Mathematical Sciences

PhD Dissertation Defense: Mr. Joe Paulson
2025-08-07 14:00 - 16:00 (America/Chicago) | EMS Building, Room E408, E408; 3200 N Cramer St., Milwaukee, WI, 53211, United States
Theory of Z_n – Structures
Mr. Joe Paulson
Graduate Student
University of Wisconsin-Milwaukee
In this defense, we discuss the boundaries of Type F_n groups; those being groups whose K(G,1) complex has a finite n-skeleton. The boundaries we develop extend the notion of Z-boundaries to what we call Z_n-boundaries. This extension centers around groups no longer acting geometrically on contractible spaces, but instead n-connected spaces. Immediately this means the major theorems of “Boundary Swapping” and “Shape Equivalence of Z-Boundaries” will need revision, but a more subtle point to be discussed is that the category of spaces must also be generalized.
After discussing the foundation work for a theory of Z_n-boundaries, we end with an exploration how these new structures can be related to other well-known compactifications such as the one-point compactification, end-point compactification, and Z-compactifications.
Advisor:
Craig Guilbault
Committee Members:
Boris Okun, Chris Hruska, Jonah Gaster, and Pamela Harris

PhD Dissertation Defense: Mr. Shenyan Pan
2025-08-08 14:00 - 16:00 | https://teams.microsoft.com/l/meetup-join/19%3aCQyl6Y73Ps7zxWXrM3dRP8rS7Q89Bvw2sceTNhSLlUw1%40thread.tacv2/1754451851629?context=%7b%22Tid%22%3a%220bca7ac3-fcb6-4efd-89eb-6de97603cf21%22%2c%22Oid%22%3a%2234947e74-60a7-40f3-ae30-4a6cd4dc57b7%22%7d
Doubly Stochastic Model With Covariates For Replicated Poisson Point Processes
Mr. Shenyan Pan
Graduate Student
University of Wisconsin-Milwaukee
Poisson point processes (PPPs) are powerful tools for modeling random point occurrences in multidimensional spaces, with applications across various fields. Although the traditional literature has focused on single realizations, replicated point processes are becoming increasingly common due to the growing availability of complex data. This dissertation develops a doubly stochastic model for replicated PPPs that incorporates covariates, extending latent component models to capture external effects. The proposed model expresses the log-intensity function as the sum of a mean function and latent component scores that vary with covariates. To ensure identifiability, component scores are constrained to be zero-mean and uncorrelated via centering and orthogonality. Parameter estimation is performed using penalized maximum likelihood, employing Newton–Raphson updates and the Laplace approximation for conditional distributions. Simulation studies assess the model’s stability across various covariate structures (linear and nonlinear), baseline rates, and sample sizes. The results demonstrate decreasing error with increasing sample size, confirming the estimators’ consistency. The model is applied to real data from the Divvy bicycle-sharing system in Chicago, analyzing daily usage at a representative station. The results reveal a nonlinear relationship between temperature and ridership, with peak usage occurring at moderate temperatures and declines observed under extreme heat or cold. This modeling framework improves the interpretability and predictive accuracy of PPPs with covariates, offering practical insights for applications such as fleet allocation in bicycle-sharing systems.
Advisor:
Prof. Daniel Gervini
Committee Members:
Prof. Lei Wang, Prof. Chao Zhu, Prof. David Spade, and Prof. Vytaras Brazauskas
Link to Event

PhD Dissertation Defense: Mr. Marco Vaassen
2025-08-11 13:30 - 15:30 | EMS Building, E495, 3200 N Cramer St, Milwaukee, WI, United States
A Bootstrap Goodness-of-Fit Test for Parametric Survival Models
Mr. Marco Vaassen
Graduate Student
University of Wisconsin-Milwaukee
In many scientific disciplines, finding a suitable model compatible with real-world observations is the basis for statistical inference and prediction. In survival analysis, this task is further complicated by censoring. This dissertation introduces a new bootstrap approach to goodness-of-fit testing for parametric survival models, based on the Kaplan–Meier process with estimated parameters. The test statistic compares the nonparametric Kaplan–Meier estimator to a fitted parametric model, quantifying deviations from the null via functionals that yield Kolmogorov–Smirnov or Cramér–von Mises-type tests. We establish the asymptotic correctness of our method by showing that the original and bootstrap test statistics have the same weak limit under the null. The result is a consistent, easily implementable framework for assessing model fit in censored settings.
Advisor:
Prof. Richard Stockbridge, Prof. Gerhard Dikta
Committee Members:
Prof. Richard Stockbridge, Prof. Gerhard Dikta, Prof. Chao Zhu, Prof. David Spade, and Prof. Vincent Larson

Community of Practice Kickoff
2025-09-05 12:30 - 13:30 | EMS Building, E495, 3200 N Cramer St, Milwaukee, WI, United States
Date: September 5, 2025
Time: 12:30-1:30
Room: E 495
Join us for the first Community of Practice meeting of the semester, stop by to say “Hi” to colleagues as we wrap up Week 1.
During this event, we will pull some grab bag questions and discuss the Community of Practice organization, schedule, and topics for this semester.
Bring any of your ideas! Light snacks will be provided.
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. If you would like to be involved in any planning, please email Hayley Nathan (henathan@uwm.edu).

Department Ice Cream Social
2025-09-05 14:00 - 16:00 | EMS Building, E495, 3200 N Cramer St, Milwaukee, WI, United States
Date: September 5, 2025
Time: 2:00pm to 4:00pm
Room: E 495
Join us for the first-ever Mathematical Sciences Department ice cream social!

MS Exam Prep Sessions
2025-09-12 15:00 - 16:30, 2025-09-19 15:00 - 16:30, 2025-09-26 15:00 - 16:30, 2025-10-03 15:00 - 16:30, 2025-10-10 15:00 - 16:30, 2025-10-17 15:00 - 16:30, 2025-10-24 15:00 - 16:30, 2025-10-31 15:00 - 16:30 and 6 more dates
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

Graduate Student Colloquium: Kimberly Hadaway
2025-09-26 12:30 - 13:30 | EMS Building, Room E495, E495; 3200 N Cramer St., Milwaukee, WI, 53211, United States
Parking Completions and Volumes of Polytopes
Kimberly Hadaway
Graduate Student
Iowa State University
Parking functions correspond with preferences of n cars which enter sequentially to park on a one-way street where (1) each car parks in the first available spot greater than or equal to its preference and (2) all cars successfully park. We generalize parking functions to parking completions: Here, we are given that some cars have already parked in a set of spots, which are indexed in a vector t. We then consider a preference vector c, where len(t)+len(c)=n. If all cars can park, we say that c is a parking completion. Adeniran, et al. (2020) state an open problem which connects the number of parking completions to the volumes of Pitman-Stanley polytopes by explicit computation on small values of n. In this talk, we provide a partial solution to this open problem by exploring edge cases.

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.

Graduate Student Colloquium: Jillian Cervantes
2025-10-24 12:30 - 13:30
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: 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.

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.

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!)

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!

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!

MS Thesis Defense: Mr. Amare Mebrahtu
2026-01-16 15:00 - 16:30
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: 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!

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.
