Mathematical Sciences

PhD Dissertation Defense: Mr. Andrew Frohmader
2026-05-01 15:00 - 16:00 (America/Chicago) | EMS Building, E495, 3200 N Cramer St, Milwaukee, WI, United States
Graded multiplicities in the Kostant-Rallis setting
Mr. Andrew Frohmader
Graduate Student
University of Wisconsin-Milwaukee
This dissertation contains two main results. First, we provide combinatorial branching rules for GL(n, C) to O(n, C) and GL(2n, C) to Sp(2n, C) extending the Littlewood restriction rules. Second, we use these branching rules and the combinatorics of GL(n, C)-crystals to derive a formula for the graded multiplicity of a K-type in the regular functions on the K-nilpotent cone for GL(n, R), GL(n, C) and GL(n, H).
Advisor:
Jeb Willenbring
Committee Members:
Allen Bell, Chris Hruska, Istvan Lauko, and Kevin McLeod

Colloquium: Dr. Dave Spade
2026-05-01 14:00 - 15:00 | EMS Building, E495, 3200 N Cramer St, Milwaukee, WI, United States
Statistical Modeling of Control of Animal Motion in Three Dimensions

This manuscript gets ahold of the control aspect of how Daphnia magna move through their surroundings in a control-type environment with still water and with no external stimuli. We present a statistical model for step lengths and roll, pitch, and yaw angles. We then use this model to describe a procedure for generating biologically realistic synthetic trajectories. The aim of this article is to provide a starting point for modeling animal motion in a variety of environmental settings.

MS Thesis Defense: Mr. Carlos Sanchez Diaz
2026-05-01 09:00 - 10:00 | EMS Building, Room E495, E495; 3200 N Cramer St., Milwaukee, WI, 53211, United States
MS Thesis Defense
Carlos Sanchez Diaz
Graduate Student
University of Wisconsin-Milwaukee
This thesis investigates the pedagogical approaches to mathematical functions in the United States and Mexico with the goal of improving instruction in mathematics for Spanish-speaking English Language Learners. By comparing the United States Illustrative Mathematics curriculum with Mexico’s Nueva Escuela Mexicana (Matemáticas IV), the study identifies a near-isomorphic relationship between Common Core Standards for Mathematical Practice and Mexico’s disciplinary competencies. This mapping provides U.S. educators with a framework to understand the prior educational experiences of Mexican immigrant students. Ultimately, these insights should enable teachers to leverage existing student knowledge and deliver more culturally responsive, effective mathematical instruction.
Committee Members:
Kevin McLeod, Suzanne Boyd, and Pamela E. Harris

Colloquium: Dr. Craig Guilbault
2026-04-24 14:00 - 15:00 | EMS Building, E495, 3200 N Cramer St, Milwaukee, WI, United States
Information coming soon!

Math Comics With Dr. Asmita Sodhi
2026-04-17 14:00 - 16:00 | EMS Building, Room W110
The wonderful mathematical artist Dr. Asmita Sodhi will Zoom in to talk about her work with math comics and run a workshop, where we will try our hand at making some of these comics ourselves! There will be free donuts, and we will bring tea (BYOM: Bring Your Own Mug)!

Colloquium: Dr. Kevin Palencia Infante
2026-04-17 14:00 - 15:00 | EMS Building, E495, 3200 N Cramer St, Milwaukee, WI, United States
“My Instructor Was Kind of a Computer”: Rethinking Faculty–Student Interactions in Calculus

Dr. Kevin Palencia Infante
Assistant Professor & Calculus Coordinator
Northern Illinois University

While computers and AI are playing a growing role in education, faculty remain essential to teaching in ways that meaningfully shape student learning. In this talk, I present findings on how calculus students experience their interactions with instructors. Drawing on a qualitative study framed by academic validation and invalidation, Black and Hispanic students share perspectives on their classroom experiences. They highlight instructional practices that support their learning, including collaborative environments, clear conceptual guidance, availability outside of class, and actions that make them feel valued. They also point to interactions that leave them feeling unsupported or not validated. Across these experiences, students emphasize the importance of compassion, care, and instructor presence. By centering student voices, this talk shows how faculty–student interactions shape students’ experiences in calculus beyond content delivery.

