## 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**, led by Prof. A J Hildebrand*n*dimensions**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