Illinois Mathematics Lab project archive

Spring 2024 Projects

ColorTaiko!, led by Prof. Igor Mineyev

Graduate leaders – Manisha Garg, Aziz Bouland, IML scholars – Anvitha Manepalli, Aditya Ved,Aditya Kshirsagar, Enson (Zhenyi) Gai, Kevin Liu, Jeongjae Park

Optimizing capacities: what shape does best when adding a dimension?, led by Carrie Clark and Prof. Richard Laugesen

Graduate leaders – Qiuling Fan, IML scholars – Chris Becraft, Ben Taylor, Haoqi Chen, Yuan Qian

Scattering Diagrams and Broken Lines, led by Prof. James Pascaleff

Graduate leaders – Chengbin Zhu, IML scholars – Joey Zhou, Saibo Xu, Matthew Leonardson, George White

Spatial Models of Evolutionary Dynamics, led by Prof. Daniel Cooney

Graduate leaders – Muhammad Raza

IML scholars – Seokhwan Moon, Chenning Xu, Ahmad Rahman, Edwin Shen, Jirui Liu, Tianyong Yao

Tennessee Traffic, led by Prof. Richard Sowers

Graduate leaders – Karthik Vasu

IML scholars – David (Weidai) He, David Li, Neha Valavala, Weijian Chen

Winter Spaces and the Stabilizer Formalism, led by Roy Araiza

Graduate leaders – Yefei Zhang

IML scholars – Adrian Calinescu, Morgan Anderson, Dheeran Wiggins, Ben Booker, Naro Panjaitan, Dilys Wu

Paintability of Multipartite Graphs, led by Peter Bradshaw

Graduate leaders – Grace McCourt, The Nguyen, Ramon Garcia Alvarez

IML scholars – Amit Krishnaiyer, Atlas Chen, Braden Dean, Tianyue Cao, Arvind Murty, Yat Hei Yung

Predictability and Competitiveness in Sports Leagues, led by Prof. AJ Hildebrand

Graduate leaders – Bingyan Liu

IML scholars – Yiqian Zhang, Yihan Gao, David Xia, Samuel Lam

Developing Inclusive Outreach Materials in Mathematics, led by Prof. Karen Mortensen

Graduate leaders – Ada Stelzer, Grace McCourt

IML scholars – Chen-Wei Chou, Anmol Shah, Jane Pak, Yuri Chen

Quantum Gates for Quantum Noise, led by Prof. Marius Junge

Graduate leaders – Advith Govindarajan

IML scholars – Arjun Aggarwal, Ashmit Dutta, Divij Garg, Minghao Shi, Stevie Ridens

(Linear) Poisson structures and their cohomology, led by Florian Zieser

Graduate leaders – Wonwoo Kang

IML scholars – Xianhao An, Xinyu Wang, Uyen Nguyen, Gabe Lewis, Dmitriy Shvydkoy, Luke Bielawski

Fall 2023 Projects
  • Linear Poisson structures in dimension 4, led by Prof. Florian Zieser
  • Automated proofs of partition congruences, led by Prof. Scott Ahlgren
  • Transforms of Functions – Theory and Applications, led by Prof. Joseph Rosenblatt
  • Win/Loss Sequences in Sports Leagues, led by Prof. AJ Hildebrand
  • Scale-free First Passage Percolation, led by Prof. Partha Dey
  • Mapping out the quantum channel zoo, led by Prof. Felix Leditzky
  • Real superalgebras, led by Prof. Dan Berwick-Evans
  • List coloring with requests for planar graphs, led by Prof. Peter Bradshaw
  • Finding the Department’s Deep Structure, led by Prof. Yuliy Baryshnikov

