Illinois Mathematics Lab project archive

Fall 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

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

Graduate Leaders – Wilmer Smilde, Nikolay Sheshko

IML scholars – Yukang Qiu, Dmitriy Shvydkoy, Leslie Hu, Xianhao An, Yichi Zhai

Automated proofs of partition congruences, led by Prof. Scott Ahlgren

Graduate Leaders – Cruz Castillo

IML scholars – Tyler Cushing, Hao Cai, Jennifer Rotter, Eeshan Zele

Transforms of Functions – Theory and Applications, led by Prof. Joseph Rosenblatt

Graduate Leaders – Wonwoo Kang, Wyatt Kuehster

IML scholars – Weijian Chen, Paul Ge, Jeffrey Liu, Yayan Jiang, Sanjay Manoj

Win/Loss Sequences in Sports Leagues, led by Prof. AJ Hildebrand

Graduate Leaders – Manisha Garg

IML scholars – Mingqian Wang, Nathan Liu, Zheer Wang, Matthew Leonardson, Benjamin Cheng, Desi Nainar

Scale-free First Passage Percolation, led by Prof. Partha Dey

Graduate Leaders – Aditya Gopalan, Daecheol Kim

IML scholars – Hansheng Liu, Haotian Ju, Shuzhen Zhang, Linzhe Teng

Mapping out the quantum channel zoo, led by Prof. Felix Leditzky

Graduate Leaders – Sujeet Bhalerao

IML scholars – Anne Que, Lumi Xu, Ben Booker, Tianshun Gao, Yuxuan Wan

Real superalgebras, led by Prof. Dan Berwick-Evans

Graduate Leaders – Yigal Kamel, Levi Poon

IML scholars – Stevie Ridens, Yi Jin, Charles Cooper, Nathan Baker, Ethan Huang, Reese Ramos

List coloring with requests for planar graphs, led by Prof. Peter Bradshaw

Graduate Leaders – Robert Krueger

IML scholars – Siyu Gan, Fawzan Ali, John Su, Saurav Chittal

Finding the Department’s Deep Structure, led by Prof. Yuliy Baryshnikov

Graduate Leaders – Haoyuan Li, Anji Dong, Ning Jiang

IML scholars – Prajeet Basu, Adam Wawrowski, Ziqi Xu, Zifan Dong, Qingyu Yi

Spring 2023 projects

Win/loss sequences in sports leagues, led by Prof. Emeritus AJ Hildebrand

Graduate leaders – Manisha Garg

IML scholars – CHARLIE MARTELL, ANH PHUNG, MOHIT SINGH, ALEX STRATTON

Mathematical Models II, led by Prof. Steven Bradlow  and Prof. Karen Mortensen

Graduate leader – Ada Stelzer

IML scholars – Emily Gutknecht, Qingwen Liu, Yuan Qian, Timothy Thieme

Quantum Information and Error Correction, led by Roy Araiza

Graduate Leader – Peixue Wu

IML scholars Jihong Cai, Yushan Chen, Abraham Holtermann, Chieh Hsu, Tushar Mohan, Zeyuan Yu

Rumor propagation on a spread-out lattice graph, led by Prof. Partha Dey

Graduate Leader – Daecheol Kim

IML scholars – Tianyi Huang, Yongzheng Yang, Hansen Liu

Talbot Effect On The 2-Sphere, led by Prof. Burak Erdogan

IML scholars –  Haotian Ju, Jiazheng Wang, Yiheng Zhou,

Graduate Leader – Ryan McConnell

Quantum Circuit, Permutations, and Quantum Machine Learning, led by Prof. Marius Junge

Graduate Leader – Ivor Yidong Chen

IML scholars – Bozhang Chen, Linzhe Teng, Yun Wang, Shuzhen Zhang

Uniform Distribution and Rigidity, led by Prof. Emeritus Joseph Rosenblatt

Graduate Leader – Sujeet Bhalerao

IML scholars – Atharv Gudi, Yi Jin, Atharva Naik, Yue Su, Ying Zhao

Data from Ukraine, led by Prof. Richard Sowers

IML scholars –Wenqi Zeng, Luke Peng, Srikar Annapragada

Fall 2022 Projects

Phase Retrieval, led by Prof. Emeritus Joseph Rosenblatt

IGL Scholars –  David James, Prasanna Jayaganesh, Aryaman Srikant, Yulan Ma, Jun Ye, Bo Yin

Shallow Quantum Circuits, Permutations, and Quantum Query Algorithms, led by Prof. Marius Junge

Graduate Leader – Ivor Yidong Chen

IGL scholars – Hassan Boukhamseen, Caleb Chiang, Sparsh Srivastava, Rishab Tirupathi, Mingqi Wang,

Detection of displacement and needs related to the Russia-Ukraine conflict, led by Prof. Richard Sowers

Graduate Leader – Jung Soo Park

IGL Scholars – Adrian Russo, Alex Stratton, Arpandeep Khatua, Hamiz Anjum, Zihan Zhou, Zijun Yu

FRACTAL FOURIER SERIES, led by Prof.  Emeritus A.J. HILDEBRAND

Graduate Leader – Manisha Garg

IGL Scholars – Saurav Chittal, Tri Do, Kevin Liu, Malachi Robinson

Mathematical Models, led by Prof. Steven Bradlow and Prof. Karen Mortensen

Graduate Leader – Ada Stelzer

IGL Scholars – Emily Gutknecht, Timothy Thieme, Cindy Wang

Detection of displacement and needs related to the Russia-Ukraine conflict, led by Prof. Jana Diesner

Graduate Leader – Pingjing Yang

IGL Scholars – Hamiz Anjum, Arpandeep Khatua, Alex Stratton

Quantum Channels and Error Correction, led by Roy Araiza

Graduate Leader – Peixue Wu

IGL Scholars – Jihong Cai, Yushan Chen, Abraham Holtermann, Tushar Mohan, Sam Pasquesi, Owen Shi, Libo Xu, Zeyuan Yu

Quantum Teleportation and Quantum State Discrimination, led by Prof. Felix Leditzky

Graduate Leader – Sujeet Bhalerao, Stephen Zhou

IGL Scholars – Mayank Bhatia, Mason Camp, Devanshi Chakrabarti, Rishi Narayanan, Praneet Rathi

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