# Achievements

### Publications and achievements submitted by our faculty, staff, and students.

Faculty Peter Goetz Mathematics Dr. Peter Goetz gave an invited talk titled "Frobenius Extensions in Noncommutative Invariant Theory" in the AMS Special Session on *Homological Techniques in Noncommutative Algebra* at the Joint Mathematics Meeting on January 3, 2024. The JMM is one of the largest international meetings of mathematicians with approximately 6000 attendees. Dr. Goetz reported on his new theorem: all dual reflection groups afford examples of (twisted) Frobenius extensions. Dr. Goetz also presented his work on the relationship between Artin-Schelter regular and Artin-Schelter Gorenstein algebras and Frobenius extensions, and examples of Frobenius extensions arising from noncommutative and noncocommutative Hopf algebra actions.

Faculty Kamila Larripa Mathematics Kamila Larripa was selected to participate in the Simons Laufer Mathematical Sciences Institute's Summer Research in Mathematics Program. She will work with collaborators on developing data-driven modeling approaches to investigate the impact of human behavior on epidemic dynamics for outbreaks such as the COVID-19 pandemic.

Faculty Kamila Larripa Mathematics Kamila Larripa and collaborators published an article in the Journal of Theoretical Biology entitled M*acrophage phenotype transitions in a stochastic gene-regulatory network model*. The study classifies cell phenotypes using a spectral clustering algorithm and quantifies transitions between phenotypes using transition path theory.

Faculty Kamila Larripa Mathematics Kamila Larripa was selected to participate in the Institute for Pure and Applied Mathematics collaborative research workshop in data science. She worked on tensor decomposition methods for machine learning.

Faculty Kamila Larripa, Bori Mazzag Mathematics Kamila Larripa and Bori Mazzag received a California Learning Lab grant to build critical mass in data science at Cal Poly Humboldt. Project team members include Enoch Hale, Rosanna Overholser and Angela Rich. The grant activities coincide with the launch of a data science major in Fall 2023, and will help move data science into the larger campus community.

Faculty Kamila Larripa Mathematics Kamila Larripa has been awarded a 3 year National Science Foundation Division of Mathematical Sciences grant for $307,661 to study immune cell activation using multi-scale mathematical models. The project includes collaborating biologists at other institutions and will incorporate and train undergraduate students in interdisciplinary research techniques.

Faculty Dr Peter Goetz Mathematics Will give a talk titled "Frobenius extensions, Artin-Schelter regular algebras and Azumaya loci" at the Spring Western Sectional Meeting of the American Mathematical Society at CSU, Fresno on Sunday, May 7, 2023. The Azumaya locus of a polynomial identity algebra is an algebraic variety that parametrizes the irreducible modules of maximal dimension. Typically the Azumaya locus is very hard to determine. Dr. Goetz will describe results from his current research project on using Frobenius extensions to compute Azumaya loci.

Faculty Tyler Evans, Alice Fialowski Mathematics My paper "Central Extensions of Restricted Affine Nilpotent Lie Algebras $n_+A_1^{(1)}(p)$" appeared in the *Journal of Lie Theory*, 33 (2023), No. 1, 195--215. This paper was written jointly with my colleague Alice Fialowski at Eötvös Loránd Tudományegyetem in Budapest, Hungary during my Spring 2022 sabbatical leave.

Faculty Dr. Peter Goetz, Dr. Andrew Conner Mathematics Published a paper titled: *QUANTUM PROJECTIVE PLANES AS CERTAIN GRADED TWISTED TENSOR PRODUCTS* in The Journal of Algebra; https://doi.org/10.1016/j.jalgebra.2022.11.033. The paper is joint with Dr. Andrew Conner at Saint Mary's College of California and will appear in the April 2023 issue. The main results of the paper are: (1) a classification up to algebra isomorphism of quadratic graded twisted tensor products of K[x,y] and K[z], and (2) the determination of which three-dimensional Sklyanin algebras contain a quantum P^1. Sklyanin algebras first arose in the late 20th century in the context of quantum inverse scattering problems in physics.

