Fred Peck & Matt Roscoe – University of Montana

Desmos Activity Builder: Technology for the Promotion of Active Learning 

Desmos Activity Builder is a free, online platform that can be used to facilitate active learning in mathematics.  The platform takes the tools of Desmos, a popular online graphing utility, and places them in a classroom-like environment where tasks can be sequenced like cards in a deck and then paced and controlled by the instructor.  The environment enables the collection and sharing of students’ mathematical ideas: verbal responses, graphical overlays, aggregate data displays and more.  In this talk you will first experience a Desmos Activity Builder lesson as a student.  Then, we will demonstrate how an activity can be controlled by the teacher.  We will review a library of publically available activities and then briefly explain how to author your own activities.  We will conclude by reflecting upon our own use of Desmos Activity Builder as a tool to encourage active learning in remote and hybrid instructional settings in the era of the COVID-19 pandemic. 

January 24, 2022 at 3:00 p.m. Math 103 & Zoom

Jennifer Harrington – University of Montana

An Analysis of Tribal Consultation: A case study of policy versus practice Confederated Salish Kootenai Tribes and Nmisuletkʷ (the Middle Fork of the Clark Fork River) As a Tribal Trust Resource 

Formal, government-to-government Consultation between sovereign nations is a process of continuous relationship-building, a partnership and an agreement made with all points-of-view included in the process, with results that have the fingerprint of all nations involved evident. The Federal Government is obligated to work with Federally- recognized Tribes as sovereign nations in matters that have or will impact each Nation’s people and places (reservations, treaty-protected areas)—a process legally known as Consultation. The Environmental Protection Agency (EPA), as a Federal agency, must uphold the Federal Trust responsibility as part of the U.S. government, which includes the act of Consulting with Federally- recognized Tribes on matters involving human health and the environment on reservations or in aboriginal territories. Consultation between Tribes and Federal agencies in general, and specifically between the EPA and Tribes, has not been successfully constructed nor implemented. 

In this thesis, I seek to understand how Consultation is defined in Federal policy and perceived by Tribes, what is not working, and what can be done to create inclusive and meaningful Consultation, specifically between the EPA and Tribes, but relevant to all federal agencies. The Confederated Salish and Kootenai Tribes (CSKT) are Natural Resource Trustees across their aboriginal homelands, which includes, Nmisuletkʷ, the Clark Fork River. The impacts of air, land, and water pollution left behind by a former mill’s operations continue to have an impact on Tribal Trust Resources. My methods for analyzing this case study include a policy analysis, direct observation, and semi-structured ethnographic interviews with involved Tribal members and representatives. Through this work, I articulate a foundation for creating (or amending) policy that better reflects a Native worldview to be more inclusive, culturally relevant, and effective for sustainable management of our shared landscapes 

Consultation between two or more sovereign nations necessitates equal footing.  The case study illuminated several barriers while also providing keys to how the EPA can create a more just and inclusive Consultation. The recommendations for improving Consultation include Indigenizing Consultation, which will create a more transparent, inclusive, and long-term relationship between Native Nations, the EPA, and the environment. 

January 31, 2022 at 3:00 p.m. Math 103 & Zoom

Ruth Plenty Sweetgrass-She Kills – Nueta Hidatsa Sahnish College

Strengthening the Food System of the Mandan, Hidatsa, and Arikara people

At one point in time, the homelands of the Mandan, Hidatsa, and Arikara (MHA) Nation was a regional trade center because of the surplus produce of the MHA people. The impacts of colonization and decades of federal policies negatively affected the food system. The past quarter of a century the Nueta Hidatsa Sahnish College has been working to revitalize the practices that had led to their food sovereignty. Dr. Plenty Sweetgrass-She Kills will share the vision of food sovereignty for the MHA Nation  that she, her colleagues, and their community partners are working towards together.  

Bio:

Dr. Plenty Sweetgrass-She Kills is an enrolled tribal citizen of the Three Affiliated Tribes of the Fort Berthold Indian Reservation in central North Dakota and is a member of the Maxoxadi (Alkali/Salted Lodge) Clan. She is also descended from the Fort Peck Sioux and Assiniboine Nation in northeastern Montana. She earned her bachelor's degree in Elementary Education from the University of North Dakota, Master's degree in Organismal Biology and Ecology from the University of Montana, and her PhD in Forest and Conservation Sciences also from the University of Montana. She is currently the Nueta Hidatsa Sahnish College's Food Sovereignty Director and Senior Research Personnel at the University of Montana.

