Publications & products from IML research groups

Publications

Note: An asterisk(*) behind an author’s name indicates that the author was an undergraduate IML scholar.

  1. Chen, Z.*, Ding, K., Huang, Y.*, Jia, X.*, Rosenblatt, J., Su, Y.*, & Xue, J.* (2025). Covering Area in a Disc by Finitely Many Triangles. The PUMP Journal of Undergraduate Research, 8, 47–56. https://doi.org/10.46787/pump.v8i.392
  2. Roy Araiza, Jihong Cai*, Yushan Chen*, Abraham Holtermann*, Chieh Hsu*, Tushar Mohan*, Peixue Wu, Zeyuan Yu*, “A note on the stabilizer formalism via noncommutative graphs”, (2023) ArXiv
  3. Yu Du*, Gabriel Kosmacher*, Yichen Liu, JeffMassman*, Joseph Palmer, Timothy Thieme*, Jerry Wu*, Zheyu Zhang*, “Packing densities of Delzant and semitoric polygons”, SIGMA 19 (2023), 081, 42 pages, ArXiv
  4. Z. Chen*, K. Ding, Y. Huang*, X. Jia*, J. Rosenblatt, Y. Su*, J. Xue*, “Alternative least squares approximations via offsets”.
  5. Z. Chen*, K. Ding, Y. Huang*, X. Jia*, J. Rosenblatt, Y. Su*, J. Xue*, “Covering area in a disc by finitely many triangles”, (2022)
  6. József Balogh, Felix Christian Clemen, Haoran Luo, “Non-degenerate Hypergraphs with Exponentially Many Extremal Constructions”. ArXiv
  7. Igor Araujo, József Balogh, Yuzhou Wang,  Maximum determinant and permanent of sparse 0-1 matrices, Linear Algebra Appl. 645 (2022), 194–228.
  8. Xiaojian Li*, Jay Reiter*, Shiang Tang, Napoleon Wang*, Jin Yi*, “P-adic incomplete gamma functions and Artin-Hasse-type series”, Ultrametric Analysis and Applications (2022) 14, 335-343. ArXiv
  9. Lucia M. Wagner, Sara M. Clifton, “Modeling the public health impact of e-cigarettes on adolescents and adults”, Chaos (2021) 31(11):113137. https://doi.org/10.1063/5.0063593
  10. Igor Araujo, Kareem Benaissa*, Richard Bi*, Sean English, Shengan Wu*, Pai Zheng*, “Rainbow Connection for Complete Multipartite Graphs”, (2023) ArXiv
  11. Albert Cao*, Felix Christian Clemen, Sean English, Xiaojian Li*, Tatum Schmidt*, Leeann Xoubi*, Weian Yin*, “Chasing the threshold bias of the 3-AP game”, Australasian J. of Combinatorics (2022) Vol. 84(1), 167-177.
  12. Abdullah Dean*, Sean English, Tongyun Huang*, Robert A. Krueger, Andy Lee*, Mose Mizrahi*, Casey Wheaton-Werle*, “Firefighting on the hexagonal grid”, Discrete Applied Mathematics (2021) Vol. 305, 16-22.  arXiv
  13. Philipp Hieronymi, Dun Ma*, Reed Oei*, Luke Schaeffer, Christian Schulz, Jeffrey Shallit, “Decidability for Sturmian words”, (2021) arXiv
  14. Reed Oei*, Dun Ma*, Christian Schulz, Philipp Hieronymi, “Pecan: An Automated Theorem Prover for Automatic Sequences using Büchi Automata”, (2021) arXiv
  15. Zhengda Mo*, Sam Qunell*, Anush Tserunyan, Jenna Zomback, “Characterization of saturated graphs related to pairs of disjoint matchings”, Illinois J. Math. 66(1): 59-77 (2022). arXiv, DOI
  16. Ali Guo*, Kieran Kaempen*, Zhengda Mo*, Sam Qunell*, Joe Rogge*, Chao Song*, Anush Tserunyan, Jenna Zomback, “Pairs of disjoint matchings and related classes of graphs”, Involve, A Journal of Mathematics (2023) 16-2, 249-264. arXiv, DOI
  17. Xinxin Chen*, Adam Dor-On, Langwen Hui*, Christopher Linden, Yifan Zhang*, “Doob equivalence and non-commutative peaking for Markov chains”, Journal of Noncommutative Geometry (2021), 15:4, 1469-1484.  arXiv
  18. Zhaodong Cai*, Matthew Faust*, A.J. Hildebrand, Junxian Li, Yuan Zhang*, “The Surprising Accuracy of Benford’s Law in Mathematics”, American Mathematical Monthly (2019) 127:3, 217-237 arXiv [Winner of the MAA Paul R. Halmos-Lester R. Ford Award, 2021]
  19. Yuying Dai*, Ankush Hore, Siqi Jiao*, Tianxu Lan*, Pavlos Motakis, “Continuous factorization of the identity matrix”, Involve, Vol. 13 No. 1 (2020) 149–164 arXiv
