Research Activities
Under the wide-ranging umbrella of Discrete Applied Mathematics, our faculty members work on theoretical, algorithmic, and computational problems arising in Combinatorics, Graph Theory, Algebra and Algebraic Geometry, and Discrete Optimization. Some of the specific topics we have worked on include: topological graph theory and various crossing numbers of graphs; chromatic graph theory including list coloring, DP-coloring, many other graph coloring variants; graph packing; largest subgraph problems; random graph models; combinatorial search; liar games and coding theory; horn formulas and hypergraph theory; computational algebra and systems of polynomials; algebraic statistics; statistical network models; network flow and combinatorial optimization.
We hold regular seminars, featuring local as well as national and international speakers and attendees.
Recent Speakers:
Laura Albert (Wisconsin), Amin Bahmanian (IL State), Emily Barnard (DePaul), Kenneth Barrese (Brescia), Michael Barrus (Rhode Island), Tanya Berger-Wolf (UIC), Anton Bernshteyn (Georgia Tech), Debra Boutin (Hamilton), Steve Butler (Iowa St), Dan Cranston (VCU), Logan Crew (Waterloo), Michael Ferrara (NSF), David Galvin (Notre Dame), Sommer Gentry (US Naval Academy), Benjamin Grimmer (Cornell), Sogol Jahanbekam (SJSU), Iyad Kanj (DePaul), Diego Klabjan (Northwestern), Sasha Kostochka (UIUC), Sarah Loeb (HSC), Ruth Luo (South Carolina), Kevin Milans (WVU), Alexander Nikolaev (SUNY Buffalo), Will Perkins (UIC), Lev Reyzin (UIC), Bruce Sagan (Michigan State), Michael Santana (GVSU), Marcus Schaefer (DePaul), Songling Shan (IL State), Papa Sissokho (IL State), Zixia Song (Central Florida), Andrew Suk (UCSD), Michael Tait (Villanova), Doug West (UIUC), Stephanie van Willigenberg (British Columbia), Xuding Zhu (ZJNU).
IIT Discrete Math Research Seminar. (
Recent talks; Forthcoming talks.)
IIT Non-linear Algebra Research Seminar. (
Recent Talks; Forthcoming talks.)
Sign up for the mailing lists using the links above (if you are an IIT member) or by emailing the organizers listed below.
Please contact the seminar organizers (Hemanshu Kaul and Sonja Petrovic, respectively) if you would like to give a talk, or if you would simply like more information.
(An Incomplete List of) Conferences Organized by Members in Applied Math
- Workshop on Algebraic, extremal, and structural methods and problems in graph coloring, February 2024.
- Program on "Algebraic statistics and our changing world: New methods for new challenges" at the Institute for Mathematical and Statistical Innovation (IMSI), Chicago, 15 weeks in Fall 2023.
- Topic-Contributed Paper Session on "Algebraic and geometric methods in inference" at the Joint Statistics Meeting in Toronto, Canada, August 2023.
- Workshop on Random Algebraic Geometry at the Banff International Research Station (Alberta, Canada), April 2023.
- Special Session on "Recent Progress in Chromatic Graph Theory" at AMS meeting, April 2023, Virtual AMS Eastern Section Meeting.
- MEGA 2022 - Effective Methods in Algebraic Geometry, June 2022, Krakow, Poland.
- Special Session on "Enumerative and Extremal Problems in Chromatic Graph Theory" at AMS meeting, May 2022, Online (originally at University of Denver).
- International Conference on Algebraic Statistics 2020, Summer 2020 postponed to May 2022, Hawaii, USA.
- Summer School on Randomness and Learning in Non-Linear Algebra, July 2019, Max Planck Institute, Leipzig, Germany.
- Menger Day at IIT with Percis Diaconis (2017), Peter Winkler (2011), Donald Saari (2010).
- Special Session Random Commutative Algebra, SIAM conference for Applied Algebraic Geometry, Aug 2017, Atlanta.