February 7, 2022 at 3:00 p.m. via Zoom

Krystal Taylor – Ohio State University

Configurations, dimension, and fractal sets 

A vibrant and classic area of research is that of relating the size of a set to the finite point configurations that it contains.  Here, size may refer to cardinality, dimension, or measure.  In this talk, we give an introduction to some problems in the general area of the study of geometric configurations.  A discussion of notions of size and dimension that are robust to the fractal setting will be included.  As particular examples, we will consider two notions of size- Hausdorff dimension and Newhouse thickness- that can be used to guarantee the existence of arbitrarily long paths within fractal subsets of Euclidean space. 

February 14, 2022 at 3:00 p.m. Math 103 & Zoom

Luis Radford – Laurentian University

Learning as a collective process: Some ideas from the theory of objectification

Each mathematics classroom, regardless of the pedagogical model it follows, can be considered as a collective. Yet, it does not mean that students are learning collectively. This is the case of the direct teaching model and, I would dare to argue, of the constructivist classroom too. The question that arises in this context is then the following: What are the conditions for collective learning to happen? In this presentation I explore this question. The collective learning that I seek to foster in my work with teachers is one in which the students encounter cultural knowledges and voices in deep conceptual mathematical ways while at the same time making the experience of collective life, solidarity, plurality, and inclusivity. From this Vygotskian and Freirean perspective, mathematics education should not be only about knowing but also about becoming.

February 28, 2022 at 3:00 p.m. Math 103 & Zoom

Bree Cummins – Montana State University

Discovering Genetic Network Interactions Through Iterative Hypothesis Reduction 

Time series transcriptomics and proteomics data typically record expression levels of thousands of gene products. Discovering the important elements of these data for a specific experimental question is daunting given the combinatorial nature of the problem. Myself and my collaborators take the approach that a sequential set of software tools can reduce hypothesis space tremendously. I will discuss the performance of a set of tools that aims to discover “core oscillators” or clock-like genetic networks that control highly stereotyped cellular phenomena such as the cell cycle and the circadian rhythm. We first reduce the space of potential gene products from thousands to tens, then the space of possible interactions from hundreds to tens, and then we refine this collection of interactions by considering global network dynamics across complex combinations of edges. The global network dynamics then can be used to revise the import actors and interactions in the gene regulatory network. We show that this set of software tools is in principle capable of finding core oscillator interactions from high-dimensional data, although sometimes the results are surprising and hard to quantify.

March 7, 2022 at 3:00 p.m. Math 103 & Zoom

Diana Crider – Animo Partnership in Natural Resources

Black Bears in México: Outliers, Local Knowledge, and Management  

The black bear (Ursus americanus) in Mexico is classified as endangered based on declines prior to the 1980’s.  However, changes in public attitude, governmental protection, and cooperative landowner efforts to protect the bear have resulted in a natural expansion and recovery. Similarly, black bear numbers are increasing throughout North America. Because of the large home ranges of bears, and the variability of bear food production and population dynamics in desert environments, bear populations are very difficult to study and monitor.  In addition, habitat suitability, as quantified in most recent publications, does not include the production of food, which may be one of the key components to bear habitat selection.  This can be highly significant in desert populations where food production is variable, and dependent on climatological events.  We intensively studied this population for 10 years, and concentrated density estimation efforts within a 100 km² area, and the total cost was approximately $750,000 USD.  Conducting density estimates of bears in desert ecosystems contains large error and has short-term value because of volatile fluctuations in weather, food production, and bear population dynamics. Because of economic constraints and different cultural perspectives in Mexico, we must adapt research tools that are more practical and culturally acceptable, and that incorporate local knowledge as part of our toolbox. 

March 28, 2022 at 3:00 p.m. Math 103 & Zoom

Racheal Kenney – Purdue University

April 4, 2022 at 3:00 p.m. Math 103 & Zoom

Jon Lenchner – IBM T.J. Watson Research Center

An Introduction to Computational Complexity Via Games 

In this talk I will discuss an approach to solving the famous P=NP question using games. For those unfamiliar with computational complexity, I will describe the complexity classes P and NP, as well as a few other complexity classes, including coNP, L and NL. I will then describe the million-dollar problem that asks whether P=NP and show how one can use a classic two-person combinatorial game, known as an Ehrenfeucht-Fraisse game (along with its relatives), to try to separate complexity classes. I will give some simple examples of how these games are played and then describe a newly rediscovered game that my colleagues and I at IBM are exploring that are potentially more powerful than these classical games.