  20. Weiru Chan*, Jared Krandel*, “Interpolating Classical Partitions of the Set of Positive Integers”,  Ramanujan Journal of Mathematics 53 (2020) 209–241, arXiv,
  21. Alexi Block Gorman, Philipp Hieronymi, Elliot Kaplan, Ruoyu Meng*, Erik Walsberg, Zihe Wang*, Ziqin Xiong*, Hongru Yang*, “Continuous regular functions”, Logical Methods of Computer Science, Vol. 16 No 1 (2020), arXiv
  22. Sara M. Clifton, Kaitlin Hill, Avinash J. Karamchandani, Eric A. Autry, Patrick McMahon*, Grace Sun*, “Mathematical Model of Gender Bias and Homophily in Professional Hierarchies”, Chaos: An Interdisciplinary Journal of Nonlinear Science 29, 023135 (2019), arXiv
  23. Zhaodong Cai*, Matthew Faust*, A.J. Hildebrand, Junxian Li, Yuan Zhang*, “Leading Digits of Mersenne Numbers”, Experimental Mathematics, (2019),  DOI: 10.1080/10586458.2018.1D551162
  24. Ivan Contreras, Boyan Xu*, “The Graph Laplacian and Morse Inequalities”, Pacific Journal of Mathematics, Vol. 300, No 2 (2019) arXiv
  25. Ivan Contreras, Michael Toriyama*, Chengzheng Yu*, “Gluing of graph Laplacians and their spectra”, Linear and Multilinear Algebra (2018), DOI: 10.1080/03081087.2018.1516727 
  26. Rachneet Kaur, Xun Lin*, Alexander Layton*, Manuel Hernandez*, Richard Sowers, “Virtual Reality, Visual Cliffs, and Movement Disorders,” 2018 40th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), pp. 81-84, DOI: 10.1109/EMBC.2018.8512246
  27. Chuan Du*, Christopher Szul*, Adarsh Manawa*, Nima Rasekh, Rosemary Guzman, Ruth Davidson, “RGB image-based data analysis via discrete Morse theory and persistent homology”, Preprint (2018), arXiv
  28. Zhaodong Cai*, A.J. Hildebrand, Yunxian Li, “A local Benford’s Law for arithmetic sequences”, Int. J. Number Theory 15 (2019), 613-638.(2018), arXiv
  29. A.J. Hildebrand, Junxian Li, Xiaomin Li*, Yun Xie*, “Almost Beatty Partitions”, J. Integer Seq. 22 (2019), Article 19.4.6 (2018), arXiv
  30. Weiru Chen*, Mo Jiao*, Calvin Kessler*, Amita Malik, Xin Zhang, “Spatial Statistics of Apollonian Gaskets”, Experimental Mathematics  (2017),  DOI: 10.1080/10586458.2017.1385037 
  31. Zhaodong Cai*, Matthew Faust*, A.J. Hildebrand, Yunxian Li, Yuan Zhang*, “Leading Digits of Mersenne Numbers”, Experimental Mathematics (2019), arXiv
  32. Ivan Contreras, Sarah Loeb, Chengzheng Yu*, “Hyperwalk Formulae for Even and Odd Laplacians in Finite CW-Hypergraphs”, Preprint (2017) arXiv
  33. Rachneet Kaur, Daan Michiels, Vivek Kaushik*, Martin Bantchev*, Manuel Hernandez, Richard Sowers, “A Brain Computer Interface Approach To Examine Changes In Anxiety While Walking In A Virtually Infinite World”, 2017 Biomedical Engineering Society Annual Meeting
  34. Yingying Ren*, Sihan Zha*, Jingwen Bi*, Jose A. Sanchez*, Cara Monical, Michelle Delcourt, Rosemary Guzman, Ruth Davidson, “A combinatorial method for connecting BHV spaces representing different numbers of taxa”, Preprint (2017), arXiv
  35. Chengzheng Yu*, “Super-walk formulae for even and odd Laplacians in finite graphs”, Rose-Hulman Undergraduate Mathematics Journal: Vol. 18 : Issue 1, Article 16, available at: https://scholar.rose-hulman.edu/rhumj/vol18/iss1/16 
  36. Jared C. Bronski, Yizhang He*, Xinye Li*, Yue Liu*, Danielle Rae Sponseller*, Seth Wolbert, “The stability of fixed points for a Kuramoto model with Hebbian interactions”, Chaos 27(2017), DOI:  10.1063/1.4983524 
  37. Jessica Li*, Laura Schaposnik, “Interface control and snow crystal growth”, Phys. Rev. E (2016),  vol. 93, no. 2 (2016), 023302, arXiv
  38. Jason Hempstead*,  “Apollonian Circle Packings and the Riemann Hypothesis,” Rose-Hulman Undergraduate Mathematics Journal: Vol. 16 : Issue 2, Article 13, available at: https://scholar.rose-hulman.edu/rhumj/vol16/iss2/13 
  39. A. Turner*, A. Uppal*, P. Xu*, “Spacing distribution of a Bernoulli sampled sequence”, Preprint (2015) arXiv