Spring 2023 projects
  • Uniform distribution and rigidity, led by Prof. Emeritus Joseph Rosenblatt
  • Talbot effect on the 2-sphere, led by Prof. Burak Erdogan
  • Math models, led by Prof. Steven Bradlow and Prof. Karen Mortensen
  • Quantum circuits and quantum machine learning II, led by Prof. Marius Junge
  • Rumor propagation on a spread-out lattice graph, led by Prof. Partha Dey
  • Win/loss sequences in sports leagues, led by Prof. Emeritus A J Hildebrand
  • Quantum channels and error correction II, led by Roy Araiza
  • Data from Ukraine, led by Prof. Richard Sowers
  • Data in Ukraine II, led by Prof. Richard Sowers
2022 projects
  • Modular forms and homotopy, led by Prof. Vesna Stojanoska
  • Developing advice for getting into graduate school, led by Prof. Susan Tolman
  • Rainbow connections in multipartite graphs, led by Sean English
  • Select topics in quantum information theory, led by Roy Araiza and Prof. Felix Leditzky
  • Optimal approximations, led by Prof. Emeritus Joseph Rosenblatt
  • Competition with random walk on random graphs, led by Prof. Partha Dey and Daesung Kim
  • Dynamics of generalized coupled spin systems, led by Joseph Palmer
  • Computing packing capacities from polygons, led by Joseph Palmer
  • Randomness in Number Theory, led by Prof. Emeritus A J Hildebrand
  • Edge colorings without small substructures, led by Sean English
  • Burning graphs, led by Sean English
  • The math department’s deep structure, led by Prof. Yuliy Baryshnikov
  • Root dynamics for random polynomials under differentiation, led by Prof. Yuliy Baryshnikov and Tomoyuki Shirai (Kyushu)
  • Distance cospectrality of networks, led by Sean English
  • Math models, led by Prof. Steven Bradlow
  •  Phase retrieval, led by Prof. Emeritus Joseph Rosenblatt
  •  Detection of displacement and needs related to the Russia-Ukraine conflict, led by Jana Diesner and Prof. Richard Sowers
  •  Fractal Fourier series, led by Prof. Emeritus A J Hildebrand
  •  Quantum channels and error correction, led by Roy Araiza
  •  Permutations and shallow quantum circuits, led by Prof. Marius Junge
  •  Quantum teleportation and quantum state discrimination, led by Prof. Felix Leditzky
2021 projects
  • Arithmetic properties of partition ranks, led by Olivia Beckwith
  • Developing exciting outreach material III, led by Prof. Philipp Hieronymi
  • Developing Pecan, led by Prof. Philipp Hieronymi
  • Gait dynamics
  • Greek drivers
  • Half integral weight Eisenstein series, led by Olivia Beckwith
  • Higher symmetries in geometry and physics, led by Prof. Daniel Berwick-Evans
  • Homotopy, modular forms, and the spectrum Q(l)
  • Interactive visualizations with Mathematica II, led by Prof. Emeritus Joseph Hildebrand
  • Packing capacities of Delzant polygons, led by Joseph Palmer
  • Packing capacities of semitoric polygons, led by Joseph Palmer
  • P-adic numbers and ultrametric calculus, led by Shiang Tang
  • Patient hospital fall dynamics, led by Prof. Richard Sowers and Mao Li
  • Semitoric helices and polygons, led by Joseph Palmer
  • Theorem proving in LEAN, led by Prof. Phillipp Hieronymi
  • Turán problems, led by Prof. Jozsef Balog
  • Uni-High Project: Representation of integers as sum of squares, led by Debmalya Basak
    • Uni-High Project: A project in learning theory, led by Jiajie Yang
    • Uni-High Project: A project in extremal combinatorics, led by Igor Albuquerque Araujo
    • Uni-High Project: Some applications of theoretical computer science, led by Rocco Davino
    • Uni-High Project: Counting infinite symmetric tiling patterns, led by Joseph Rennie
    • Building a computer by braiding colorful knots II, led by Eric Samperton
    • Competition among random walks on torus, led by Prof. Partha Dey and Daesung Kim
    • Detecting knottedness with quantum computers, led by Eric Samperton
    • Developing exciting outreach material IV, led by Prof. Susan Tolman
    • Interactive Visualizations with Mathematica III, led by Prof. Emeritus A J Hildebrand
    • Modular forms and the homotopy of Q(l), led by Prof. Vesna Stojanoska
    • Toric and semitoric packing capacities, led by Joseph Palmer
    • Zeros of electrical fields, led by Prof. Emeritus Joseph Rosenblatt
2020 projects
  • Building a computer by braiding colorful knots, led by Eric Samperton
  • Building a theorem prover, led by Prof. Philipp Hieronymi
  • Cyclic vectors for certain D-modules, led by Prof. Aron Heleodoro
  • Developing exciting outreach material II, led by Prof. Philipp Hieronymi
  • Finding Weierstrass equations for elliptic curves
  • Finite subalgebras of the Steenrod algebra and their modules, led by Dominic Culver
  • Firefighters on graphs, led by Sean English
  • Game theory with arithmetic progressions, led by Sean English
  • Higher-shuffles operads II, led by Aron Heleodoro
  • Interactive visualizations with Mathematica, led by Prof. Emeritus A J Hildebrand
  • Majestic colorings of graphs, led by Sean English
  • Pairs of disjoint matchings, led by Anush Tserunyan
  • Saturation problems for paths in hypergraphs, led by Sean English
  • Uni-High Project: Exploring algorithms, led by Weihang Wang
  • Uni-High Project: Geometric group theory and computation, led by Heejoung Kim
  • Uni-High Project: “Interactive theorem proving in Lean: Can we teach proofs to a computer?”, led by Vaibhav Karve
  • Uni-High Project: Investigations in combinatorial game theory, led by Bob Krueger
  • Uni-High Project: The hunt for great graphs, led by Madie Farris
  • Calculus, geometry, and probability in n dimensions, led by Prof. A J Hildebrand
  • Developing exciting outreach material, led by Prof. Philipp Hieronymi
  • Exploring divisibility patterns in colored partitions, led by Olivia Beckwith
  • Mathematics of change—Ringing and the Altgeld Chimes, led by Prof. Jeremy Tyson
  • Pecan: An automated theorem prover, led by Prof. Philipp Hieronymi
  • Polygonal billiard tables with obstacles, led by Chandrika Sadanand
  • Theorem proving in LEAN, led by Prof. Philipp Hieronymi
  • Traveling along straight lines on an infinite surface with finite area, led by Chandrika Sadanand
  • Traveling along straight lines on a symmetric infinite surface, led by Chandrika Sadanand