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Monday, April 27
 

7:59am CDT

The 34th Annual UWEC Mathematics Retreat
Monday April 27, 2026 7:59am - 4:30pm CDT
The UWEC Mathematics retreat is a celebration of the research done in the Math department at UWEC. The event features talks given by students and faculty members on topics that they have been researching independently, in the context of student-faculty research, and during their classes. During the afternoon it concludes with a keynote speaker and a fun team-based mathematics competition.
Monday April 27, 2026 7:59am - 4:30pm CDT
Hibbard Hall

8:25am CDT

Wallpaper Groups
Monday April 27, 2026 8:25am - 8:40am CDT
From ancient carvings and historic motifs, wallpaper groups and frieze patterns have been presented for years. Focusing on specific frieze patterns and wallpapers groups, this presentation explains the symmetries and markings that make up repetition. By using reflections, rotations, and transformations, I will explain useful ways to identify and create frieze patterns and wallpaper groups.

Presenters
RC

Rylie Christnovich

University of Wisconsin - Eau Claire

Faculty Mentor
CL

Chloe Lewis

Mathematics, University of Wisconsin - Eau Claire
Monday April 27, 2026 8:25am - 8:40am CDT
Hibbard Hall 320 124 Garfield Ave, Eau Claire, WI 54701, USA

8:30am CDT

Area Proof of the Pythagorean Theorem
Monday April 27, 2026 8:30am - 8:50am CDT
Area proofs of the Pythagorean theorem provide a geometric approach to understanding the relationship between the sides of a right triangle. These visual proofs use the additivity and moving principles to demonstrate equality of area and convey the theorem clearly without relying on algebraic manipulation. Students enrolled in the Spring 2026 Math 304 course will engage attendees in a variety of area proofs in this informal presentation.
Presenters
NH

Natalie Houle

University of Wisconsin - Eau Claire

RG

Renee Giese

University of Wisconsin - Eau Claire
KJ

Kailey Johnson

University of Wisconsin - Eau Claire
GS

Gabe Sanders

University of Wisconsin - Eau Claire

LE

Lydia Edison

University of Wisconsin - Eau Claire
AN

Ava Northamer

University of Wisconsin - Eau Claire

BL

Becky Lueloff

University of Wisconsin - Eau Claire

GD

Gabi DeRoma

University of Wisconsin - Eau Claire

MT

Mykayla Tharp

University of Wisconsin - Eau Claire
CR

Cathy Roche

University of Wisconsin - Eau Claire

Faculty Mentor
KR

Katrina Rothrock

Mathematics, University of Wisconsin - Eau Claire
Monday April 27, 2026 8:30am - 8:50am CDT
Hibbard Hall 323 124 Garfield Ave, Eau Claire, WI 54701, USA

8:30am CDT

Fermat's Christmas Theorem: Proving Prime Numbers as the Sum of Two Squares
Monday April 27, 2026 8:30am - 8:50am CDT
On Christmas Day in 1640, Pierre de Fermat sent a letter to a fellow mathematician famously claiming that every prime number of the form 4k+1 can be uniquely expressed as the sum of two integers. This conjecture was unsolved until Euler proved it over a century later; much time after, many mathematicians would come up with their own iterations and versions of proving the theorem. In this presentation, we will review and go into detail with some of the most popular proofs on this theorem, which will include Euler's proof of infinite descent, Zagier's "one-sentence proof," and the Gaussian Integer proof.
Presenters
TD

Thomas Davidsaver

University of Wisconsin - Eau Claire
Faculty Mentor
AM

aBa Mbirika

Mathematics, University of Wisconsin - Eau Claire
Monday April 27, 2026 8:30am - 8:50am CDT
Hibbard Hall 203 124 Garfield Ave, Eau Claire, WI 54701, USA

8:30am CDT

The Locker Problem
Monday April 27, 2026 8:30am - 8:50am CDT
Welcome to the “Locker Problem” where we will take a very complex problem and break it down step by step for you to go home and wow your friends and family. In this presentation you will see how even the strangest and most complex problems are solved by the simple components of numbers and basic mathematics. Our presentation will cover the infamous “Locker Problem” and how to solve it, along with showing you more ways to solve extensions of this problem and ultimately become the towns (quote unquote) biggest NERD!
Presenters
JC

Joshua Cole

University of Wisconsin - Eau Claire
ND

Noah DeMoss

University of Wisconsin - Eau Claire
ND

Nolan Diffor

University of Wisconsin - Eau Claire
Faculty Mentor
JH

Jennifer Harrison

Mathematics, University of Wisconsin - Eau Claire
Monday April 27, 2026 8:30am - 8:50am CDT
Hibbard Hall 231 124 Garfield Ave, Eau Claire, WI 54701, USA

8:30am CDT

Topology and Geometry of Latent Spaces in Scientific Deep Learning: Applications to Dark Matter Reconstruction and Single-Cell Tracking
Monday April 27, 2026 8:30am - 8:50am CDT
Deep learning models are increasingly used to analyze complex scientific data, yet the internal structure of these models remains poorly understood. Central to every such model is a latent space (LS): a compressed representation of the input data that encodes what the model has learned. We develop a framework for characterizing the shape and structure of LSs using Topological Data Analysis (TDA) and sub-Riemannian geometry (sRG). Specifically, persistent homology is used to quantifies global features such as clusters and holes of the Ls, and sRG is used to discover curvature and distance in high-dimensional, constrained spaces. Together, these tools provide a principled, interpretable window into how scientific deep learning models organize learned representations.  We apply this framework to two scientific domains:  1. Carlton applies the framework to single-cell tracking, learning a neural stochastic differential equation model for cell trajectories, and examining whether LS structure predicts position-estimation error over time. By comparing results across antibody types, this work aims to identify structural signatures in the LS that are characteristic of tracking performance. 2. Scott trains a neural operator model to reconstruct three-dimensional dark matter density fields from two-dimensional gravitational lensing images. The role and impact of the learned LS structure on dark matter density field reconstructions is addressed. Together, these projects demonstrate that TDA and sub-Riemannian geometry offer actionable insight into how scientific deep learning models represent and process complex physical data.
Presenters
SS