Wolfram Demonstrations

  1. Alex Jin*, Efstathios Konstantinos Chrontsios Garitsis, A.J.  Hildebrand:  “Random Walks Based on Continued Fraction Expansions of Real Numbers”, http://demonstrations.wolfram.com/RandomWalksBasedOnContinuedFractionExpansionsOfRealNumbers,  Published: July 11, 2022
  2. Nick Kokkines*, Andre Park*, Efstathios Konstantinos Chrontsios Garitsis, A.J. Hildebrand:  “Fractal Curves Generated by Fourier Series”, https://demonstrations.wolfram.com/FractalCurvesGeneratedByFourierSeries,  Published: March 22, 2022.
  3. Xiaojun Jia*, Troy Yang*, Sarah Zimmerman*, Efstathios Konstantinos Chrontsios Garitsis: “Julia Sets Produced by Cubic Polynomials”,  https://demonstrations.wolfram.com/JuliaSetsProducedByCubicPolynomials, Published: July 26, 2021.
  4. Adithya Swaminathan, Dimitrios Tambakos*, A. J. Hildebrand: “Fractal Curves Generated by the Sum-of-Digits Function”,  https://demonstrations.wolfram.com/FractalCurvesGeneratedByTheSumOfDigitsFunction, Published: June 17, 2021.
  5. Ka Fung Tjin*: “Pseudorandom Walks with Generalized Gauss Sums”,     https://demonstrations.wolfram.com/PseudorandomWalksWithGeneralizedGaussSums, Published: June 25, 2020.
  6. Erqian Wang*: “Gauss Sum Walks”, https://demonstrations.wolfram.com/GaussSumWalks, Published: June 22, 2020.
  7. Yikai Teng*: “Simulating the Coupon Collector Problem”, http://demonstrations.wolfram.com/SimulatingTheCouponCollectorProblem, Published: May 30, 2019. 
  8. Raymond Harpster*: “Method of Lagrange Multipliers”, http://demonstrations.wolfram.com/MethodOfLagrangeMultipliers, Published: May 14, 2019
  9. Tianli Li*: “Randomness Test in Coupon Collecting”, http://demonstrations.wolfram.com/RandomnessTestInCouponCollecting, Published: May 6, 2019.
  10. Yiyin Shen* and Yitao Meng*: “Floating Random Walk Solution to the Dirichlet Problem”, http://demonstrations.wolfram.com/FloatingRandomWalkSolutionToTheDirichletProblem, Published: April 1, 2019.
  11. Cameron Nachreiner*: “Random Walk Solutions to the Dirichlet Problem for the Laplace Equation”, http://demonstrations.wolfram.com/RandomWalkSolutionsToTheDirichletProblemForTheLaplaceEquatio/, Published: March 5, 2019.    
  12. Yirui Luo*: “Random Walks and the Heat Equation”, http://demonstrations.wolfram.com/RandomWalksAndTheHeatEquation, Published: February 13, 2019.   
  13. Yuheng Chang*: “Discrete Harmonic Functions and Dirichlet’s Relaxation Method”, http://demonstrations.wolfram.com/DiscreteHarmonicFunctionsAndDirichletsRelaxationMethod/, Published: January 22, 2019
  14. Baihe Duan*: “Examples of 2D Harmonic Functions”, http://demonstrations.wolfram.com/ExamplesOf2DHarmonicFunctions, Published: January 18, 2019.
  15. Zelin Li* and A. J. Hildebrand:  “The 1860 US Presidential Election under Different Voting Methods”, http://demonstrations.wolfram.com/The1860USPresidentialElectionUnderDifferentVotingMethods/, Published: February 2016 

Websites

  1. Website “Video as a Sensor”, http://www.math.uiuc.edu/~r-sowers/ResearchGroup/VAS.html Work conducted for Rich Sowers and Dan Work’s Spring 2017 IGL project Geometry of Autonomous Vehicles and Summer 2017 IGL project Video as a Sensor.
  2. Website “Traffic Patterns in Manhattan”, http://www.math.uiuc.edu/~r-sowers/ResearchGroup/MTP.html Work conducted for Rich Sowers and Dan Work’s Fall 2016 and Spring 2017 IGL project Traffic Patterns in Manhattan.
  3. Website “Visual Cliffs and Virtual Reality”, http://www.math.uiuc.edu/~r-sowers/ResearchGroup/VRVC.html Work conducted for Rich Sowers and Manuel Hernandez’s Spring 2017 and Summer 2017 IGL project Visual Cliffs, Virtual Reality and Movement Disorders.
  4. The online site “Project 415x” (http://p415x.xyz) is based on Cary Malkiewich and Jenya Sapir’s Fall 2015 IGL research project Interactive Learning Tools for Linear Algebra.
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Email: math-iml@illinois.edu
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