Colloquium: Dr. Peter Hinow
2026-04-17 14:00 - 15:00 | EMS Building, E495, 3200 N Cramer St, Milwaukee, WI, United States

Colloquium: Dr. Steve Butler
2026-04-10 14:00 - 15:00 | EMS Building, E495, 3200 N Cramer St, Milwaukee, WI, United States
A Short Course in Spectral Graph Theory
Prof. Steve Butler
Morrill Professor of Mathematics
Iowa State University
Graphs are used to model relationships (edges) between objects (vertices). A graph’s structure can efficiently stored in an array format. We can go one step further and replace arrays by matrices (which are arrays with benefits!), the eigenvalues of these matrices tell us some information about the graph. The extent to which we can understand the structure of the graph from these eigenvalues is spectral graph theory. We will do a quick walk through of some of the flavors of matrices that are studied in spectral graph theory, and some results that arise from their study.

Community of Practice: Student Feedback
2026-04-10 12:30 - 13:30 | EMS Building, Room E495, E495; 3200 N Cramer St., Milwaukee, WI, 53211, United States
Student Feedback: “I Just Want to Have Fun”
Now is one of the most challenging points in the academic year. How do we combat the post-spring-break lull, student and instructor burnout, and the “is the semester over yet!?!?” mentality? While worksheets and problems up at the board are powerful, can we design active learning that students find more “fun”? We’ll demo and design content-centered games or activities. Have an activity/idea to share? Bring it with!!!
What is the Community of Practice?
The Community of Practice is a space for everyone in the department (lecturers, GTAs, faculty) to come together and have chats, professional development, speakers, workshops, and more related to teaching and learning. There’s no sign-up; simply attend if you want! If you would like to be involved in any planning or would like to run a session, please email me (henathan@uwm.edu) and let me know.
The Community of Practice Canvas Site
We have a Community of Practice Canvas site where we keep a signup and modules for past sessions. If you would like to enroll, here is the link: https://uws-td.instructure.com/enroll/XK96LD

UWM Marden Lecture in Mathematics: Juggling Counts
2026-04-09 16:30 - 17:30 | Lubar Hall N140, 3202 N Maryland Ave, Milwaukee, WI, 53211, United States
Juggling Counts
Presented by Prof. Steve Butler, Morrill, Professor of Mathematics at Iowa State University
Mathematics is a language which can help us describe and explore patterns. One source of patterns that mathematicians have been exploring comes from juggling (the tossing of objects, usually balls or clubs). We will look at multiple ways to describe juggling patterns that allow us to find new juggling patterns, and to count how many possible patterns exist. We can compare answers to various problems to give a combinatorial proof of Worpitzky’s identity. We will also look at a few juggling-based problems that mathematics has not yet succeeded in answering.
This event is a part of the Marden Lecture Series, each Spring the Department of Mathematical Sciences invites a distinguished mathematician to lecture to a general audience. The Marden Lecture honors Morris Marden (1905 – 1991), who founded our graduate program and made our department a research department. The Marden lecture is funded through the Miriam and Morris Marden Fund and is co-sponsored by the Department of Mathematical Sciences.
A banquet will be held in the LEC AmFam Dream Studio following the lecture.

Colloquium: Prof. Genevieve Walsh
2026-04-03 14:00 - 15:00 | EMS Building, E495, 3200 N Cramer St, Milwaukee, WI, United States
Quasi-isometric Hyperbolic and Cusped Relatively Hyperbolic Groups are Symmetric
Prof. Genevieve Walsh
Professor of Mathematics
Tufts University
This talk will first describe hyperbolic groups and relatively hyperbolic group pairs, and give some key examples. We then delve into understanding when the cusp space for a relatively hyperbolic group can be quasi-isometric to a hyperbolic group. For example, real hyperbolic spaces admit uniform and non-uniform lattices. We show that this is the exception. In particular, if a hyperbolic group is quasi-isometric to a cusped space for a relatively hyperbolic group, then both groups are lattices acting on a rank-1 symmetric space.
This is joint work with Daniel Groves, Emily Stark, and Kevin Whyte.