Sophia Scott

University of Wisconsin - Eau Claire
GC

Gracie Carlton

University of Wisconsin - Eau Claire
Faculty Mentor
JA

Julian Antolin Camarena

Mathematics, University of Wisconsin - Eau Claire

Monday April 27, 2026 8:30am - 8:50am CDT
Hibbard Hall 302 124 Garfield Ave, Eau Claire, WI 54701, USA

8:45am CDT

Quaternions
Monday April 27, 2026 8:45am - 9:00am CDT
This talk introduces the quaternion group, an example of a non-abelian group of order eight. We will explore its structure, including its elements, multiplication rules, and subgroups. We will also explore how the quaternion group differs from more familiar groups.
Presenters
BG

Brooke Gerry

University of Wisconsin - Eau Claire
AW

Abby Wynne

University of Wisconsin - Eau Claire
KD

Keira Darnall

University of Wisconsin - Eau Claire
Faculty Mentor
CL

Chloe Lewis

Mathematics, University of Wisconsin - Eau Claire
Monday April 27, 2026 8:45am - 9:00am CDT
Hibbard Hall 320 124 Garfield Ave, Eau Claire, WI 54701, USA

9:00am CDT

Consecutive and Parity-Consecutive Complete Lucas Sequences when the Period Equals the Modulus (Part 1 of 2)
Monday April 27, 2026 9:00am - 9:20am CDT
The Lucas sequence of the first kind (LSFK) is denoted (Un(p, q))n≥0, where Un is its nth term.It is defined recursively by Un = pUn−1 − qUn−2 with initial terms U0 = 0 and U1 = 1, forintegers p and q. A sequence is uniformly distributed modulo m when each residue appears thesame number of times over the full period π(m), the number of repeating terms in any sequencemodulo m. However, the sequences modulo m in which each residue occurs exactly once withinthe full period are not classified. The following definitions for LSFK emerge from this observation.Complete sequences (CS) are defined by the two conditions: π(m) = m and the m repeating termsof (Un(p, q) (mod m))π(m)−1n=0 are some permutation of the values 0, 1, 2, . . . , m − 1. Completeconsecutive sequences (CCS) satisfy the congruence Un ≡ n (mod m) for all 0 ≤ n ≤ m − 1.Parity-consecutive complete sequences (PCCS) occur when (Un(p, q))n≥0 (mod m) decomposesinto the disjoint union of the two subsequences (U2n(p, q))n≥0 and (U2n+1(p, q))n≥0 modulo mcontaining all even and odd terms, respectively. The semi-quasi Lucas sequences (SQL) are notnecessarily complete, but they satisfy the relation, Un = Un−1 + Un−2 and Un + Un+1 = Un+2. Ourresearch determines the values of p and q that yield CS, CCS, PCCS, and SQL sequences undercertain moduli m.
Presenters
GB

Grace Blegen

University of Wisconsin - Eau Claire
SO

Sarah O'Malley

University of Wisconsin - Eau Claire
PS

Paige Simanski

University of Wisconsin - Eau Claire
Faculty Mentor
AM

aBa Mbirika

Mathematics, University of Wisconsin - Eau Claire
Monday April 27, 2026 9:00am - 9:20am CDT
Hibbard Hall 203 124 Garfield Ave, Eau Claire, WI 54701, USA

9:00am CDT

Loss Plus Loss Equals Win
Monday April 27, 2026 9:00am - 9:20am CDT
Our presentation will explore Parrondo's paradox, a phenomenon in probability theory where two losing strategies, can be combined to unexpectedly produce a winning outcome. We will mathematically explain the structure of this paradox, illustrate how the interaction between randomness and state-dependent rules creates this reversal, and demonstrate its relevance through real-world analogies. While also highlighting how “bad” options can generate positive results when sequenced strategically.
Presenters
BA

Brennon Anderson

University of Wisconsin - Eau Claire
LB

Lucas Bean

University of Wisconsin - Eau Claire
KB

Kyle Brandberg

University of Wisconsin - Eau Claire
GM

Garrett Mahlum

University of Wisconsin - Eau Claire
Faculty Mentor
JH

Jennifer Harrison

Mathematics, University of Wisconsin - Eau Claire
Monday April 27, 2026 9:00am - 9:20am CDT
Hibbard Hall 231 124 Garfield Ave, Eau Claire, WI 54701, USA

9:00am CDT

The Importance of Remaining Stationary: Variational Calculus and the Euler-Lagrange Equations
Monday April 27, 2026 9:00am - 9:20am CDT
In a first semester calculus course you learn the derivative can be used to find minimums and maximums of functions, both global and local. Variational calculus lets us extend the idea of criticality to functions satisfying given constraints/functionals, and boundary conditions. The Lagrangian formalism and the principle of stationary action from physics make heavy use of these optimization techniques. Stationary action gives a tool to describe systems from projectile motion and electrodynamics all the way through SU(3) gauge symmetries holding the standard model together. Here I will derive the Euler-Lagrange equations, establish the principle of stationary action, and work through an example of their utility. 
Presenters
DK

Duncan Koepke

Alumni, University of Wisconsin - Eau Claire
Monday April 27, 2026 9:00am - 9:20am CDT
Hibbard Hall 312 124 Garfield Ave, Eau Claire, WI 54701, USA

