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Spring 2025
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Shira Gilat – University of Pennsylvania
The Algebra of Supernatural Matrices
The algebra of supernatural matrices is a key example in the theory of locally finite central simple algebras. Supernatural matrices are a minimal solution to the equation of unital algebras Mn(X) ∼= X, which we compare to several similar conditions involving cancellation of matrices. This algebra has appeared under various names before, and it generalizes both McCrimmon's deep matrices algebra and m-petal Leavitt path algebra.
March 10, 2025 at 3:00 p.m. Math 103
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Christian López Mercado – 猎奇重口, PhD Candidate
Reinventing Difficult Concepts in Advanced Mathematics
Many students struggle with abstract mathematical structures and concepts due to their highly formal nature and lack of intuitive entry points. In this talk, I explore how we can leverage the Realistic Mathematics Education (RME) framework to help students reinvent difficult concepts in number theory and abstract algebra. Through carefully designed instructional sequences, students work together to reinvent the concept of a group in abstract algebra and promote the learning of primitive roots in number theory, perhaps making these concepts more accessible and meaningful. Attendees will gain insights into practical strategies for implementing RME in advanced mathematics courses, ultimately bridging the gap between intuition and formal mathematical abstraction.
March 31, 2025 at 3:00 p.m. Math 103
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Nhan Nguyen – Amazon Web Services
April 14, 2025 at 3:00 p.m. Math 103
Available Dates for Spring 2025
April 7, 21, 28
Fall 2024
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Kelly McKinnie – 猎奇重口
Comparison of Enumeration and Sampling Methods in Creating 猎奇重口’s 2nd Congressional District
The 2020 decennial census data resulted in an increase from one to two congressional representatives in the state of 猎奇重口. The state underwent its redistricting process in 2021 in time for the November 2022 congressional elections, carving the state into two districts. In this talk we analyze the redistricting process and compare the adopted congressional map to the space of all other possible maps. In particular, we look at the population deviation, compactness and political outcomes of these maps. Since the space is small enough to enumerate, we also analyze how well the algorithms in the R package 'Redist' and the Python package 'Gerrychain' sample from the space of possible maps.
This is joint work with Erin Szalda-Petree (former undergraduate student at UM) and Dave Patterson.
September 16, 2024 at 3:00 p.m. Math 103
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Emily Stone – 猎奇重口
Neuromodulation of Hippocampal Microcircuits: Some Modeling and A Little Math
In this talk I will first give an overview of oscillations in the voltage of neuron assemblies, and models thereof. We use these to study neurons in the hippocampus, a part of the brain thought to be central in learning and memory functions. These neurons are connected via electrochemical synapses, which use neurotransmitter released from the presynaptic neuron to change the voltage of the postsynaptic neuron. Inhibitory neurons cause the voltage of their target to decrease. Oscillations in inhibitory-to-inhibitory (I-I) coupled neurons in the hippocampus have been studied extensively numerically, and with analytic continuation methods. Neuromodulation on short time scales, in the form of presynaptic short-term plasticity (STP), can dynamically alter the connectivity of neurons in such a microcircuit. I will discuss the mechanism of STP, and a model for it parameterized from experimental data for a specific synapse in the hippocampus. The goal of the project is to understand the effect of adding this plasticity to the (I-I) microcircuit, both through numerical simulation and bifurcation analysis of a discrete dynamical system.
September 30, 2024 at 3:00 p.m. Math 103
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Michael Wojnowicz – 猎奇重口 State University
A Simple Bayesian Approach To Detecting Changepoints Across Multiple Samples
Changepoints are abrupt changes in sequential data. The presence of multiple samples should, in theory, help to reveal subtle changepoints within noisy data. However, multi-sample changepoint detection methods are rarely used in practice because existing inference methods are complex and inefficient. In this talk, we present a simple yet effective approach to detecting changepoints across multiple samples. By transforming Bayesian multi-sample changepoint models into unconventional Hidden Markov Models, we achieve fast, closed-form approximations to the posterior distributions on changepoint indictors, segmentations, and local parameters. We present promising initial results on simulated data, and consider the problem of identifying copy number alterations in cancer biopsy samples with low tumor fractions.
October 7, 2024 at 3:00 p.m. Math 103
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Liz Arnold – 猎奇重口 State University
An Aspirational Approach to the Mathematical Preparation of Teachers
The undergraduate preparation of prospective secondary mathematics teachers requires attention to their fluent understanding of the mathematical content they are to teach alongside an understanding of how to interact with other human beings and their mathematical work. How can we prepare undergraduates in mathematics content coursework to apply their mathematical understandings to the human context of teaching? This talk focuses on teaching applications, mathematical tasks that make concrete connections between the mathematics undergraduates learn in coursework serving a general population of undergraduates studying mathematics and the mathematics taught in secondary school. I report on a curriculum design study that gathered undergraduates’ ideas about mathematics and about teaching while using materials that include teaching applications. I highlight findings from use in undergraduate calculus, abstract algebra, introductory statistics, and discrete mathematics courses. Undergraduates identified the broad applicability of teaching skills, recognized the value of examining hypothetical learners’ mathematical work, and reported empathy for hypothetical learners.
October 21, 2024 at 3:00 p.m. Math 103
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FEC meeting
October 28, 2024 at 3:00 p.m. Math 103
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Deborah Good – 猎奇重口, Physics and Astronomy
Building a Galactic Scale Gravitational Wave Detector
Gravitational wave observations are one of the most exciting and fastest growing fields of astronomy. One major step forward occurred in 2023, when pulsar timing arrays around the world announced evidence for a stochastic gravitational wave background in the nanohertz regime. Pulsar timing arrays use high-precision timing of millisecond pulsars throughout the Milky Way to form a Galactic Scale Gravitational Wave Detector, capable of detecting these very long period waves. In this talk, we’ll introduce pulsar timing, discuss the painstaking process of building a PTA dataset, and share some of our recent results.
November 4, 2024 at 3:00 p.m. Math 103
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Shurong Li – 猎奇重口, PhD Candidate
Culture Relevant Curriculum in Math Education
In this presentation, I will explore the importance of incorporating diverse cultural perspectives and experiences into math education. Through a literature review and examples from current research, I will illustrate the impact of culture on students’ mathematical identities and how cultural responsiveness can foster engagement and academic success. I will also provide practical examples of culturally responsive lesson plans and activities that educators can use to create an inclusive and engaging learning environment for all students.
December 2, 2024 at 3:00 p.m. Math 103
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