Graduate Student Colloquium: Jonathan Walker-Moses
2026-04-03 12:30 - 13:30 | EMS Building, E495, 3200 N Cramer St, Milwaukee, WI, United States
The Beautiful Interplay of Rotation Groups in Three Dimensions

We’ll explore the connections between the rotation Lie groups (SU(n) and SO(n)) in two and three dimensions. In doing so, we’ll prove a remarkable theorem about the way that SU(2) and SO(3) relate using quaternions and then discuss some connections to complex analysis at the end. In doing so, we’ll take a very fun and (in my opinion) mind-blowing journey through spheres of different dimensions. Absolutely no knowledge of Lie theory is expected and I’ll be happy to clarify any details from topology or group theory that come up that you aren’t familiar with.

Colloquium: Dr. Jennifer Elder
2026-03-13 14:00 - 15:00 | EMS Building, E495, 3200 N Cramer St, Milwaukee, WI, United States
Doing Anything You Want With Combinatorics
Dr. Jennifer Elder
Assistant Professor of Mathematics
Missouri Western State University
When Mathematical Reviews first launched as a journal in 1940, combinatorics was not listed as a research area. The Seven Bridges of Königsberg was solved in 1736, so this absence is not due to later development of the field. Combinatorics has simply been hard to define on its own, given that it is used as a tool in so many different areas of mathematics.
This talk will take the opposite point of view. We will center our focus on several research problems motivated from a combinatorial standpoint, and the connections to other fields of research. These connections can be simple, such as bridging different subareas of combinatorics: a study of a specific set of words uncovering unexpected properties of intervals in a lattice. Or the connections can be more odd, connecting widely different areas of mathematics: a study of braid diagrams on k strands as a dynamical algebraic system.

SIAM Student Chapter: Agentic Implementations of Modern Applications
2026-03-13 12:30 - 13:30 | EMS Building, EMS E495, 3200 Cramer St, Milwaukee, WI, 53211, United States
Agentic Implementations of Modern Applications
We’ll be hearing from Kolin Konjura, a Senior Solutions Engineer at Microsoft with a Bachelor of Science in Mathematics from UWM and a Master’s Degree in Mathematics. He will discuss how modern agentic systems are being implemented across industry applications, highlighting opportunities for students in applied mathematics, data science, and computational fields.
This event is hosted by the SIAM Student Chapter, UWM

Colloquium: Dr. Elaine Spiller
2026-03-06 14:00 - 15:00 | EMS Building, E495, 3200 N Cramer St, Milwaukee, WI, United States
Uncertainty Quantification for Geophysical Hazard Analysis
Dr. Elaine Spiller
Professor of Applied Math and Statistics
Marquette University
Geophysical flows — landslides, storm surge, tsunamis, volcanic flows, etc — pose a serious threat to nearby populations. Ideally, probabilistic hazard assessments combine available knowledge about physical mechanisms of the hazard, data on past hazards, and any available precursor information. Systematically assessing the probability of rare, yet catastrophic hazards adds a layer of difficulty due to limited observational data. Via computer models, one can exercise potentially dangerous scenarios that may not have happened in the past but are probabilistically consistent with the aleatoric nature of previous geophysical behavior in the record.
I will discuss recent work and ongoing methodological challenges toward making efficient and flexible geophysical hazard maps focusing on applications to volcanic flows (pyroclastic density currents) and post-fire debris flows.

Graduate Student Colloquium: Ilana Lavene
2026-03-06 12:30 - 13:30 | EMS Building, E495, 3200 N Cramer St, Milwaukee, WI, United States
An Introduction to Boundaries of Groups
We introduce a generalization of parking functions in which cars are limited in their movement backwards and forwards by two nonnegative integer parameters k and ℓ, respectively. In this setting, there are n spots on a one-way street and m cars attempting to park in those spots, and 1≤m≤n. We let α= (a1,a2,…,am) in [n]^m denote the parking preferences for the cars, which enter the street sequentially. Car i drives to their preference a_i and parks there if the spot is available. Otherwise, car i checks up to k spots behind their preference, parking in the first available spot it encounters if any. If no spots are available, or the car reaches the start of the street, then the car returns to its preference and attempts to park in the first spot it encounters among spots a_i+1,a_i+2,…,a_i+l. If car i fails to park, then parking ceases. If all cars are able to park given the preferences in α, then α is called a (k,l)-pullback (m,n)-parking function. Our main result establishes counts for these parking functions via a recursive formula.