9:00am CDT

Topology and Geometry of Generative and Language Model Representation Spaces: Memorization in Diffusion Models and the Structure of Language Embeddings
Monday April 27, 2026 9:00am - 9:20am CDT
Every deep learning model builds an internal representation of its training data in a high-dimensional geometric object called a latent or embedding space whose shape encodes what the model has learned. Despite their importance, these spaces remain poorly understood. We develop a framework for characterizing their topology and geometry using persistent homology, a technique from Topological Data Analysis (TDA) that identifies global structural features such as clusters and voids, and sub-Riemannian geometry, which describes curvature and distance in high-dimensional constrained spaces. Our aim is to bring greater interpretability and theoretical clarity to the internal workings of modern deep learning models.  We apply this framework to two fundamental questions: 1. Edmundson investigates memorization in diffusion models --- generative models that synthesize data by reversing a learned noising process. Memorization, in which a model reproduces training examples rather than generalizing, has significant implications for privacy and robustness. By analyzing how latent space topology and geometry evolve during training, this work seeks structural signatures that are predictive of or diagnostic for memorization. 2. Theisen analyzes the embedding spaces of large language models (LLMs), where words, sentences, and concepts are encoded as geometric vectors. These embedding spaces may be thought of as the LLM analog of the diffusion model's latent space. Using our TDA and geometry tools, this work characterizes how semantic and syntactic structure manifest in these spaces and how organizational patterns vary across architectures and scales. Together, these projects advance our understanding of what deep learning models learn and how that learning is geometrically structured, with implications for interpretability, safety, and model design.
Presenters
HT

Henry Theisen

University of Wisconsin - Eau Claire
OE

Owen Edmundson

University of Wisconsin - Eau Claire
Faculty Mentor
JA

Julian Antolin Camarena

Mathematics, University of Wisconsin - Eau Claire

Monday April 27, 2026 9:00am - 9:20am CDT
Hibbard Hall 302 124 Garfield Ave, Eau Claire, WI 54701, USA

9:05am CDT

Twin Primes
Monday April 27, 2026 9:05am - 9:20am CDT
A twin prime is defined as a pair of prime numbers (p_1,p_2) such that p_1 + 2 = p_2. We can ask the question: does this pattern continue forever? The twin prime conjecture addresses that question which still remains unsolved; however, it is widely believed to be true. We will discuss the recent progress in understanding the gaps between prime numbers, as well as the uncertainties that remain.
Presenters
CL

Claire Lewis

University of Wisconsin - Eau Claire
MP

Morgan Presler

University of Wisconsin - Eau Claire
Faculty Mentor
CL

Chloe Lewis

Mathematics, University of Wisconsin - Eau Claire
Monday April 27, 2026 9:05am - 9:20am CDT
Hibbard Hall 320 124 Garfield Ave, Eau Claire, WI 54701, USA

9:25am CDT

The Rubik’s Cube
Monday April 27, 2026 9:25am - 9:40am CDT
We will explore a Rubik’s cube through the lens of Abstract Algebra. Specifically Group Theory, by modeling its moves as elements of a mathematical group and what it means to be in that group.  The focus is on invariants—properties such as edge orientation and corner twists that remain unchanged under all legal moves. A traditional 3x3 Rubik’s cube will be used to illustrate these concepts, but you are welcome to bring your own!
Presenters
KS

Kaitlyn Smith

University of Wisconsin - Eau Claire
BS

Bree Stanford

University of Wisconsin - Eau Claire
Faculty Mentor
CL

Chloe Lewis

Mathematics, University of Wisconsin - Eau Claire
Monday April 27, 2026 9:25am - 9:40am CDT
Hibbard Hall 320 124 Garfield Ave, Eau Claire, WI 54701, USA

9:30am CDT

Area Proofs of the Pythagorean Theorem
Monday April 27, 2026 9:30am - 9:50am CDT
Area proofs of the Pythagorean theorem provide a geometric approach to understanding the relationship between the sides of a right triangle. These visual proofs use the additivity and moving principles to demonstrate equality of area and convey the theorem clearly without relying on algebraic manipulation. Students enrolled in the Spring 2026 Math 304 course will engage attendees in a variety of area proofs in this informal presentation.
Presenters
SH

Sam Haines

University of Wisconsin - Eau Claire

KH

Kalli Huckabee

University of Wisconsin - Eau Claire
EM

Emma Martin

University of Wisconsin - Eau Claire

GB

Gabby Brucker

University of Wisconsin - Eau Claire
LW

Lucy Wibel

University of Wisconsin - Eau Claire
Faculty Mentor
KR

Katrina Rothrock

Mathematics, University of Wisconsin - Eau Claire
Monday April 27, 2026 9:30am - 9:50am CDT
Hibbard Hall 312 124 Garfield Ave, Eau Claire, WI 54701, USA

9:30am CDT

Consecutive and Parity-Consecutive Complete Lucas Sequences when the Period Equals the Modulus (Part 2 of 2)
Monday April 27, 2026 9:30am - 9:50am CDT
The Lucas sequence of the first kind (LSFK), denoted Un(p, q)n≥0, is defined recursively by its nthterm, Un = pUn−1 − qUn−2 with the initial terms U0 = 0 and U1 = 1, for integers p and q. For anodd prime p, the sequence Un(p, q)n≥0 (mod p) is known to be uniformly distributed when pdivides the discriminant. A uniformly distributed LSFK containing each residue exactly once definesComplete sequences (CS). The conditions that result in CS have not previously been classified. Thestudy of Complete sequences leads naturally to the notions of Complete Consecutive sequences(CCS) and Parity Consecutive Complete sequences (PCCS). When Un(p, q)n≥0 is CompleteConsecutive for some modulo m, the moduli producing Complete sequences for the same p and qvalues depend entirely on m. Furthermore, the subsequences U−2n(p, q)n=0 and U2n+1(p, q)n=0 of aComplete Consecutive Un(p, q)n≥0 (mod m) directly relate to the disjoint subsequences of a samemodulo Parity Consecutive Complete sequence. These relations show the underlying conditionsthat produce the various forms of complete sequences, providing a complete classification of theiroccurrences. Our research has classified the values of p and q that yield CS, CCS, and PCCS undercertain moduli m.
Presenters
GB

Grace Blegen

University of Wisconsin - Eau Claire
SO

Sarah O'Malley

University of Wisconsin - Eau Claire
PS

Paige Simanski

University of Wisconsin - Eau Claire
Faculty Mentor
AM

aBa Mbirika

Mathematics, University of Wisconsin - Eau Claire
Monday April 27, 2026 9:30am - 9:50am CDT
Hibbard Hall 203 124 Garfield Ave, Eau Claire, WI 54701, USA

