Mathematical Sciences

Colloquium: Dr. Elaine Spiller
2026-03-06 14:00 - 15:00 (America/Chicago) | 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
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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, 2025-11-28 15:00 - 16:30, 2025-11-21 15:00 - 16:30, 2025-11-14 15:00 - 16:30, 2025-11-07 15:00 - 16:30, 2025-10-31 15:00 - 16:30, 2025-10-24 15:00 - 16:30 and 4 more dates | 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!)

Colloquium: Dr. Daniel Noelck
2025-10-31 14:00 - 15:00 | EMS Building, E495, 3200 N Cramer St, Milwaukee, WI, United States
Exponential Stability Of The Discrete Stochastic Filter Via Non-degeneracy Andanalytic Stability Of The Signal
Dr. Daniel Noelck
Senior Research Associate
Illinois Institute of Technology
The stability of discrete time filters has been an active field of research, particularly when applied to numerical filter approximation schemes. Most results in the field are obtained on a compact signal space, but there is no reason to believe the results should not carry over to non-compact spaces. In this talk, we will introduce the discrete time filtering problem, discuss some well known results on compact spaces, and the difficulties of expanding those results to non-compact spaces, and then introduce recent results for stability on those non-compact spaces. Finally, we will discuss the future work available in the continuous time setting.

Colloquium: Prof. Greg Ongie
2025-10-24 14:00 - 15:00 | EMS Building, E495, 3200 N Cramer St, Milwaukee, WI, United States
A Function Space View of Neural Networks
Prof. Greg Ongie
Assistant Professor
Marquette University
Many mathematical analyses of deep learning focus on how neural network (NN) parameters evolve during training. A complementary perspective is to view NN training as fitting a function belonging to a function space implicitly defined by the architecture and training procedure. In particular, when parameter norms are explicitly or implicitly constrained, NNs exhibit a bias toward functions with low “representation cost,” defined as the minimal parameter norm required to realize the function with a given NN architecture. This talk surveys recent results that characterize representation cost of shallow NN architectures in terms of Banach space norms, and through non-linear notions of function rank for deeper NN architectures. Finally, we discuss how bias towards low representation cost functions helps to explain generalization in various applications.

Graduate Student Colloquium: Jillian Cervantes
2025-10-24 12:30 - 13:30 | WI
The Axiom of Choice and Non-Lebesgue Measurable Sets
Jillian Cervantes
Graduate Student
University of Wisconsin-Milwaukee
In this expository talk, we explore an interesting connection between the axiom of choice and the existence of non-Lebesgue measurable subsets of mathbb{R}. We state the axiom of choice and discuss its meaning and significance before reviewing properties of measures, Lebesgue measure, and Lebesgue measurable sets. The talk concludes with a construction which uses the axiom of choice to prove the existence of non-Lebesgue measurable sets.

Colloquium: Dr. Dexuan Xie
2025-10-10 14:00 - 15:30 | EMS Building, E495, 3200 N Cramer St, Milwaukee, WI, United States
Recent Advances in Nonlocal Dielectric Continuum Models for Predicting Protein and Ion Channel Electrostatics
Dr. Dexuan Xie
Professor
University of Wisconsin-Milwaukee
The calculation of electrostatics for proteins and ion channels is a fundamental challenge in structural biology, computational biochemistry, biophysics, and mathematical biology. Traditional dielectric continuum models, such as the Poisson–Boltzmann equation and its variants, are widely used for this calculation. However, their prediction accuracy often deteriorates near highly charged biomolecular surfaces because they neglect the polarization correlations of water molecules. To address these limitations, a nonlocal dielectric continuum modeling approach was introduced roughly four decades ago. Over the past decade, this approach has seen substantial theoretical and computational advances, largely driven by our group’s work under support from the National Science Foundation.
In this seminar, I will present our nonlocal dielectric theory and report our recent progress in developing nonlocal dielectric continuum models and finite element solvers for proteins and ion channels. I will also compare the predictions of our novel nonlocal models with those of the traditional local models and present numerical results demonstrating the efficiency of our solvers and the high performance of our software package. This work is a collaboration with my students, Liam Jemison and Matthew Stahl. It has been partially supported by the National Science Foundation under award DMS-2153376 and by the Simons Foundation under research award 711776.
