Miles was a PhD student working with me 2020-2025. His dissertation was on Exploration and Approximation on Discrete Structures. He worked on various problems in statistical network modeling, random sampling, and optimization. 

• Research, in his own words: "My research focuses on the intersection of algebraic geometry, discrete optimization, and statistics. Specifically, I study methods for sampling generating sets of integer lattices, such as Markov, Gröbner, and Graver bases, to explore large, finite sets known as fibers. My work has also involved a variety of topics including: goodness-of-fit testing, graph/network analysis, image processing, and topology optimization." 

• Selected activities: in summer 2023, Miles received a SIAM travel grant to present at the SIAM-AG 23 conference at TU Eindhoven, Netherlands, and spent two summers (2023 & 2024) as a Givens Associate and research aide at the Argonne National Laboratory.

• Support: partially supported, as a research assistant, by my DOE grant joint with Argonne.

Ivan started his PhD work with Matthew Dixon, and then continued working with me 2023-2025, switching to projects on random sampling algebraic structures using reinforcement learning.  His dissertation  was on "Design and Application of Reinforcement Learning to Algebraic and Financial Optimization". 

• Research, in his own words:  "I specialize in Reinforcement Learning, Machine Learning, and Applied AI, with a focus on solving complex financial, statistical, and algebraic problems using scalable algorithms and intelligent systems. My research spans actor-critic methods, Q-learning, graph-based models, and large language models (LLMs). I’ve developed novel RL algorithms for problems like optimal consumption under Epstein-Zin preferences, high-dimensional fiber sampling, and combinatorial optimization (e.g., TSP).
  I’ve interned at Argonne National Lab and CCC Intelligent Solutions, where I built scalable AI systems for real-world applications—from crash prediction using GNNs to reinforcement learning for route optimization. I’ve also implemented Neo4j graph databases, LLM-based text classification pipelines, and efficient RL agents for sparse, high-dimensional structures." 

• Support: partially supported, as a research assistant, by my DOE grant joint with Argonne.

• Next position: Machine Learning Engineer at Wisdom

Mateja was a UIC student who worked under my supervision for her dissertation, but since she was at UIChicago, she was formally supervised by Jan Verschelde. Her dissertation "Goodness of fit test for network models" extends the work for our joint JRSS-B paper on testing model fit for discrete exponential families. 

• Research: temporal network models, optimization, stochastic blockmodels.

• Support: research assistant for a semester under my AFOSR grant on 'Algebraic statistics for network models' (2013-2017). 

• Next position: Associate Director, Secretariat Economists

Sara was a postdoc with me during 2018-2020, after which she moved to Lake Forest College as an Assistant Professor of Computer Science and Mathematics. Soon after joining Lake Forest, she became the Director of the Applied Data Center. 

We have worked on machine learning for non-linear algebra and threaded Gröbner bases in Macaulay2 and Python.

• 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.

• Awards and other positions: Despina received the Marie Curie ER Fellowship at the Laboratory for Internet Computing, Department of Computer Science, University of Cyprus and spent 2014 - 2015 there. Despina is a co-PI on our joint collaborative NSF grant Randomized and Structure-Based Algorithms in Commutative Algebra with UC Davis.

Elizabeth was a PhD student working with me 2010-2013. Her dissertation was on Algebraic complexity problems in statistics using combinatorial and tensor methods.  

• Support&awards:

  • 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. As of 2021, when she recieved an NSF CAREER award, she is an associate professor at the University of Hawaii at Manoa. 

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 performing 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.