About the Speaker: Jon is a member of the research staff at the IBM T.J. Watson Research Center in New York. Jon has been with IBM for the last 25 years. Along with several colleagues, he developed the strategy component of the IBM Watson Jeopardy-playing system that in 2011 defeated the two most successful human Jeopardy players on live television. He has built two commercial robots and worked with the Toronto Raptors of the National Basketball Association on a system to help with trades and draft picks.  From 2016-2018 Jon was the chief scientist of IBM’s two African research labs, one in Nairobi, Kenya, and the other in Johannesburg, South Africa. Since returning from Africa, Jon’s work has focused on applications of mathematical logic to theoretical questions in computer science, like the P=NP question.

This is an in-person talk also available via Zoom. 

April 11, 2022 at 3:00 p.m. Math 103 & Zoom

John Finlay – PhD Candidate

Rainbow Connectivity of Randomly Perturbed Graphs 

In this talk I will explore the following graph model: For an arbitrarily dense graph H, we create a graph G by adding m additional edges uniformly at random. We then edge-color G randomly with r colors. I will talk about what it means for a graph to be rainbow connected and show that with r ≥  5 and m a large enough constant, G is rainbow connected with high probability. This was conjectured by Anastos and Frieze in 2019 and proven by József Balogh, Cory Palmer and myself. This talk will cover all of the concepts required to understand our result and survey the proof. 

April 15, 2022 at 3:00 p.m. Math 103 & Zoom

Math Education Graduate Student Research Projects

This colloquium will be a talking circle Q&A with the math education stidents who did research this semester as a way to share their experiences.

April 18, 2022 at 3:00 - 5:00 p.m. Math 103 & Zoom

Judith Packer – University of Colorado at Boulder

Cohomology related to commuting k-tuples of local homeomorphisms 

Suppose we are given k commuting surjective local homeomorphisms acting on a compact metric space X.  Then we can construct a locally compact Hausdorff groupoid G from this data. This talk will go over the construction of both the groupoid G and its associated groupoid C*-algebra C*(G). We review the continuous 1-cocycles in the groupoid G taking on values in a locally compact abelian group, and provide a characterization of these, given in terms of k-tuples of continuous functions on the unit space of G satisfying certain canonical identities. When the locally compact abelian group being considered is the additive group of real numbers, we discuss the construction of a one-parameter automorphism group acting on C*(G) corresponding to the continuous 1-cocycle on G, and relate this to KMS states on C*(G). 

April 25, 2022 at 3:00 p.m. Math 103 & Zoom

JD Nir – University of Manitoba

Close Enough! How to (Probably) Calculate the Chromatic Number

How many colours does it take to paint every vertex of a graph if edges can't connect vertices of the same colour? This is a difficult problem to answer, so instead, let's figure out how to make the smartest guess. Rather than writing an algorithm that determines this so-called chromatic number, what can we say about its distribution when a graph is chosen at random? This problem boasts over seventy years of clever tricks, not only from probability and graph theory but also linear algebra, complex analysis, and even statistical physics. In this talk, we'll look at some of these breakthroughs as well as some recent progress I've made with coauthors Karen Gunderson and Xavier Pérez-Giménez.

May 2, 2022 at 3:00 p.m. Math 103 & Zoom

Doctoral Dissertation Defense

John Finlay – University of Montana
PhD Candidate

Randomly Perturbed Graphs And Rainbow Connectivity

This defense will examine the following random graph model: for an arbitrary dense graph H, construct a graph G by randomly adding m edges to H and randomly coloring the edges of G with r colors. In 2019 Anastos and Frieze conjectured that for m a large enough constant and r ≥ 5, every pair of vertices in G are joined by a rainbow path, hence G is rainbow connected. My defense will prove that this conjecture is true and entertain related questions.