9:30am CDT

Cryptarithms
Monday April 27, 2026 9:30am - 9:50am CDT
In this presentation, we will discuss what Cryptarithms are and how they work. Cryptarithms are a type of math puzzle where numbers are replaced by letters with the goal of determining the numerical value of each letter so that the arithmetic is correct. We will explain how to solve these logic puzzles and provide our audience with the opportunity to try it themselves.
Presenters
KD

Keira Darnall

University of Wisconsin - Eau Claire
ML

Mai Lee

University of Wisconsin - Eau Claire
BL

Ben Lockman

University of Wisconsin - Eau Claire
MW

Matt Wojcik

University of Wisconsin - Eau Claire

Faculty Mentor
JH

Jennifer Harrison

Mathematics, University of Wisconsin - Eau Claire
Monday April 27, 2026 9:30am - 9:50am CDT
Hibbard Hall 231 124 Garfield Ave, Eau Claire, WI 54701, USA

9:30am CDT

How To Start Coding With Math
Monday April 27, 2026 9:30am - 9:50am CDT
In our presentation, we will talk about the utility and relevance of using programming to solve problems in mathematics. We will discuss why one might use coding in mathematics in addition to some easy ways to get started. At the end, the audience will be able to try to solve some basic mathematics problems using coding.
Presenters
SW

Sloan Welch

University of Wisconsin - Eau Claire
Faculty Mentor
RH

Ryan Harrison

Mathematics, University of Wisconsin - Eau Claire
Monday April 27, 2026 9:30am - 9:50am CDT
Hibbard Hall 302 124 Garfield Ave, Eau Claire, WI 54701, USA

9:45am CDT

Cayley Graphs
Monday April 27, 2026 9:45am - 10:00am CDT
TBD
Presenters
KL

Kevin LeClair

University of Wisconsin - Eau Claire

Faculty Mentor
CL

Chloe Lewis

Mathematics, University of Wisconsin - Eau Claire
Monday April 27, 2026 9:45am - 10:00am CDT
Hibbard Hall 320 124 Garfield Ave, Eau Claire, WI 54701, USA

10:00am CDT

Harmonic Conjugate Pairs in Two-Dimensional Heat Conduction and Fluid Flow
Monday April 27, 2026 10:00am - 10:20am CDT
This project studies how a harmonic conjugate pair – a potential and a stream function – can describe isotherms and flow lines around a two‑dimensional cylinder. The goal is to show, in clear terms, how complex analytic structure encodes both temperature distribution and heat or fluid flux in a homogeneous medium. Building on classical potential flow and steady heat conduction theory, the work interprets the real and imaginary parts of a complex potential as orthogonal families of isotherms and flow lines around a circular obstacle, using the Cauchy–Riemann equations to connect them. The approach uses the standard complex potential for uniform flow past a cylinder, derives the associated harmonic conjugate pair, and then reads these functions as temperature and flux fields. The main outcome is a geometric picture where every isotherm intersects every flow line at right angles, illustrating Fourier’s law and incompressible potential flow, and where boundary conditions on the cylinder are automatically satisfied by the chosen complex potential. The project concludes that harmonic conjugate pairs, supported by results like the Maximum Principle and uniqueness theorems for harmonic functions, offer a compact and powerful way to teach and analyze two‑dimensional conduction and ideal flow around obstacles.
Presenters
CB

Clara Bartlett

University of Wisconsin - Eau Claire
CL

Claire Lewis

University of Wisconsin - Eau Claire
Faculty Mentor
AH

Aiham Hassan

Mathematics, University of Wisconsin - Eau Claire
Monday April 27, 2026 10:00am - 10:20am CDT
Hibbard Hall 302 124 Garfield Ave, Eau Claire, WI 54701, USA

10:00am CDT

The Insolvability of the Quintic by Radicals
Monday April 27, 2026 10:00am - 10:20am CDT
This project examines why general polynomial equations of degree five cannot be solved using radicals. The aim of this research is to explain the algebraic structures that prevent the existence of a general radical formula for the quintic equation.The problem of solving polynomial equations has a long mathematical history. While formulas for quadratic, cubic, and quartic equations were discovered, mathematicians later proved that no similar formula exists for the general quintic. This result was first established by Niels Henrik Abel and later explained structurally through Galois Theory developed by Évariste Galois. Understanding this shift from formula-based algebra to structural reasoning is central to modern abstract algebra.The presentation introduces key ideas from field extensions and permutation groups and explains how the solvability of a polynomial relates to the structure of its Galois group. In particular, the project discusses why the general quintic has a Galois group isomorphic to S_5, which is not solvable.This work aims to clarify the algebraic reasons behind the insolvability of the quintic and highlight the significance of Galois Theory in understanding polynomial equations.
Presenters
JS

Johnny Stevenson

University of Wisconsin - Eau Claire
HG

Hannah Greeno

University of Wisconsin - Eau Claire
Faculty Mentor
AM

aBa Mbirika

Mathematics, University of Wisconsin - Eau Claire
Monday April 27, 2026 10:00am - 10:20am CDT
Hibbard Hall 203 124 Garfield Ave, Eau Claire, WI 54701, USA

10:00am CDT

Too Many Queens on the Board
Monday April 27, 2026 10:00am - 10:20am CDT
We all know the most powerful piece on a chess board is the Queen, but is it possible to have too many? In this presentation, we'll take a look at the "N-Queens" problem. Join us as we take on progressively harder puzzles in an effort to fit as many Queens as we can on a chess board, while discussing possibility elimination and constraint.
Presenters
CE

Clay Estes

University of Wisconsin - Eau Claire
Faculty Mentor
JH

Jennifer Harrison

Mathematics, University of Wisconsin - Eau Claire
Monday April 27, 2026 10:00am - 10:20am CDT
Hibbard Hall 231 124 Garfield Ave, Eau Claire, WI 54701, USA