Community of Practice
2026-02-20 12:30 - 13:30 | EMS Building, Room W110
From Beliefs to Practice, Expanding Collaboration in Mathematics Classrooms
Collaboration in mathematics classrooms is not only a logistical challenge. It is a belief-driven one. This interactive conversation will explore how instructor beliefs and instructional identities shape how we design tasks, structure class sessions, and respond to student thinking. Participants will examine strategies for supporting small-group collaboration that work (even in less-than-ideal physical spaces) while also reflecting on how mathematical joy broadens what feels possible for students and instructors alike.
Facilitated by: Dr. Anne Marie Marshall
***
What is the Community of Practice?
The Community of Practice is a space for everyone in the department (lecturers, GTAs, faculty) to come together and have chats, professional development, speakers, workshops, and more related to teaching and learning. There’s no sign-up; simply attend if you want! If you would like to be involved in any planning or would like to run a session, please email me (henathan@uwm.edu) and let me know.

The Community of Practice Canvas Site
We have a Community of Practice Canvas site where we keep a signup and modules for past sessions. If you would like to enroll, here is the link: https://uws-td.instructure.com/enroll/XK96LD

SIAM Student Chapter
2026-02-20 12:30 - 13:30 | EMS Building, EMS E495, 3200 Cramer St, Milwaukee, WI, 53211, United States
Life After the PhD, Alumni Career Panel
Join us for a discussion with distinguished alumni as they share their experiences transitioning from graduate school to academic careers. Pizza will be provided!
Topics include:

Academic job market
Postdocs and faculty positions
Teaching-focused vs research-focused paths
Lessons learned after the PhD

Panelists:

Dr. Kimberly J. Harry –Northeastern State University
Dr. Kathryn Boddie – University of Louisiana at Lafayette
Dr. Daniel Noelck – Illinois Institute of Technology
Dr. Daniel Gulbrandsen – Hampden–Sydney College (VA)

This event is hosted by the SIAM Student Chapter, UWM

Colloquium: Prof. Trevor Leslie
2026-02-13 14:00 - 15:00 | EMS Building, E495, 3200 N Cramer St, Milwaukee, WI, United States
Sticky Particle Solutions of the Euler Alignment system
This talk is about the Euler Alignment system from the field of collective behavior. After a primer on modeling considerations and the equations at issue, we discuss the weak solution theory developed by Leslie and Tan via using a sticky particle discretization technique pioneered by Brenier and Grenier. The special structure of the equations allows us a detailed look into the time-asymptotic behavior of the system, including the structure of so-called “flocking states”.

Graduate Student Colloquium: Kushlam Srivastava
2026-02-13 12:30 - 13:30 | EMS Building, E495, 3200 N Cramer St, Milwaukee, WI, United States
An Introduction to Boundaries of Groups
A key idea in the field of geometric group theory is to study geometric and topological objects associated with groups. Boundaries of groups are examples of such objects. In this talk we will look at boundaries of (relatively) hyperbolic groups and see how their topology is directly related to algebraic properties of groups. This expository talk is meant to be an entry point for the audience to explore geometric group theory and no prior knowledge except basic topology is needed.