May 13, 2022 at 3:00 p.m. Math 103

Jonathan Brown – University of Dayton

Regular Ideals, Ideal intersections, and quotients

Ideals in commutative C*-algebras are well understood. The study of ideals in more general C*-algebras is aided by the presence of large commutative subalgebras. We say a commutative subalgebra B of A has the ideal intersection property if every nontrivial ideal of A has nontrival intersection with B: thus reducing the study of ideals in A to the well understood commutative context. In this talk we will explore the ideal intersection property in some familiar examples such as matrix algebras and see that this property does not always pass to quotients. However, in many cases the ideal intersection property will pass to quotients by regular ideals. We will discuss regular ideals and their properties, culminating in a proof that the ideal intersection property passes to quotients by regular ideals under some mild hypotheses. This is joint work with A. Fuller, D. Pitts, and S. Reznikoff.

September 12, 2022 at 3:00 p.m. Math 103

Daryl Deford – Washington State University

Political Geometries: Graphs, Geometry, and Gerrymandering

The problem of constructing "fair" political districts and the related problem of detecting intentional gerrymandering has received a significant amount of attention in recent years. Attempting to analyze these issues from a mathematical perspective leads to a wide variety of interesting problems in geometry, graph theory, and probability. In this talk, I will discuss recent work centered around Markov chain sampling of districting plans that has motivated theoretical questions in these fields, including designing proposal distributions, evaluating the computational complexity of sampling, and measuring the geometric and partisan properties of districts. Beyond the mathematical developments, this work has also appeared in court challenges, commission-based map making, and legislative reform efforts. I will discuss what it is like to participate in these outreach experiences as a mathematician and some of the related data and computational challenges. 

September 19, 2022 at 3:00 p.m. Math 103

Emily Stone – University of Montana

A comparison of spatio-temporal patterns in seasonal flu and COVID 19 in a rural US state.

In this talk I will describe the result of using a variant of Principal Component Analysis called Archetypal Analysis (Cutler and Breiman, 1994) to split the spatial and temporal parts of a time series in 56 dimensions. The spatial part are characteristic patterns of outbreak across the counties of the state of Montana, and the temporal part describes which pattern appears at what point of time. A data set of seasonal flu case counts over 8 years is compared to the data set of COVID 19 over the three different outbreaks we have experienced in the last two years. The mutual information between different counties during the outbreaks is used to initially pull out the most “influential” counties and reduce the dimension of the data set analyzed by archetypes.

September 26, 2022 at 3:00 p.m. Math 103

Sam Gunningham  – Montana State University

The finiteness conjecture for skein modules 

Skein relations are certain rules for simplifying knotted pieces of string in 3-dimensional space. The skein module (of a 3-manifold M) is the vector space spanned by all knots and links in M modulo certain skein relations. A few decades after their discovery in the late 80s by Przytycki and Turaev, Edward Witten put forward a surprising conjecture: that the (generic Kauffman bracket) skein module of any closed 3-manifold should be finite-dimensional. In this talk I will give a motivated introduction to the theory of skein modules and explain some aspects of our recent proof of the finiteness conjecture (joint with David Jordan and Pavel Safronov). The proof itself makes essential use of ideas and techniques from non-commutative algebra (D-modules and deformation quantization). 

October 10, 2022 at 3:00 p.m. Math 103

Faculty Evaluation Committee

October 24, 2022 at 3:00 p.m. - 5:00 p.m. Math 103

Anh Nguyen – Computer Science

Wearable Sensor Development For Health Monitoring & Personalized Medicine  

Generated by the functioning of many bodily sources, physiological signals hold essential information about the state of the body’s major structures, including brain activities, eye movements, muscle contractions, and cardio-respiratory features, to name a few. Therefore, monitoring and stimulating such biosignals widely help diagnose, treat, and prevent several health conditions and diseases. Unfortunately, the current “gold standard” for studying patients’ sleep is obtrusive, expensive, and often inaccurate. This talk will introduce our novel wearable systems that promise unobtrusive, low-cost, and accurate sensing and stimulation capabilities for reliable physiological signals in comfortable in-home settings. I will discuss how our wearable cyber-physical systems can provide clinical-grade solutions to simultaneously sense multiple biosignals at non-standard locations and perform real-time brain entrainment for closed-loop personalized sleep care practices. I will also identify potential research on deploying these systems in more diverse real-world healthcare directions, such as overall health monitoring, mental illness and brain disorders detection, treatment, and prevention, and brainpower unlocking. Lastly, I will take a broader look at challenges in making wearable CPSs an open sensing and stimulation platform. 

