Department of Applied Mathematics

Discrete Applied Mathematics

The discrete applied mathematics research group studies theoretical, algorithmic, and computational problems in the fields of graph theory, discrete optimization, combinatorics, and algebraic geometry, with applications in biology, computer science, physics, management sciences, and engineering. Network science, with fundamental concepts from graph theory and computational techniques from discrete optimization, is widely applied to problems arising in transportation/communication, distribution, and security of resources and information. Combinatorial search incorporates graph theory, set systems, and algorithms to tackle information-theoretic questions in topics such as message transmission, data compression, and identification of defective samples in a population. Computational algebra joins tools from algebraic geometry with randomized algorithms from discrete geometry to develop methods to solve systems of polynomial equations arising in statistical inference and mathematical modeling.


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    Faculty with a Primary or Secondary Interest in Discrete Applied Mathematics

    Michael Pelsmajer
    Associate Professor of Applied Mathematics
    Sonja Petrovic
    Associate Professor of Applied Mathematics
    Robert Ellis
    Associate Professor of Applied Mathematics
    Despina Stasi
    Associate Teaching Professor of Applied Mathematics
    Hemanshu Kaul
    Co-Director, M.S. in Computational Decision Science and Operations Research (CDSOR) Associate Professor of Applied Mathematics
    Maggie Cheng
    Professor of Applied Mathematics Director, Center for Interdisciplinary Scientific Computation
    Associate Teaching Professor, Department of Applied Mathematics, Jeong-Hyun Kang
    Associate Teaching Professor of Applied Mathematics, Director of Applied Mathematics Masters Programs
    Post-doctorial Scientist
    Associate Teaching Professor of Applied Mathematics

    Related Seminars

    Ph.D. Students

    • Bahareh Kudarzi, adviser: H. Kaul
    • Miles Bakenhus, adviser: S. Petrovic
    • Gunjan Sharma, adviser: H. Kaul
    • Amirreza Eshraghi, adviser: S. Petrović
    • Daniel Dominik, adviser: H. Kaul
    • Alaittin Kirtisoglu, adviser: H. Kaul

    Recent Research Grants

    • DOE Office of Science Award number 1010629 (PI Petrović):  Randomized Algorithms for Scientific Computing, 2022-2025. (Joint with Argonne National Laboratory.)
    • Simons Foundation (PI S. Petrović) Collaboration Grant for Mathematicians 854770 (2021-2022) and a Travel Support for Mathematicians Gift (2022-2026)
    • NSF DMS-1522662 (PIs S. Petrovic and D. Stasi): Randomized Algorithms in Computational Algebra, 2015-2019.

    Recent Publications

    • Radoslav Fulek, Michael J. Pelsmajer, and Marcus Schaefer. Hanani-Tutte for Radial Planarity II. Electron. J. Comb. 30(1) (2023)
    • Jelena Mojsilović, Dylan Peifer, and Sonja Petrović. Learning a performance metric of Buchberger's algorithm, Involve, a Journal of Mathematics 16-2 (2023), 227--248. 
    • William K. Schwartz, Sonja Petrović, and Hemanshu Kaul. Longitudinal network models and permutation-uniform Markov chains,  Scandinavian Journal of Statistics, (2022).
    • Elizabeth Gross, Vishesh Karwa, Sonja Petrović. Algebraic statistics, tables, and networks: The Fienberg advantage. In: Carriquiry, A.L., Tanur, J.M., Eddy, W.F. (eds) Statistics in the Public Interest. (2022) Springer Series in the Data Sciences. Springer, Cham.
    • Tobias Boege, Sonja Petrović, and Bernd Sturmfels. Marginal independence models,   In Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation (ISSAC ’22), July 4–7, 2022, Villeneuve-d’Ascq, France. ACM, New York, NY, USA.
    • Vishesh Karwa, Sonja Petrović and Denis Bajić. DERGMs: Degeneracy-restricted exponential random graph models, Network Science, Volume 10, Issue 1, March 2022 , pp. 82 - 110.
    • Sonja Petrović and Shahrzad Jamshidi Zelenberg. Threaded Gr\"obner Bases: a Macaulay2 package, Journal of Software for Algebra and Geometry, Vol. 11 (2021), 123–127. 
    • Hemanshu Kaul, Jeffrey A. Mudrock and Michael J. Pelsmajer. On equitable list arboricity of graphs, Australas. J. Comb. 80, 419–441 (2021)
    • Radoslav Fulek, Michael J. Pelsmajer, and Marcus Schaefer. Strong Hanani-Tutte for the Torus. SoCG 2021: 38:1-15
    • John R. Jungck, Michael J. Pelsmajer, Camron Chappel, and Dylan Taylor. Space: The Re-Visioning Frontier of Biological Image Analysis with Graph Theory, Computational Geometry, and Spatial Statistics. Mathematics 9(21), 2726 (2021).
    • Hemanshu Kaul, Jeffrey A. Mudrock, and Michael J. Pelsmajer. Partial DP-coloring of graphs. Discrete Math. 344(4), 112306 (2021).
    • Hemanshu Kaul, Jeffrey A. Mudrock, Michael J. Pelsmajer, and Benjamin Reiniger. A simple characterization of proportionally 2-choosable graphs. Graphs and Combinatorics 36 (2020): 679-687.
    • Marta Casanellas, Sonja Petrović and Caroline Uhler. Algebraic Statistics in Practice: Applications to Networks, Annual Reviews of Statistics and its Applications (2020). 7 (1), 227-250.
    • Hemanshu Kaul, Jeffrey A. Mudrock, Michael J. Pelsmajer, and Benjamin Reiniger. Proportional choosability: a new list analogue of equitable coloring Discrete Mathematics 342(8), 2371-2383 (2019).
    • S. Petrovic. What is ... a Markov Basis? Notices of the American Mathematical Society (August, 2019).
    • S. Petrovic, A. Thoma, and M. Vladoiu. Hypergraph Encodings of Arbitrary Toric Ideals, Journal of Combinatorial Theory, Series A (2019), Vol. 166, pp. 11-41.
    • S. Petrović, A. Thoma, and M. Vladoiu. Bouquet Algebra of Toric Ideals. Journal of Algebra (2018), Vol. 512, pp. 493-525.