- EXCILL III: Extremal Combinatorics at Illinois, August 2016, Illinois Institute of Technology, Chicago.
- Special Session on Algebraic Statistics and its Interactions with Combinatorics, Computation, and Network Science, AMS Central Sectional Meeting, Oct, 2015, Loyola University, Chicago.
- Workshop in honor of Professor Douglas West's 60th Birthday, June 2014, Institute of Mathematics and its Applications (IMA), University of Minnesota, Minneapolis.
- Biennial Conference on Algebraic Statistics, May 2014, Illinois Institute of Technology, Chicago.
- Special Session on Graph Theory, AMS-MAA-SIAM Annual Joint Meetings, Jan 2013, San Diego.
- Special Session on Graphs and Hypergraphs at AMS Meeting, November 2010, University of Notre Dame.
- 17th International Symposium on Graph Drawing, September 2009, DePaul University, Chicago.
- 47th Midwest Graph Theory Conference, November 2008, Illinois Institute of Technology, Chicago.
- Buck Fest in Honor of Fred McMorris, May 2008, Illinois Institute of Technology, Chicago.
- Special Session on Graph Theory at AMS Meeting, April 2008, Indiana University, Bloomington.
- Special Session on Graph Theory at AMS Meeting, October 2007, Depaul University, Chicago.
Educational Programs
Faculty and Long-term Visitors
Faculty in Applied Math
Faculty in other departments with related interests
- Computer Science:
- ECE:
- Other:
Long-term visitors in Applied Math
- Samantha Dahlberg, postdoc, 2022-2024.
- Shahrzad Jamshidi Zelenberg, postdoc, 2018-2020.
- Benjamin Reiniger, postdoc, 2016-2018.
- Rogers Mathew, visiting professor, Indian Institute of Technology Hyderabad, India, July 2022.
- Jeffrey Mudrock, visiting professor, College of Lake County, 2019-2020.
- Joungmin Song, visiting professor, Gwangju Institute of Science and Technology, South Korea, 2018-2019.
- Jeong-Hyun Kang, visiting professor, University of West Georgia, 2012-2013.
Current Graduate Students in Applied Math
- Gunjan Sharma. [advisor: Kaul]
Extremal and Enumerative problems on DP-coloring of graphs.
- Daniel Dominik. [advisor: Kaul]
Probabilistic problems on DP-coloring of graphs.
- Bahareh Kudarzi. [advisor: Kaul]
- Alaittin Kirtisoglu.
- Jason Cho. [advisor: Kaul]
Recent Alumni from Applied Math
PhD from IIT
- William Schwartz, 2021. [advisors: Kaul and Petrovic]
Temporal Network Models: including Permutation-uniform Markov chains of networks, temporal stochastic block models, dynamic algorithms for the lexicographic Winner Determination Problem.
Honorable mention, NSF Graduate Fellowship, 2016.
Associate Director, Secretariat Economists.
- Adam Rumpf, 2020. [advisor: Kaul]
Mathematics of Civil Infrastructure Network Optimization: including Network simplex algorithm for interdependent network flows, Network design of public transit with social access objectives, and Trilevel network interdiction game for interdependent networks.
Assistant Professor of Teaching in Applied Math, Florida Polytechnic University, Lakeland, FL, USA.
- Dane Wilburne, 2018. [advisor: Petrovic]
Probabilistic methods in commutative algebra, algebraic statistics, computational algebra, statistical network modeling, combinatorics.
Postdoc at ICERM, Brown University.
- Jeffrey Mudrock, 2018. [advisor: Kaul]
The List Coloring problem and its Equitable Variants: including Alon-Tarsi number and chromatic-choosability of graphs, criticality and list-color function for graph choosability, equitable list coloring, and proportional choosability.
Won the Menger Student Award, IIT, 2018
Professor of Mathematics at the College of Lake County, Illinois, USA.