Colloquium: Dr. Joseph Rennie
2026-02-06 14:00 - 15:00 | EMS Building, E495, 3200 N Cramer St, Milwaukee, WI, United States
(Higher) Categorical Galois Theory for the Aspiring Mathematician
Here we focus on the function/motivation of specific structures (most likely new to the audience) in high-level mathematics with the aim of highlighting major themes in the broader canvas of modern mathematics. Specifically, Galois Theoretic ideas emerge across disciplines, all as instances of a single theorem in (higher) category theory. This talk uses that idea to motivate a journey through three main themes relevant to any area:

The ubiquity of presheaf localizations
The concept of a classifying object
The pervasiveness of Algebro-Geometric duality

In some parts, I will use categorical-theoretic language not with the expectation that people speak the language, but rather as a demonstration of the beauty of the perspective gained by acquiring fluency. (What better way to motivate oneself to learn a new language than to listen to some of its poetry?)
This talk also serves as an onboarding for those interested in research projects on this topic. Though the talk should also inspire those who have no interest in category-theoretic research.

Community of Practice: Goal Setting and Organizational Meeting
2026-02-06 12:30 - 13:30 | EMS Building, EMS E495, 3200 Cramer St, Milwaukee, WI, 53211, United States
What goals do you have for your teaching this semester? We’ll explore and share various goals and what we might need as a group/department to help us move forward in our goals.
If you are involved in the PAIR Mentoring program, this is an excellent space for initial goal-planning!
We will also use some time to organize and plan Community events for the Spring 2026 semester.
What is the Community of Practice?
The Community of Practice is a space for everyone in the department (lecturers, GTAs, faculty) to come together and have chats, professional development, speakers, workshops, and more related to teaching and learning. There’s no sign-up; simply attend if you want! If you would like to be involved in any planning or would like to run a session, please email me (henathan@uwm.edu) and let me know.
The Community of Practice Canvas Site
We have a Community of Practice Canvas site where we keep a signup and modules for past sessions. If you would like to enroll, here is the link: https://uws-td.instructure.com/enroll/XK96LD

Colloquium: Dr. Alison Marzocchi
2026-01-30 14:00 - 15:00 | EMS Building, E495, 3200 N Cramer St, Milwaukee, WI, United States
Dr. Alison Marzocchi
Supporting Mathematics Faculty Instructional Improvement with Reflection Cycles
Dr. Alison Marzocchi
Professor of Mathematics
California State University, Fullerton
Many mathematics faculty desire to improve their instruction but may feel they lack the knowledge, confidence, skills, or time to do so. Among numerous professional development activities, our mathematics department at California State University, Fullerton offers Reflection Cycles, both student-facilitated and peer-facilitated. Peer-facilitated Reflection Cycles involve pairs of faculty taking turns leading each other in three phases: planning, implementation, and debrief. The planning phase involves setting specific goals for an upcoming lesson. The implementation phase involves observation during a regularly scheduled class session, with a focus on the goals set by the instructor. The debrief phase involves reflection on the implementation and setting new goals for the future. A second Reflection Cycle can then be scheduled to continue working on the same goals or to set new goals. Reflection Cycles allow for gradual, sustained, individualized improvement of instruction. They are facilitated in-house and can additionally improve department camaraderie.

Graduate Student Colloquium: Q&A Session with Dr. Pamela Harris
2026-01-30 12:30 - 13:30 | EMS Building, E495, 3200 N Cramer St, Milwaukee, WI, United States
This event will still take place on 01/30/2026 from 12:30 – 1:30 pm in EMS E495
The first graduate student colloquium this semester features our Chair, Dr. Pamela Harris. This will be an informal conversation between the department chair and graduate students. There will also be a portion of our time to answer questions posed anonymously. This is a great opportunity to meet our Chair and get your burning questions answered! This can range from department life, teaching, research, and more. Please come and join us in the conversation and bring any topics you would like talk about or have questions on. We hope to see you there!
Pizza will be served after this event, before the department colloquium!