10:00am CDT

A New Lower Bound for Clasp Number on 3-Component Links
Monday April 27, 2026 10:00am - 10:50am CDT
A C-complex is a union of Seifert surfaces for the components of a link which intersect each other in clasps. The clasp number of a link is the minimal number of clasps amongst all C-complexes it bounds It gives a measure of complexity and can be used to provide bounds on other useful characteristics of a link. This paper provides a new lower bound for the number of clasps of all C-complexes bounded by a given 3-component link improving results of Amundsen-Anderson-D.-Guyer. Furthermore, we construct links that achieve these bounds. In order to do so, we express the triple linking numbers as the area bounded by three curves, called word curves, and then perform the geometry and discrete optimization needed to minimize the length of these curves.
Presenters
NP

Nathan Phillips

University of Wisconsin - Eau Claire
JP

Jack Paulsen

University of Wisconsin - Eau Claire
DL

David Lawrence

University of Wisconsin - Eau Claire
Faculty Mentor
CD

Christopher Davis

Mathematics, University of Wisconsin - Eau Claire
Monday April 27, 2026 10:00am - 10:50am CDT
Hibbard Hall 312 124 Garfield Ave, Eau Claire, WI 54701, USA

10:00am CDT

Next Gen Math Tools: Practical Technology Integration in the Classroom
Monday April 27, 2026 10:00am - 10:50am CDT
UW-EC undergraduate mathematics education students share their discoveries and designs of technology resources for the classroom. Join us for an exploratory session of math technology in which we will discuss appropriate implementation strategies, barriers to integration, and troubleshooting techniques. Personal computer recommended for this session!
Presenters
BG

Brooke Gerry

University of Wisconsin - Eau Claire
KS

Kaitlyn Smith

University of Wisconsin - Eau Claire
BS

Bree Stanford

University of Wisconsin - Eau Claire
ML

Mai Lee

University of Wisconsin - Eau Claire
Faculty Mentor
MT

Melissa Troudt

Mathematics, University of Wisconsin - Eau Claire
Monday April 27, 2026 10:00am - 10:50am CDT
Hibbard Hall 323 124 Garfield Ave, Eau Claire, WI 54701, USA

10:05am CDT

Germain Primes
Monday April 27, 2026 10:05am - 10:20am CDT
In our presentation, we will talk about Germain Primes, which are prime numbers p such that (2p+1) is also prime. We will explore why we should care about them as well as their uses in the real world.
Presenters
BM

Brayden Mau

University of Wisconsin - Eau Claire

JL

Jacob Lynch

University of Wisconsin - Eau Claire

MW

Matt Wojcik

University of Wisconsin - Eau Claire

Faculty Mentor
CL

Chloe Lewis

Mathematics, University of Wisconsin - Eau Claire
Monday April 27, 2026 10:05am - 10:20am CDT
Hibbard Hall 320 124 Garfield Ave, Eau Claire, WI 54701, USA

10:25am CDT

RSA Cryptography
Monday April 27, 2026 10:25am - 10:40am CDT
RSA Encryption is essential in protecting private information. It encrypts data when it is being transferred using a public and private key. RSA Encryption uses modular arithmetic using the public key to encrypt it and then later the private key to decrypt it. Modular Arithmetic is a system for integers where numbers wrap around after reaching a value called the modulus. This presentation will show how such a simple mathematical concept can be used to help make the digital world more secure.
Presenters
DM

Daniel Moore

University of Wisconsin - Eau Claire
JH

Jack Hoverson

University of Wisconsin - Eau Claire
JA

Joel Acevedo

University of Wisconsin - Eau Claire
Faculty Mentor
CL

Chloe Lewis

Mathematics, University of Wisconsin - Eau Claire
Monday April 27, 2026 10:25am - 10:40am CDT
Hibbard Hall 320 124 Garfield Ave, Eau Claire, WI 54701, USA

10:30am CDT

Fourier Series and Fourier Transforms
Monday April 27, 2026 10:30am - 10:50am CDT
This talk provides a broad introduction to Fourier series and Fourier analysis, concepts first introduced in the early nineteenth century by Joseph Fourier. We will explore the central idea behind Fourier methods: representing complex functions as sums of simpler trigonometric components. The presentation will briefly discuss the historical origins of these ideas, the basic mathematical framework, and how Fourier methods are used today. Along the way, we will highlight examples of applications in areas such as signal processing, engineering, and applied mathematics. This talk is intended as a short crash course that gives an overview of the ideas and why they are so widely used.
Presenters
avatar for Maddie Sasse

Maddie Sasse

University of Wisconsin - Eau Claire
AH

Aleya Hadenfeldt

University of Wisconsin - Eau Claire
PS

Paige Simanski

University of Wisconsin - Eau Claire
Faculty Mentor
AH

Aiham Hassan

Mathematics, University of Wisconsin - Eau Claire
Monday April 27, 2026 10:30am - 10:50am CDT
Hibbard Hall 302 124 Garfield Ave, Eau Claire, WI 54701, USA

10:30am CDT

Risky Business
Monday April 27, 2026 10:30am - 10:50am CDT
Actuarial science is a field full of solving problems and probability. Exactly what you’ll be using in this presentation! Get ready to explore concepts like Venn diagrams and conditional probability. Combined with learning, you’ll have the opportunity to practice with others to get to the bottom of a business case. In this session, we will discuss how using probability rules can inform decision making in not just classes, but real-world scenarios, like an actuary!
Presenters
EL

Ethan Leeser

University of Wisconsin - Eau Claire
ML

Mason Lijewski

University of Wisconsin - Eau Claire
Faculty Mentor
JH

Jennifer Harrison

Mathematics, University of Wisconsin - Eau Claire
Monday April 27, 2026 10:30am - 10:50am CDT
Hibbard Hall 231 124 Garfield Ave, Eau Claire, WI 54701, USA