- Christodoulos Mitillos, 2016. [advisor: Kaul]
The Fall-Coloring of Graphs: including existence conditions for and construction of graphs with arbitrary Fall colorings, Fall coloring with regard to unary and binary graph operators.
Lecturer, Mathematics, University of Cyprus, Cyprus.
- Jinyu Huang, 2015. [advisor: Kaul]
Approximation Algorithms for Matroid Optimization: including Online algorithms for matroid secretary problem, results towards Matroid Expansion Conjecture, complexity of linear matroid intersection and linear matroid parity problems.
Assistant Professor of Computer Science at the Sichuan University of Science and Engineering, China.
- Gergely Balint, 2014. [advisor: Ellis]
Non-adaptive group testing, Steiner systems, and latin squares.
Lecturer, CS, University of Debrecen, Hungary.
- Oscar Ortega, 2008. [advisor: McMorris]
Concensus and Location: The Mean Function on Trees.
Professor, Mathematics, Harold Washington College (City Colleges of Chicago).
MS from IIT
- Christian Tomlins. [advisors: Ellis and Kaul]
Distinguishing List Colorings of Graphs.
Analyst, Dept. of Defense.
- Quinn Stratton, 2020. [advisor: Kaul]
Research on DP-Coloring of Cartesian Products of Graphs
Lecturer of Mathematics at Lewis University.
- James Panek, 2017. [advisor: Ellis]
Graph partitioning with eigenvectors.
- Hongwei Jin, 2015. [advisor: Kaul]
New stochastic optimization models and algorithms for ``Microgrid with Renewable Energy''.
PhD Candidate in Computer Science at UIC.
- Melinda Bulin Clardy, 2015. [advisor: Ellis]
Disjunctness properties resulting from concatenation of group testing matrices.
- Yunjiao Liu, 2014. [advisor: Pelsmajer]
Maximum Induced Subgraphs of K-Trees With Components of Order 1 Or 2.
- Lujia Wang, 2013. [advisor: Pelsmajer]
Two Problems on Crossing Numbers of Graphs.
PhD candidate, Math, UIC.
- Mary Fidler, 2011. [advisor: Kaul]
New algorithms for "The Simple Equal Flow Problem On Generalized Networks".
Researcher in New Mexico Consortium for applications of discrete optimization.
- Daniel Tietzer, 2011. [advisor: Ellis]
Adaptive covering codes in the q-ary hypercube.
- James Williamson, 2011. [advisor: Ellis]
Analysis of the application of the liar machine to the q-ary pathological liar game with a focus on lower discrepancy bounds.
- Hong Liu, 2010. [advisor: Pelsmajer]
Dominating sets in triangulations on surfaces.
PhD candidate, Math, UIUC
- Joseph Srigiri, 2009. [advisor: Kaul]
Computational Discrete Geometry and Optimization on ``Stochastic Models for the Art Gallery Problem: A Computational Study''.
Commodities trader in Finance industry.
PhD from other universities
- Dan Kosmas, BS IIT 2017, PhD Candidate Math, RPI.
- Benjamin Grimmer, MS IIT 2017, PhD OR, Cornell, 2021.
- Hongwei Jin, MS IIT 2015, PhD Candidate CS, UIC.
- Lujia Wang, MS IIT, 2013; PhD Math (Combinatorics), UIC, 2018.
- Cory Knapp, BS IIT, 2011; PhD CS (Mathematical Foundations), U. of Birmingham, 2018.
- Hannah Kolb, BS IIT 2010; PhD Math (Graph theory), UIUC, 2016.
- Hong Liu, MS IIT 2010; PhD Math (Combinatorics and Graph Theory), UIUC, 2015.
- Kevin Ventullo, BS IIT 2009; PhD Math (Algebraic Number Theory), UCLA, 2014.
- Jon Beagley, BS IIT 2008, PhD Math (Discrete Geometry), George Mason U., 2013.
Any updates? Any questions? Email: Hemanshu Kaul