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Ryan James, PhD – Reddit

Multivariate Information Theory: Difficulties and Recent Progress

Information theory has been widely applied within the sciences. Much of the appeal comes from it providing a substraight-agnostic method of quantifying the interactions within a system. In the bivariate case, many measures have reasonably robust interpretations stemming from their status as solutions to operational problems. In the multivariate case, however, most measures are extensions of their bivariate cousin, but lack the operational interpretation. In this talk, we review many multivariate information measures that have been employed in data analysis, their interpretational difficulties, and some recent progress in producing interpretable, robust multivariate measures.

February 12, 2024 at 3:00 p.m. Math 103

Anna Halfpap – Iowa State University

Proper Rainbow Saturation Numbers 

A graph G is F-saturated if G does not contain F as a subgraph, and is edge-maximal with regards to this property. That is, for any edge e that G is "missing", the graph G + e obtained by adding e to G contains one or more subgraphs isomorphic to F. The study of F-saturated graphs informs the core questions in extremal graph theory. The extremal number ex(n, F) is the maximum number of edges possible in an n-vertex graph which does not contain F -- that is, ex(n, F) is the maximum number of edges in an n-vertex, F-saturated graph. On the other hand, the saturation number sat(n, F) is the minimum number of edges in an n-vertex, F-saturated graph. Both ex(n, F) and sat(n, F) are extensively studied, and naturally generalize to a variety of settings.

In this talk, we will discuss a variation on saturation numbers which arises in an edge-colored setting. An edge coloring of a graph is an assignment of colors (typically, some subset of the positive integers) to the graph's edges. We say that an edge coloring is proper if any two edges which share an endpoint receive distinct colors, and is rainbow if any two edges receive distinct colors. In 2007, Keevash, Mubayi, Sudakov, and Verstraete introduced the rainbow extremal number, which combines extremal graph theory questions with edge coloring. The rainbow extremal number of F is the maximum number of edges in a graph G such that, under some proper edge-coloring, G does not contain a rainbow copy of F. Rainbow extremal numbers have received substantial attention over the last fifteen years, but the corresponding rainbow saturation question was only posed very recently. In this talk, we will introduce and motivate rainbow F-saturated graphs and share some new results on rainbow saturation for cycles. 

March 11, 2024 at 3:00 p.m. Math 103

Kelvin Rivera-Lopez – Gonzaga

An algebraic approach to scaling limits of up-down chains

An up-down chain is a Markov chain in which each transition can be decomposed into a growth step followed by a reduction step. In general, these two steps can be unrelated, but if they satisfy a natural commutation relation, the up-down chain turns out to be particularly amenable to analysis.

In this talk, we will present a general framework for analyzing these special up-down chains. This approach will mainly be algebraic but will lead to convergence results. If time permits, we will discuss an example in the context of permutations and permutons.

Based on joint work with Valentin Féray.

March 25, 2024 at 3:00 p.m. Math 103

Van Magnan – Ñý¼§Ö±²¥, PhD Candidate

Ramsey-Turán Results

The celebrated Turán's Theorem sits at the heart of extremal combinatorics, yielding the maximum number of edges in a graph free of cliques of some proscribed size. Graphs achieving this maximum are highly structured, with large sets of vertices free from edges. The Ramsey-Turán problem reformulates this problem by asking for the maximum to the Turán problem of a less structured graph. We explore the history and more recent results in this area. 

April 1, 2024 at 3:00 p.m. Math 103

Regina Souza – Ñý¼§Ö±²¥

Active Learning in College Algebra, College Trig and Precalc: A Demonstration 

Ñý¼§Ö±²¥ one and a half years ago, with the support of Rick Darnell, Fred Peck, and Josh Herring, I started exploring the 'Building Thinking Classrooms' practices (by Peter Liljedahl) in my own classroom. Since last semester, all sections of College Algebra, Trig, and Precalc have been using this approach. The learning assistants program has been vital to this implementation: the program trains and supports these wonderful undergraduate Ñý¼§Ö±²¥, who have been very important in creating activities, fostering community, and energizing both Ñý¼§Ö±²¥ and instructors.

This will be an 'untalk', designed for you to experience a few of the practices, hear from the instructors and learning assistants who have been implementing them, and form your own opinion about the pros and cons.

April 8, 2024 at 3:00 p.m. Math 103

Lucia Williams – Computer Science

Decomposing Flow Networks for DNA Sequencing 

Finding a maximum flow through network is a classical problem in computer science, celebrated for its deep theoretical properties and diverse applications. In this talk, we shift focus to a less explored but related problem: the decomposition of a network flow into weighted paths. We will see that this problem also has many interesting theoretical properties and practical applications, focusing especially on its usefulness in assembling genomes. 

April 15, 2024 at 3:00 p.m. Math 103

Ellen Weld – Sam Houston State University

A Gentle and Brief Introduction to \(L^p\)-Operator Algebras 

Originally defined by Herz in the 1970s, \(L^p\)-operator algebras are Banach algebras which can be isometrically represented on an \(L^p\)-space for \(p\in [1,\infty)\) and in many ways generalize the notion of operator algebras. However, \(L^p\)-operator algebras did not receive wider interest until Phillips' 2013 paper computing the K-theory of analogs of Cuntz algebras after which a number of authors have explored what well known operator algebra properties do and do not extend to \(L^p\)-operator algebras.

In this talk, we will gently introduce \(L^p\)-operator algebras and provide motivating examples suitable for non-experts as well as discuss exciting results and trends in this area of research. Knowledge of operator algebras is not required. 

April 22, 2024 at 3:00 p.m. Math 103

José Martinez – Ñý¼§Ö±²¥, PhD Candidate

Farey Recursive Functions for Hyperbolic Dehn Filling 

Hyperbolic geometry is frequently encountered in low-dimensional topology, and it is known that many 3-manifolds admit a hyperbolic structure. William Thurston's hyperbolic Dehn filling theorem predicts how the geometric structure of a hyperbolic 3-manifold changes when a topological operation called Dehn filling is performed on the manifold. In this talk, we will give an overview of some of the basic ideas in hyperbolic geometry, the theory of 3-manifolds, and Dehn filling, and show how these ideas can be understood using special triangulations and Farey recursive functions. 

April 29, 2024 at 3:00 p.m. Math 103

Kelly McKinnie – Ñý¼§Ö±²¥

Comparison of Enumeration and Sampling Methods in Creating Montana’s 2nd Congressional District 

The 2020 decennial census data resulted in an increase from one to two congressional representatives in the state of Montana. 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

Emily Stone – Ñý¼§Ö±²¥

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

Michael Wojnowicz – Montana 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

Liz Arnold – Montana 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

FEC meeting

October 28, 2024 at 3:00 p.m. Math 103

Deborah Good – Ñý¼§Ö±²¥, 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

Shurong Li – Ñý¼§Ö±²¥, 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 Ñý¼§Ö±²¥’ 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 Ñý¼§Ö±²¥. 

December 2, 2024 at 3:00 p.m. Math 103