10:30am CDT

The Snake of the Algebra
Monday April 27, 2026 10:30am - 10:50am CDT
The Snake Lemma is a classical result in homological algebra that connects kernels and cokernels arising from a commutative diagram of algebraic structures with exact rows. From such a diagram, the lemma constructs a new exact sequence that reveals deep relationships between the underlying homomorphisms. In particular, it introduces a “connecting homomorphism” that links information lost in one part of a diagram to information appearing elsewhere. This result plays a central role in many areas of modern mathematics, including algebraic topology, module theory, and homological algebra, where it is used to construct long exact sequences and study the structure of algebraic objects. In this talk, we will introduce the necessary background on exact sequences, kernels, cokernels, and commutative diagrams before presenting the statement and intuition behind the Snake Lemma. We will outline the idea of the proof using diagram-chasing techniques and illustrate how the lemma creates a bridge between algebraic structures. Finally, we will discuss why mathematicians care about this result and briefly describe some contexts where it appears. Interestingly, the Snake Lemma has even appeared in popular culture the opening scene of the 1980 film “It’s My turn” features a mathematician presenting a proof of the lemma.
Presenters
ST

Sashreek Tirunagari

University of Wisconsin - Eau Claire
Faculty Mentor
AM

aBa Mbirika

Mathematics, University of Wisconsin - Eau Claire
Monday April 27, 2026 10:30am - 10:50am CDT
Hibbard Hall 203 124 Garfield Ave, Eau Claire, WI 54701, USA

11:00am CDT

Area Proofs of the Pythagorean Theorem
Monday April 27, 2026 11:00am - 11:20am CDT
Area proofs of the Pythagorean theorem provide a geometric approach to understanding the relationship between the sides of a right triangle. These visual proofs use the additivity and moving principles to demonstrate equality of area and convey the theorem clearly without relying on algebraic manipulation. Students enrolled in the Spring 2026 Math 304 course will engage attendees in a variety of area proofs in this informal presentation.
Presenters
CV

Cadhla Von Asten

University of Wisconsin - Eau Claire

SM

Sydnee Millsap

University of Wisconsin - Eau Claire
HB

Hannah Burns

University of Wisconsin - Eau Claire

OC

Olivia Corr

University of Wisconsin - Eau Claire
LM

Lukas Milas

University of Wisconsin - Eau Claire

Faculty Mentor
KR

Katrina Rothrock

Mathematics, University of Wisconsin - Eau Claire
Monday April 27, 2026 11:00am - 11:20am CDT
Hibbard Hall 323 124 Garfield Ave, Eau Claire, WI 54701, USA

11:00am CDT

Finding Linear Equations with Technology
Monday April 27, 2026 11:00am - 11:20am CDT
In this presentation we will provide a brief overview on the importance of using technology in the classroom and how it can assist with mathematical skills. We will focus on google sheets and it’s many useful features, specifically when it comes to linear equations and how to find them given two coordinates. By the end of the presentation, our audience will be able to use google sheets to produce a line from two points.
Presenters
KD

Keira Darnall

University of Wisconsin - Eau Claire
EJ

Elaynah Jaschob

University of Wisconsin - Eau Claire
Faculty Mentor
RH

Ryan Harrison

Mathematics, University of Wisconsin - Eau Claire
Monday April 27, 2026 11:00am - 11:20am CDT
Hibbard Hall 231 124 Garfield Ave, Eau Claire, WI 54701, USA

11:00am CDT

Introduction to Liouville's Theorem in Complex Analysis and Applications to Physical Systems.
Monday April 27, 2026 11:00am - 11:20am CDT
Liouville’s Theorem states that any bounded, entire function must be constant. Although the results at first may not be obvious, we will explore an intuitive analog for describing the theorem. Furthermore, we will investigate the applications of this theorem and its following corollaries with a focus on thermal physics and chemistry, quantum mechanics, and electrodynamics. These applications include the extrapolation of Laplace’s equation to electrostatic systems, and the posit that no non-constant electric potential can be bound over infinite space. In Thermodynamic instances, it describes phase transitions in the complex plane. Finally, it verifies fundamental ideas of quantum mechanics and quantum field theory, wherein it serves to keep probability distributions bounded.
Presenters
JW

Jeremy Worden

University of Wisconsin - Eau Claire
RG

Ryan Glaser

University of Wisconsin - Eau Claire
AL

Aidan Leddick

University of Wisconsin - Eau Claire
Faculty Mentor
AH

Aiham Hassan

Mathematics, University of Wisconsin - Eau Claire
Monday April 27, 2026 11:00am - 11:20am CDT
Hibbard Hall 302 124 Garfield Ave, Eau Claire, WI 54701, USA

11:00am CDT

The Monster Behind Moonshine: Exploring the Monster Group and Monstrous Moonshine
Monday April 27, 2026 11:00am - 11:20am CDT
Finite simple groups are divided into two categories: infinite families and sporadic groups. Asporadic group is a finite simple group that does not belong to any infinite family generated by ageneral construction. For example, cyclic groups of prime order form one of the 18 infinite families.For every prime number, p, the cyclic group Zp is simple. Among the sporadic groups, the MonsterGroup is the largest, having an order roughly equal to 8.08 × 1053. Of the 26 sporadic groups, theMonster Group contains 20 as subquotients; these sporadic groups are collectively known as theHappy Family. In the late 1970s, mathematicians discovered a surprising relationship between theMonster Group and certain modular functions. In particular, the Fourier expansion of the modularj-function has coefficients corresponding to sums of the dimensions of irreducible representationsof the Monster Group. For example, the first nontrivial coefficient, 196884, can be written as196883 + 1. Here, 196883 is the dimension of the smallest nontrivial irreducible representationof the Monster Group, and 1 is the dimension of the trivial representation. This unexpectedrelationship became known as Monstrous Moonshine and was later proven by Richard Borcherdsin 1992.
Presenters
SO

