlinear dynamical systems, random processes
Necessary background: Math 44 and experience using Matlab or python Background in biology & neuroscience is not required, but you should find it interesting
Additional information on my website:https://www.swarthmore.edu/joshua-goldwyn/summer-projects
Email with questions and interest:[email protected]
Prof. Victor Barranca -- Applied Mathematics(Mathematical Neuroscience and Network Dynamics)
My research interests in applied mathematics give me the opportunity to study a wide array of fascinating scientific problems. A central thread of my work is characterizing the relationship between the structure of a network and its function, particularly in the context of high dimensional systems with nonlinear dynamics.
I mostly find myself involved in the exciting field of theoretical neuroscience. My research uses new mathematical approaches to investigate the neuronal computations underlying sensory processing and the role of neuronal network connectivity in facilitating brain function.
Much of this research has raised theoretical questions in other fields. So, I also investigate intriguing problems in the realms of network science, mathematical biology, and signal processing.
More information about recent research activities can be found here: http://www.swarthmore.edu/NatSci/vbarran1/research.html
Prof. Victor Barranca -- Applied MathematicsPotential Projects May Involve Applications in:
•Data compression, signal processing, and binocular rivalry in the visual system
Skills Involved and Developed:
•Mathematical Programming •Mathematical Modeling
•Simulation, Data Analysis, and Visualization
•Math Analysis using Dynamical Systems, Probability, and Approximation Theory
Core Prerequisites:
Differential Equations (Math 43 or 44) and Programming Ability (CS 21 or equivalent)
Helpful Additional Coursework:
Modeling (Math 56), Probability (Stat 51), and Stochastic and Numerical Methods (Math 66)
No neuroscience experience needed: only interest in applications of math to biology required
If Interested:
•Contact Prof. Barranca over email at [email protected] for more information. Please send along a short paragraph explaining your interest in the research and relevant background. Feel free to reach out with any questions!
Statistics — Prof. Steve WangI develop statistical methods for analyzing paleontological data.
I am not yet sure what specific projects we’ll be working on this summer, but you can read brief summaries of work by previous students here:
http://www.swarthmore.edu/NatSci/swang1/personnel.html
My work mainly involves computer programming, so you should have taken CS 21 or the equivalent. (CS 35 is helpful but not necessary.) The ideal statistical preparation would be Stat 51, but Stat 11 might work as well. No experience in paleontology is expected.
If you’re interested, please send a resume/CV to [email protected].
You can find more information on my research here:
http://www.swarthmore.edu/NatSci/swang1/research.html
Feel free to ask if you have any questions!
Statistics Research -- Prof. Amanda Luby
I research statistical methods for understanding complex decision-making, often using Bayesian tools. I’m currently funded by the Center for Statistics and Applications in Forensic Evidence for my work in forensic science.
Forensic science is a huuuge field that consists of many different sub-disciplines. I work in fingerprint analysis, which involves elements of databases, image processing and analysis, matching algorithms, and cognitive and decision science. Right now, I'm focusing on the decision-making side where I analyze data from annual proficiency tests and research studies completed by fingerprint examiners.
Next summer, I’ll be developing Item Response Theory-based models for forensic proficiency testing. Item Response Theory is the class of models used to calculate student scores when they sit for different versions of the same exam (e.g. SAT and ACT). The basic idea is that we model the probability of a correct response as a function of both participant proficiency AND item difficulty, which are estimated from the data. If you've seen logistic regression in Stat21, it's the exact same idea but with funky covariates. (and if you haven't, it's closely related to linear regression).
Statistics Research -- Prof. Amanda LubyProjects will include:
1) Coding R or python programs 2) Researching the current state of proficiency testing in forensics3) Data analysis of fingerprint analysis decisions
Further Reading:
● A chapter I wrote for the e-book Open Forensic Science in R for a short introduction to human factors in forensic science and IRT models.
● A talk I gave "at" a conference last summer giving an overview of the problem and a more complicated model
● The FBI's Black Box study paper -- this is the main source of data I've been working with. All data is freely available online.
Preferred background:
At least Stat21, or Stat11 + programming background. If you’d like to work with me in Summer 2022, I’d like you to be able to commit to some work (paid or for credit) in Spring 2021
If you’d like to work with me: send me an email at aluby1@swarthmore with a current CV/resume and a short paragraph on why you are interested in this work
Swarthmore Summer Scholars Program (S3P) MentorAs we have learned in the 6 years of the Program, the Student Mentors are the ‘secret sauce’ to the S3P recipe for a successful program. The job is a combination of teaching assistant and resident assistant. Please direct any questions to Amy Vollmer, S3P Director [email protected]. Six Student Mentors will be hired: 2 to support each subject: Math, Writing, Lab Science (Biology in 2021) Schedule for summer 2021:Weeks of July 12, July 19 training for RA and TA roles Weeks of July 26, Aug 2, 9, 16 supporting 16 S3P scholars Week of Aug 23 follow up with Director of S3P
Responsibilities: Support 16 summer scholars during the 4 weeks of the summer Program, serve as subject matter teaching assistants (TAs) to support the faculty who will be teaching, run the 5 study hall sessions each week, serve as RAs – even in a virtual program: providing virtual tours, talking about resources on campus to support academics, physical and mental health, social activities, train for 2 weeks before the Program formally begins, attend and report at weekly S3P staff meetings during the summer, follow up with the Director in the week following the summer Program
Strong candidates: have demonstrated knowledge and performance in the subject area that they will support, have strong commitment to inclusive diversity in the Swarthmore community, are dependable team members with strong communication skills, have awareness of first-gen/low-income (FLI) student challenges and opportunities
Swarthmore Summer Scholars Program (S3P) Mentor
Frequently Asked QuestionsCan I apply to support more than one subject? Yes, but you will be hired to support only one subject Do you hire alumni of the S3P? Sometimes, but it is not a requirement of applicants How much is the stipend? The same amount as is paid for 10-week summer research ($5K); even though involvement is only for 7 weeks, but there is much more work in the evenings and on weekends during the ProgramI know there is a 5th week of the Program prior to the spring semester; are student mentors involved with that? No; your involvement ends with the week of follow up after the summer Program Can I get paid for a summer research project AND be an S3P student mentor? No; to be fair to other students: one stipend per summer Can I apply for this as a graduating senior? No; unless you are returning in the fall to complete student teaching in Education Can I have another job during the training and S3P summer session? No; this is a full time commitment Will S3P be on campus or virtual this coming summer? Mostly virtual with – at most – one final week on campus; this decision will be made by the time mentors are hired at the end of March 2021.
External Math/Stat Research OpportunitiesThe NSF funds a number of REU’s in the mathematical sciences across the US. The AMS also maintains a list of REU opportunities. (Note that NSF-funded positions are restricted to US citizens or permanent residents)
Summer@ICERM program at Brown University
The Summer Institute in Biostatistics is an NIH-funded program across six different universities
Stanford Population Health Summer Research Program is a virtual program for under-represented and historically excluded students in the health sciences with a focus on quantitative methods for population health
** Feel free to leave a comment with any other opportunities, and I will add them to the document 😊