Current: Spring 2026
■ February 18, 4pm-5pm, Room UP222
Hannah Steger, USD
Title: Barycentric Subdivision and Hyperbolic Geometry
Abstract: Barycentric subdivision of a triangle is the geometrical process of repeatedly subdividing a triangle by connecting the midpoints of the sides to the opposite vertices. The transformations which determine this subdivision form a group acting on the hyperbolic plane, action which we will show is topologically transitive. We will also analyze cases leading to flat triangles.
■ February 27, 4pm-5pm, Room UP222
Alexander Kunin, Creighton
Title: From Brains to Binary Matrices
Abstract: The hippocampus is a brain region associated with memory formation and learning. It’s also the brain’s GPS: Certain neurons, called place cells, turn on when you are the cell’s corresponding place field, a specific location in your environment. When standing in the intersection of some place fields, the corresponding place cells will be active, while the rest silent. Thus, the patterns of active and inactive neurons form a combinatorial encoding of overlapping subsets of a Euclidean space. A natural question that arises is whether any set of patterns can be realized in this way. The answer is, “it depends,” and the first half of this talk will attempt to figure out, “on what.” This will include some ongoing work with an undergraduate student. This portion of the talk concludes with the relationship between this question and the missing axiom of matroid theory. We will then see that the mathematics developed in pursuit of this problem has a surprising application: it helps us solve matrix factorization problems. We show how to use the theory developed in the first half of the talk to solve the Boolean matrix equation AX = B (entries in our matrices are 0 or 1, and 1+1=1), extending results dating back to the 1950s and, surprisingly, yielding further insight to the combinatorial problem posed in the first half. The talk will conclude with some open questions and something of an invitation to the field of mathematical neuroscience.
■ March 2, 4pm-5pm, Room UP222
Olivia Roberts, University of Michigan
Title: : Transitions in ENDS and cigarette use among youth in the PATH Study from 2015–2023: a multistate transition modeling analysis
Abstract: Monitoring trends in transitions in the use of electronic nicotine delivery systems (ENDS) and cigarettes among youth is important for understanding the public health impacts of these products. Using a weighted Markov multistate transition model accounting for complex survey design, we estimated transition rates and one-year transition probabilities between never, non-current, ENDS-only, and cigarette use (with or without dual use of ENDS) among 26,744 youth aged 12–17 who participated in at least two consecutive waves from Waves 2–7.5 (approximately 2015–2023) of the nationally representative Population Assessment of Tobacco and Health (PATH) Study. We also estimated transitions stratified by ages 12–14 and 15–17 years.
Conclusion. ENDS-only use initiation has changed over time, peaking around 2019 and subsequently plateauing, but cessation rates for both ENDS and cigarettes have remained relatively stable. Thus, interruption of tobacco product initiation may be the most effective approach to reducing tobacco product use among youth