MS Thesis Defense: Mr. Amare Mebrahtu
2026-01-16 15:00 - 16:30 | WI
Exploring the Levels of Mathematical Modeling Prompts in the Illustrative Mathematics Algebra I and Geometry Curricula
Amare Mebrahtu
Graduate Student
University of Wisconsin-Milwaukee
This event will take place virtually over Teams on Friday, January 16th from 3:00pm–4:30pm.
The Common Core State Standards for Mathematics highlight the importance of mathematical modeling in enhancing students’ problem-solving abilities and critical thinking in mathematics. To this end, incorporating the various characteristics and levels of modeling problems is pivotal to designing and implementing mathematical modeling for students. This talk will explore the levels of mathematical modeling in the Illustrative Mathematics (IM) Algebra I and Geometry curricula.
Drawing on the California Framework for Mathematical Modeling, we will classify selected mathematical modeling problems in IM using five core characteristics: problem context, questions provided, student autonomy, modeling process, and iteration. The findings reveal that most IM modeling prompts align with intermediate levels in the framework, balancing structured guidance with opportunities for student-driven decision-making and iterative refinement.
Advisor:
Prof. Kevin McLeod
Committee Members:
Prof. Suzanne Boyd
Prof. Jeb F Willenbring

Graduate Student Colloquium: Alex Wilson
2025-12-18 13:00 - 17:00 | EMS W434
Representation Theory Through Parking Functions
This talk is about parking spaces. No, not the kind in a grocery store parking lot, rather a kind of space that appears when you want to study the symmetries of a set of combinatorial objects. If the terms vector space, group, and parking functions are already familiar to you, you’re going to see a topic where they intersect. If those terms mean nothing to you, then you’ll learn a little about what they are through a concrete example. I hope you’ll come with curiosity, stay for the pretty pictures, and leave with a different perspective through which you can view any mathematical objects you’re interested in.
Presented by by Alex Wilson, Postdoctoral Visitor at York University.
Join us for pizza before the talk from 12:30PM-1:00PM!

SIAM Student Chapter Presents: Dr. Carlos Martinez Mori
2025-12-18 11:30 - 12:30 | EMS W434
Cooperation and the Design of Public Goods
We consider the cooperative elements that arise in the design of public goods, such as transportation policies and infrastructure. These involve a variety of stakeholders: governments, businesses, advocates, and users. Their eventual deployment is critically dependent on the decision maker’s ability to garner sufficient support from each of these groups; we formalize these strategic requirements from the perspective of cooperative game theory. Specifically, we introduce non-transferable utility, linear production (NTU LP) games, which combine the game-theoretic tensions inherent in public decision-making with the modeling flexibility of linear programming. We derive structural properties regarding the non-emptiness, representability, and complexity of the core, a solution concept that models the viability of cooperation. In particular, we provide fairly general sufficient conditions under which the core of an NTU LP game is guaranteed to be non-empty, prove that determining membership in the core is co-NP-complete, and develop a cutting plane algorithm to optimize various social welfare objectives subject to core membership. Lastly, we apply these results in a data-driven case study on service plan optimization for the Chicago bus system. We illustrate how, while cooperation is necessary for the successful deployment of transportation service plans, it may also have adverse and/or counterintuitive distributive implications.
This is joint work with Alejandro Toriello.
Presented by Dr. Carlos Martinez Mori, Assistant Professor at the University of Colorado Denver.
Pizza will be served immediately following the lecture!

MS Exam Prep Sessions
2025-12-12 15:00 - 16:30, 2025-12-05 15:00 - 16:30 | WI
Come join our Algebra & Analysis Prep Sessions to review key concepts, practice problems, and build confidence for the department’s Master’s Preliminary Exams! Sessions will start on September 12th and run until December 12th.
Analysis Session
Facilitated by: Liam
from 3:00 – 4:30
in EMS W434
Algebra Session
Facilitated by: Stephen
from 3:00 – 4:30
in EMS E408

Math Department Holiday Party!
2025-12-12 12:00 - 15:00 | EMS Building, E495, 3200 N Cramer St, Milwaukee, WI, United States
Friday, Dec 12th
Noon to 3 pm in EMS E495
Bring a sweet or savory dish to share or donate to the pizza fund! We are suggesting a $10 donation from staff and a $5 donation from students
You can give cash to Jill Meyers in EMS E412 or Venmo Hayley Nathan at @Hayley-Nathan
Please make all donations by 3 pm, Thursday Dec 11th
For anyone who wishes to participate, we will have a white elephant coffee mug game at 2 pm!
If you wish to play, bring a wrapped coffee mug to the party! (Do not spend a lot of money on the mug please!)