Sarah O'Malley

University of Wisconsin - Eau Claire
Faculty Mentor
AM

aBa Mbirika

Mathematics, University of Wisconsin - Eau Claire
Monday April 27, 2026 11:00am - 11:20am CDT
Hibbard Hall 203 124 Garfield Ave, Eau Claire, WI 54701, USA

11:00am CDT

The Use of Audio and Video Softwares When Teaching Trigonometric Functions
Monday April 27, 2026 11:00am - 11:20am CDT
Trigonometric functions are difficult to comprehend through real-world applications for students because most applications are not able to be perceived with the senses easily. With Audacity and Muse Score Studio, a decently intuitive assignment can be made for students to convert their limited understandings of trigonometric functions into actual music with limited setup. By the end of this presentation, the audience will have a sufficient introduction into some audio software that can assist in creating engaging activities for a mathematics classroom.
Presenters
MH

Michael Holtz

University of Wisconsin - Eau Claire
CE

Clay Estes

University of Wisconsin - Eau Claire
Faculty Mentor
RH

Ryan Harrison

Mathematics, University of Wisconsin - Eau Claire
Monday April 27, 2026 11:00am - 11:20am CDT
Hibbard Hall 320 124 Garfield Ave, Eau Claire, WI 54701, USA

11:30am CDT

Abstract Algebra and the Rubik’s Cube
Monday April 27, 2026 11:30am - 11:50am CDT
The 3x3 Rubik’s cube is a prime example or a system that can be represented and analyzed using group theory. Using this information, many interesting results have been proven, such as a strict limit on the minimum number of moves needed to solve any state, and identifying a polynomial that allows it to be represented as a Galois group over the rationals. This talk will go over the group behavior of the puzzle, along with some of the interesting properties it possesses.
Presenters
NP

Nathan Phillips

University of Wisconsin - Eau Claire
Faculty Mentor
AM

aBa Mbirika

Mathematics, University of Wisconsin - Eau Claire
Monday April 27, 2026 11:30am - 11:50am CDT
Hibbard Hall 203 124 Garfield Ave, Eau Claire, WI 54701, USA

11:30am CDT

Population Dynamics with a Periodic Carrying Capacity
Monday April 27, 2026 11:30am - 11:50am CDT
This talk will describe an interesting generalization of the famous logistic equation from population dynamics. The logistic equation assumes that the environment's carrying capacity is a constant. We generalize this scenario to allow for periodic fluctuations in the environment's carrying capacity. This provides an elementary model of seasonal changes in the environment. Some interesting results include: (1) solutions to the model must be obtained using numerical approximations, as standard solution methods cannot provide exact formulas for solutions; (2) solutions with differing initial populations converge to a single, periodic solution; (3) the model may provide some insight into real population dynamics in biology.
Presenters
JW

James Walker

Mathematics, University of Wisconsin - Eau Claire
Monday April 27, 2026 11:30am - 11:50am CDT
Hibbard Hall 323 124 Garfield Ave, Eau Claire, WI 54701, USA

11:30am CDT

Spreading Knowledge
Monday April 27, 2026 11:30am - 11:50am CDT
Technology can be a powerful tool for exploring mathematics, yet many students use it only for basic calculations. The goal of this presentation is to demonstrate how Google Sheets can be used to investigate mathematical patterns, model equations, and efficiently solve problems. Using spreadsheet formulas, tables, and graphs, students can quickly test ideas and see mathematical relationships that would otherwise take significant time to compute by hand.During this session, we will present examples showing how spreadsheets can generate sequences, solve equations, and explore mathematical concepts such as functions and patterns. By introducing these tools, we aim to show students how the technology they already have access to can support experimentation, organize calculations, and deepen mathematical understanding.
Presenters
JL

Jacob Lynch

University of Wisconsin - Eau Claire

ND

Nolan Diffor

University of Wisconsin - Eau Claire
Faculty Mentor
RH

Ryan Harrison

Mathematics, University of Wisconsin - Eau Claire
Monday April 27, 2026 11:30am - 11:50am CDT
Hibbard Hall 231 124 Garfield Ave, Eau Claire, WI 54701, USA

11:30am CDT

The Laplace Transform: Evolution and Applications
Monday April 27, 2026 11:30am - 11:50am CDT
Mathematicians have a seemingly never-ending supply of "tricks up their sleeve" that they can utilize to attack a problem. One such "trick" is the Laplace transform, which is a kind of integral transform that converts a function of the time domain into a function of the complex domain. This project aims to demonstrate how such a transformation can convert a differential or integral equation into an algebraic equation, allowing for analysis of real-world systems. Within this poster, we will outline the history and development of the Laplace transform, and discuss its mathematical basis. We will also dive into some of the applications of the Laplace transform, especially in the context of physics and engineering.
Presenters
EP

Elaina Plonis

University of Wisconsin - Eau Claire
TH

Tay Hoffmann

University of Wisconsin - Eau Claire
Faculty Mentor
AH

Aiham Hassan

Mathematics, University of Wisconsin - Eau Claire
Monday April 27, 2026 11:30am - 11:50am CDT
Hibbard Hall 302 124 Garfield Ave, Eau Claire, WI 54701, USA

11:30am CDT

In how many ways can you fold a strip of stamps?
Monday April 27, 2026 11:30am - 12:20pm CDT
The labeled stamp folding problem asks how many distinct ways there are to fold a strip of stamps so that the stamps are stacked on top of each other. Somewhat surprisingly, the problem does not have a known formula (if such a formula exists). We will explore multiple distinct methods for determining the number of stamp foldings. This talk will be fun, interactive, and suitable for people regardless of math background.
Presenters
BW

Briar Weston

University of Wisconsin - Eau Claire
Faculty Mentor
AB

Allison Beemer

Mathematics, University of Wisconsin - Eau Claire
Monday April 27, 2026 11:30am - 12:20pm CDT
Hibbard Hall 320 124 Garfield Ave, Eau Claire, WI 54701, USA