October 31, 2022 at 3:00 p.m. Math 103

Kelly McKinnie & Dave Patterson –  University of Montana

Legislative Redistricting in Montana 

The Districting and Apportionment Commission of the state of Montana is currently re-drawing the district lines for its 100 house seats. When this job is complete (Nobember/December 2022), they will pair the 100 house seats to make 50 senate seats. In this talk we will explore what an ensemble of legislative maps created using a Monte Carlo Markov Chain algorithm says about the space of possible maps and where the four currently proposed maps fit. This is preliminary work coming out of an undergraduate research project. 

November 7, 2022 at 3:00 p.m. Math 103

Megan Wickstrom – Montana State University

Math Metaphors: A Window into Students' Mathematical Experiences 

What tales would your students tell about their mathematical experiences? In this talk, I will share the Math Metaphor task and explore how students' responses can help us, as instructors, better understand their mathematical experiences with respect to emotions, agency, and identity. We will explore several examples, including our own, and discuss implications for supporting learners and building community in the classroom. 

November 14, 2022 at 3:00 p.m. Math 103

Matt Lorentz – Michigan State University

The Hochschild Cohomology of Roe Type Algebras

In order to help us better understand the structure of a space we look for invariants, not only of the space but also invariants of its algebra of functions. One such invariant is the Hochschild (co)homology. Using the Hochschild-Kostant-Rosenberg theorem (for sufficiently well behaved commutative algebras) one may identify the Hochschild homology with differential forms and the cohomology with multivector fields. Thus, for a noncommutative algebra we may consider its Hochschild (co)homology as noncommutative analogs of differential forms and multivector fields respectively.

Many times in analysis we focus on the "small scale" structure of a metric space, e.g. continuity, derivations, etc. However, to examine the "large scale" structure of a metric space we turn to coarse geometry. To help us study the coarse geometry of a space we again look at invariants, and one such invariant is the uniform Roe algebra of the space. Indeed, if a metric space (X,d_X) is coarsely equivalent to (Y, d_Y) then their uniform Roe algebras are isomorphic. Originally looked at as a method compute higher index theory, uniform Roe algebras are a highly tractable C*-algebra contained in the bounded operators on square summable sequences indexed by a metric space X (note that purely topological definitions exist). We will first give the relevant definitions and look at a few examples. We will then explore the Hochschild cohomology of uniform Roe algebras with coefficients in various uniform Roe bimodules. Time permitting, we will briefly discuss how our methods might be generalized to crossed product C*-algebras and C*-Algebras generated by groupoids. For this talk we will not assume any prior knowledge of C*-algebras or (co)homology.

November 21, 2022 at 3:00 p.m. Math 103

Jordan Malof, Computer Science – University of Montana

Deep Learning the Properties of Metamaterials

Unlike conventional materials, metamaterials derive their properties primarily from their structure rather than their bulk construction materials.  With a carefully-chosen structure, electromagnetic metamaterials have been shown to exhibit exotic properties that are not achievable with conventional materials, and now underpin many technologies.  In principle even more exotic and useful properties are achievable, but the modeling and design of advanced metamaterials is challenging, and a major bottleneck to continued progress.   In this talk I discuss the challenges of modeling and designing advanced metamaterials, and how recent advances in deep learning – a branch of machine learning - have shown the potential to overcome some of these challenges.  In particular, I discuss recent deep learning methods – some developed by myself with collaborators at Duke University - that can dramatically accelerate both the modeling and design of complex metamaterials.  In principle these methods can also be applied to many other natural systems, accelerating scientific progress and technological development.  I close by discussing some open challenges at the intersection of machine learning and scientific computing. 

November 28, 2022 at 3:00 p.m. Math 103

Aditya Adiredja – University of Arizona

What is Deficit Discourse in (Undergraduate) Mathematics Education and What Can We Do About It?

In this presentation, I will share what I have come to understand about deficit discourse in math education through my research and teaching at the undergraduate level. Recognizing that deficit discourse in mathematics education insidiously exists and operates at the individual, local, and societal level, I will briefly share promising outcomes from my previous anti-deficit projects. This will lead into some preliminary findings from an ongoing project focusing on the development of anti-deficit teaching. I will use the case of an instructor in the study to illustrate the complexity of engaging in anti-deficit teaching and the effort it takes to meaningfully challenge deficit discourse in mathematics education.

December 5, 2022 at 3:00 p.m. Math 103