Faculty Liza Boyle, Sonja Manor, Bori Mazzag Mathematics

Dr. Liza Boyle (Environmental Resources Engineering), Sonja Manor and Dr. Bori Mazzag (Mathematics) presented a workshop entitled "Humboldt Solar Panel Projects". The workshop was held on Feb. 1 in the Mathematical Association of America "Curriculum Renewal Across the First Two Years" workshop series. The workshop showcased course materials developed for Math 109 Calculus I and Math 101T Trigonometry that connect mathematical content to solar energy production. Projects explore local data and discuss broader social implications of the use of solar energy and highlight applications of math to local issues.

Student Viri Macias, Ana Sammel, Emma Villegas, Bori Mazzag, Kamila Larripa Mathematics

Viri Macias, Ana Sammel and Emma Villegas presented their mathematical work at the CSU PUMP Symposium. Viri presented a model for calcium signaling and Ana and Emma presented a model for COVID-19 and immune cell interactions. The projects were mentored by Bori Mazzag and Kamila Larripa.

Faculty Kamila Larripa Mathematics

Kamila Larripa was selected to conduct research at the American Institute of Mathematics in June. She and collaborators will build stochastic models for immune cell dynamics.

Student Bridget Opperman, Kamila Larripa Mathematics

Math student Bridget Opperman will present a research poster on "Mathematical Analysis of Virus-Immune Dynamics and Implications for Treatment" at the National Conferences on Undergraduate Research.

Faculty Bori Mazzag Mathematics

Dr. Bori Mazzag and Dr. Julie Glass, CSU East Bay, co-organized a series of CSU-wide talks in January as part of the year-long Math Council Colloquium series. The theme of the January talks was "Peer Instruction". We aimed to connect faculty and staff across the CSU who work on providing academic support services to students in mathematics and statistics courses. In addition to the talks, we collected some information on the structure of the tutoring and peer instruction on the various campuses. CSU campuses were broadly represented in the series, including speakers from Humboldt State University's Learning Center.

Faculty Peter Goetz, Andrew Conner Mathematics

Published the article "Classification, Koszulity and Artin-Schelter regularity of certain graded twisted tensor products" in the Journal of Noncommutative Geometry, DOI: 10.4171/JNCG/395

Student Cianna Balderama, Daisy Montalvo, Ashley Tran, Ana Sammel, Emma Villegas, Bridget Opperman, Makani Bright, Hunter Kahn, Soeon Park, Tanner Hooven,  Kevin Chung, Diego Rodriguez Moreno  Mathematics

Twelve CNRS students competed in the international Mathematical Contest in Modeling-- an annual four day intensive competition. Teams of 3 worked intensely to apply mathematics to a real world problem. Students worked on mathematical models applied to competing populations of fungi, musical influence, and optimizing our nation's delivery of higher education. The contest happened virtually due to the pandemic.

Faculty Kamila Larripa Mathematics

Kamila Larripa and co-authors had their paper accepted to the Journal of Theoretical Biology. The paper is entitled "Bifurcation and sensitivity analysis reveal key drivers of multistability in a model of macrophage polarization" and investigates how a specific immune cell responds to cytokine signals.

Faculty Peter Goetz Mathematics

Recently published the single-authored paper "Graded Coherence of Certain Extensions of Graded Algebras" in Communications in Algebra, June 2020, https://doi.org/10.1080/00927872.2020.1775844

The paper studies when the coherence property is inherited by certain extensions of algebras.

Faculty Bori Mazzag, Kamila Larripa, Viri Macias, Megan Johnson, Ana Sammel and Emma Villegas Mathematics

Bori Mazzag and Kamila Larripa each received a CSU PUMP grant to mentor students in mathematical research for the 2020/2021 academic year. Mazzag will investigate calcium dynamics using differential equations and graph theory with Viri Macias and Megan Johnson, and Larripa will model the interaction between Sars-CoV-2 and the host's immune system, working with Ana Sammel and Emma Villegas.

Faculty Steven Railsback, Bret Harvey Mathematics

Steven Railsback (adjunct faculty, Mathematics) and Bret Harvey (adjunct, Fisheries Biology) just published the book "Modeling Populations of Adaptive Individuals", volume 63 in the prestigious Princeton Monographs in Population Biology series. The book presents a new kind of theory for adaptive behavior of individual organisms (e.g., when and where to forage, considering both growth and predation risk) that works in complex individual-based population models. The book builds on HSU's long tradition in individual-based ecological modeling. https://press.princeton.edu/books/paperback/9780691195285/modeling-populations-of-adaptive-individuals