12:00pm CDT

An Introduction to the Mandlebrodt Set
Monday April 27, 2026 12:00pm - 12:20pm CDT
A brief overview on the fractal geometry and underlying complex equation of the Mandlebrodt Set. We build the recursive equation from the ground up, first using the real numbers and then extending to the complex plane. We then explore the image that follows: one of the most beautiful and iconic images in mathematics.
Presenters
JC

Joe Callanan

University of Wisconsin - Eau Claire
DC

Derrick Chute

University of Wisconsin - Eau Claire
IG

Isaiah Gengembre

University of Wisconsin - Eau Claire
Faculty Mentor
AH

Aiham Hassan

Mathematics, University of Wisconsin - Eau Claire
Monday April 27, 2026 12:00pm - 12:20pm CDT
Hibbard Hall 302 124 Garfield Ave, Eau Claire, WI 54701, USA

12:00pm CDT

Bridging to Correct from Erased Frame Coefficients
Monday April 27, 2026 12:00pm - 12:20pm CDT
This project investigates how signals can be accurately reconstructed when some transmitted measurements are lost. Frame theory provides a mathematical framework for representing signals with redundancy, allowing recovery even when certain frame coefficients are erased. We study a reconstruction method called bridging, which estimates missing frame coefficients by approximating the corresponding frame vectors using combinations of the remaining vectors. Two strategies for selecting these vectors are considered: NormCut, which selects vectors based on distance, and AngleCut, which selects vectors based on directional alignment in the Hilbert space. Numerical experiments analyze how reconstruction accuracy depends on frame redundancy, the number of erased coefficients, and the number of vectors used in the approximation. The results show that both bridging methods significantly improve reconstruction compared to partial recovery, with the AngleCut method consistently producing the lowest reconstruction error.
Presenters
AH

Aleya Hadenfeldt

University of Wisconsin - Eau Claire
Faculty Mentor
SS

Sam Scholze

Mathematics, University of Wisconsin - Eau Claire
Monday April 27, 2026 12:00pm - 12:20pm CDT
Hibbard Hall 323 124 Garfield Ave, Eau Claire, WI 54701, USA

12:00pm CDT

Cyclotomic Polynomials
Monday April 27, 2026 12:00pm - 12:20pm CDT
Roots of unity are complex numbers that when raised to some positive integer power are equal to one. Cyclotomic polynomials are irreducible polynomials with integer coefficients constructed using primitive roots of unity, a more specific type of root of unity. Their interesting properties and use in the factorization of another set of polynomials have led to fascinating and impactful mathematical study. Through adjoining a primitive root of unity to the set of rational numbers, one can create a new cyclotomic field.
Presenters
JP

Jack Paulsen

University of Wisconsin - Eau Claire
Faculty Mentor
AM

aBa Mbirika

Mathematics, University of Wisconsin - Eau Claire
Monday April 27, 2026 12:00pm - 12:20pm CDT
Hibbard Hall 203 124 Garfield Ave, Eau Claire, WI 54701, USA

12:00pm CDT

Encouraging Engagement Inside and Outside of the Math Classroom Using Prodigy Math
Monday April 27, 2026 12:00pm - 12:20pm CDT
Prodigy Math is an online, game-based learning platform that turns math practice into an adventure. In this presentation, we will introduce how Prodigy engages students in a nontraditional way by combining role-playing game mechanics with curriculum-aligned math questions. Our goal is to show prospective teachers, parents, and math enthusiasts how game-based learning can encourage logical reasoning, persistence, and mathematical understanding. We will demonstrate how the platform works, highlighting both the benefits and limitations of using Prodigy in educational settings. Attendees will also have the opportunity to briefly explore the game themselves and experience how the system motivates players to solve math problems in order to progress. Join us for a fun, interactive look at how digital games like Prodigy can support math learning while keeping students engaged.
Presenters
AW

Abby Wynne

University of Wisconsin - Eau Claire
AS

Annyka Schnettler

University of Wisconsin - Eau Claire
RC

Rylie Christnovich

University of Wisconsin - Eau Claire

Faculty Mentor
RH

Ryan Harrison

Mathematics, University of Wisconsin - Eau Claire
Monday April 27, 2026 12:00pm - 12:20pm CDT
Hibbard Hall 231 124 Garfield Ave, Eau Claire, WI 54701, USA

2:00pm CDT

Andrew Balas Lecture (Keynote Address): Statistical Methods for Multi-Stage Optimal Decision-Making
Monday April 27, 2026 2:00pm - 2:50pm CDT
Decisions made at a given stage of a process can constrain or enable future actions, thereby influencing long-term outcomes. In many scientific domains, such as precision medicine, public policy, and economics, the quality of an initial decision cannot be evaluated solely by its immediate effect, but rather by its consequences across an entire sequence of future decision points. For example, an initially modestly effective chemotherapy option may lead to improved long-term survival when followed by an appropriate salvage regimen. This motivates statistical methods that explicitly account for downstream interventions, evolving covariate processes, and future decision rules. Within the framework of dynamic treatment regimes and reinforcement learning, estimation of optimal sequential decisions requires modeling both immediate and future conditional gains or rewards. In this talk, we will discuss Q-learning as a statistical learning approach for estimating optimal dynamic treatment regimes. I will emphasize its interpretation, implementation, and theoretical properties, as well as its strengths and limitations relative to alternative methods. The goal is to illustrate how forward-looking statistical decision strategies can yield improved long-term outcomes.
Presenters
DA

Dr. Abdus Wahed

University of Rochester
Monday April 27, 2026 2:00pm - 2:50pm CDT
Hibbard Hall 102 124 Garfield Ave, Eau Claire, WI 54701, USA

3:30pm CDT

Mathematics Competition
Monday April 27, 2026 3:30pm - 4:30pm CDT
The 34th Annual Math Retreat will conclude with the Mathematics Competition.  Join our students as they compete to solve a series of challenging Mathematics problems. 
Monday April 27, 2026 3:30pm - 4:30pm CDT
Hibbard Hall 102 124 Garfield Ave, Eau Claire, WI 54701, USA
 

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