NONLINEAR ALGEBRA & STATISTICS
We work on fun & challenging problems in nonlinear algebra, nonlinear statistics, and at their intersection.
Join us at the seminars!
Postdocs, PhD students, MS thesis students
Sara was a postdoc with me during 2018-2020, after which she moved to Lake Forest College as an Assistant Professor of Math&Computer Science.
We have worked on machine learning for non-linear algebra and threaded Groebner bases in Macaulay2 and Python.
Dane was a PhD student working with me 2013-2018. His dissertation was on Quantifying uncertainty in random algebraic objects using discrete methods.
Research: applied algebraic geometry, applied commutative algebra, and algebraic statistics.
Support: supported under my AFOSR grant on 'Algebraic statistics for network models' (2013-2017), and partly under joint NSF grant 'Randomized and Structure-Based Algorithms in Commutative Algebra' (2015-2017).
Awards: Dane has spent summer 2015 visiting ISM in Tokyo under the NSF-EAPSI program. He received the department's Teaching Assistant Award in 2017. He was awarded a SIAM Student Travel Award to attend the SIAM Conference on Applied Algebraic Geometry (AG17) July 31 – August 4, 2017, at Georgia Institute of Technology in Atlanta. Dane had also been co-organizing the weekly Algebraic Statistics seminar at IIT (except Spring 2017).
Next position: Dane went on to be a postdoc at Brown University's ICERM program on non-linear algebra, followed by a postdoc at York University working with Hélène Massam. He now works at the Mitre corporation.
Despina was a postdoctoral researcher working with me 2012-2014 at both Penn State and Illinois Tech, and then I was lucky to be able to hire her again 2015-2017. Her research includes statistical network models, structure-based algorithms, random structures.
Support: her positions have been funded by DARPA and AFOSR grants on Algebraic Statistics for Network Models.
Elizabeth was a PhD student working with me 2010-2013. Her dissertation was on Algebraic complexity problems in statistics using combinatorial and tensor methods.
AY2011/12 funded as a visiting graduate student from Penn State statistics (my home department at that time).
AY2012/13 funded by the Dean's scholar award at UIC.
Next position: Upon graduation, Elizabeth was awarded an NSF Graduate Fellowship with Seth Sullivant at NCSU, and a tenure-track position at San Jose State University which she started in Fall 2014.
Martin Dillon - MS 2016
Masters of Applied Mathematics student. Research group member 2015-2016.
Research: Martin's Masters Thesis research spanned various aspects of computational and applied mathematics and statistics. His thesis focused on a mixing time problem for Markov chains arising in algebraic statistics. In particular, in his thesis `Runtime for perfomring exact tests on the p1 statistical model for random graphs', he showed that the chain we developed by Gross-P.-Stasi for the p1 random graph model mixes rapidly on all fibers where the simple switch chain does.
Support: Formerly undergraduate student: In summer 2015, his research on complexity of Markov bases for contingency tables was supported by the F.R. "Buck" McMorris Summer Research Stipend. He presented a poster on this research at Menger Day 2016.
Next position: Quantitative Analyst, Financial Risk Management, Milliman.
Research assistants - Masters & Undergraduate
Undergraduate research assistant 2019-2021.
Groebner bases: database & predictions of computational complexity and structure. Next position: PhD Mathematics program at Purdue
Weronika SwiechowiczUndergraduate. Research group member 2014-2016.
Applied and computational algebra. College of Science Dean's Undergraduate Research Stipend awardee. SIAM Undergraduate Research Online (SIURO) journal publication. Next position: graduate student in mathematical and computational finance at Stanford.
Xintong LiUndergraduate. Research group member summer 2015.
Solving polynomial systems with special structure: theory and computation. College of Science Dean's Undergraduate Research Stipend awardee. Research presented at IIT Research Day 2016, Undergrad Math Symposium at UIC Oct 2016.
Focused research groups
Learning Algebra 2019 group
Phillip Hosu, Travis Koehring, Jelena Mihajlovic-Klaric.
Spring / summer 2019: undergraduate research group, jointly supervised with Despina Stasi and Shahrzad Zelenberg.
Research: learning and computation for problems in non-linear algebra.
Support: this research project is funded by the grant NSF DMS-1522662 on Randomized and Structure-Based Algorithms in Commutative Algebra.
RMI 2017 group
Genevieve Hummel, Parker Joncus, Daniel Kosmas, Richard Osborn, Monica Yun, and Tanner Zielinski.
Summer 2017 undergraduate research group for Random Monomial Ideals, jointly supervised with Despina Stasi.
Research: Completing a Macaulay2 package for random monomial ideals, based on arXiv:1701.07130, and studying various model extensions.
Support: the summer research project is funded by the grant NSF DMS-1522662 on Randomized and Structure-Based Algorithms in Commutative Algebra.
Awards: Richard Osborn, under Despina Stasi's supervision, is supported by the College of Science summer research stipend. Daniel Kosmas, under my supervision, is supported by the McMorris summer research stipend from the Department of Applied Mathematics.
Each researcher and each research group has their own philosophy when it comes to mentorship, advising, grades, etc. I recently came across the fantastic Lab Philosophy page by Bradley Voytek, whom I had the luck of meeting through SoReMo Forum. With his permission, I am linking to his page here; I hope you will read a bit about mentoring, grades, and the imposter syndrome.
The professor is in: grad school advice!
How do I join?
If you are interested in research in algebraic statistics, and/or relations to discrete applied math and combinatorics, please take part in the algebraic statistics seminar, and feel free to stop by for a chat after you have explored my research interests a bit.
What can I read?
The Spring 2013 page for the algebraic statistics reading seminar I organized at Penn State offers some reading material and introductory references.
How to choose your grad school?
That's a tough one to answer on a website. Here are some of my thoughts about the graduate school experience: UK Math Alumni Spotlight page.