September 13 – Jeff Boersema
Jeff Boersema – Seattle University
K-Theory: Algebraic Topology and Non-commutative Algebraic Topology
This will be a gentle introduction to K-theory, first in the context of topological spaces and then in the context of operator algebras. We will discuss both real K-theory and complex K-theory, and the interplay between them. At the end, I will present two important classification theorems for real C*-algebras using K-theory. I will assume no prior knowledge of K-theory.
September 13, 2021 at 3:00 p.m. in Math 103
September 27 – Leonid Hanin
Leonid Hanin – Idaho State University
Mathematical Discovery of Natural Laws in Biomedical Sciences with Application to Metastasis
Mathematical modeling of systemic biomedical processes faces two principal challenges: (1) enormous complexity of these processes and (2) variability and heterogeneity of individual characteristics of biological systems and organisms. As a result, in the grand scheme of things, mathematical models have played so far an auxiliary role in biomedical sciences. I propose a new methodology of mathematical modeling that would allow mathematics to give, in certain cases, definitive answers to important biomedical questions that elude empirical resolution. The new methodology is based on two ideas: (1) to employ mathematical models that are so general and flexible that they can account for many possible mechanisms, both known and unknown, of biomedical processes of interest; (2) to find those model parameters whose optimal values are independent of observations. These universal parameter values may reveal general regularities in biomedical processes (that can be called natural laws). Existence of such universal parameters presupposes that the model does not meet the conditions required for the consistency of the maximum likelihood estimator.
I illustrate this approach with the discovery of a natural law governing cancer metastasis. Specifically, I will show that under minimal mathematical and biological assumptions the likelihood-maximizing scenario of metastatic cancer progression is always the same: complete suppression of metastatic growth before primary tumor resection followed by an abrupt growth acceleration after surgery. This scenario is widely observed in clinical practice, represents a common knowledge among veterinarians, and is supported by a wealth of experimental studies on animals and clinical observations accumulated over the last 115 years. Furthermore, several biological mechanisms, both hypothetical and experimentally verified, have been proposed that could explain this natural law. The above scenario does not preclude other possibilities that are also observed in clinical practice. In particular, metastases may surface before surgery or may remain dormant thereafter.
September 27, 2021 at 3:00 p.m. in Math 305
October 11 – Leonid Kalachev
Leonid Kalachev – University of Montana
Classical infectious disease modeling paradigms shifted by the SARS-CoV-2 pandemic
Classical infectious disease models during epidemics have widespread usage, from predicting the probability of new infections to developing vaccination plans for informing policy decisions and public health responses. However, it is important to correctly classify reported data and understand how this impacts estimation of model parameters. The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic has provided an abundant amount of data that allows for thorough testing of disease modeling assumptions, as well as how we think about classical infectious disease modeling assumptions. We use simulations to demonstrate the minimal data (infected, active, quarantined, and recovered) needed for collection and reporting that are sufficient for reliable model parameter identification and prediction accuracy. Using a classical example of influenza epidemics in an England boarding school, we show that the Susceptible-Infected-Quarantined-Recovered model is more appropriate than the commonly employed Susceptible-Infected-Recovered model. We demonstrate the role of misclassification and the importance of correctly classifying reported data to the proper compartment in a COVID-19 disease model and implications of using “right” data in the “wrong” model. The role of misclassification and the importance of correctly classifying reported data will have downstream impacts on predictions of number of infections, as well as minimal vaccination requirements.
October 11, 2021 at 3:00 p.m. in Math 305
October 18 – Aaron Luttman
Aaron Luttman – Senior Technical Advisor, Pacific Northwest National Laboratory
Mathematics Research for Security and Science in the US National Laboratories
The US Department of Energy (DOE) maintains 17 national laboratories, which employ hundreds of mathematicians, working on research from modeling of coastal ecosystems, to advanced energy solutions, to nuclear security. We build computational codes for modeling and simulation; we develop algorithms for analyzing scientific data; and we’re beginning to play an essential role in the advance of machine learning and artificial intelligence (AI/ML). In this presentation, we’ll highlight a few mathematical research programs that are currently underway in the DOE complex, including modeling of nuclear fusion devices, design of AI/ML models for characterizing the structure and performance of materials like uranium, and some of the graduate level mathematics that underwrites why some deep neural networks actually work. Each of these topics has important open problems, and we’ll also discuss how to get involved in research and get jobs in our community, as well as some of the details of the national lab ecosystem and work environments.
October 18, 2021 at 3:00 p.m. in Math 305
October 25 – FEC meeting
Faculty Evaluation Committee meeting, 3:00 p.m. in Math 103
November 1 – Chad Topaz
Chad Topaz – Williams College, co-founder of the Institute for the Quantitative Study of Inclusion, Diversity, and Equity
Mathematical and Computational Approaches to Social Justice
Civil rights leader, educator, and investigative journalist Ida B. Wells said that "the way to right wrongs is to shine the light of truth upon them." This talk will demonstrate how mathematical and computational approaches can shine a light on social injustices and help build solutions to remedy them. We will present quantitative social justice projects on topics ranging from diversity in art museums to equity in criminal sentencing to affirmative action, health care access, and other fields. The tools engaged include crowdsourcing, clustering, hypothesis testing, statistical modeling, Markov chains, data visualization, and more. I hope that this talk leaves you informed about the breadth of social justice applications that one can tackle using quantitative tools in careful collaboration with other scholars and activists.
November 1, 2021 at 3:00 p.m. in Math 305
November 8 – Katie Oliveras
Katie Oliveras – Seattle University
November 8, 2021 at 3:00 p.m. in Math 305
November 15 – Ryan Grady
Ryan Grady – Montana State University
November 15, 2021 at 3:00 p.m. in Math 305
November 22 – Anna Halfpap
Anna Halfpap – University of Montana
November 22, 2021 at 3:00 p.m. in Math 305
November 29 – Emily Stone
Emily Stone – University of Montana
Data Science meets Public Health Data in Montana: My adventures with seasonal and SARS-CoV-2 flu from Montana counties.
November 29, 2021 at 3:00 p.m. in Math 305
December 6 – Jasper Weinburd
Jasper Weinburd – Harvey Mudd College
December 6, 2021 at 3:00 p.m. in Math 305
February 7, 14, 28
March 7, 14, 28
April 4, 11, 18, 25
January 24 – Bree Cummins
Bree Cummins – Montana State University