About

I am a Ph.D. candidate in the mathematics department at the University of Utah in the field of mathematical biology, under the supervision of Aaron Fogelson. My research focuses on the formation of fibrin polymer gel during blood clotting, and I am particularly interested in how interactions of the precursor molecule, fibrinogen, affects the formation of the fibrin gel. In 2020-2021, I am on the job market and expect to graduate May 2021.



I am committed to teaching excellence and math education, and have experience mentoring graduate students and postdocs in their teaching. I have facilitated the Instructor Training workshop for incoming math graduate students and postdocs for three years at Utah. Additionally, I co-organized a graduate student teaching mentorship program through funding from a University of Utah Teaching Assistantship.

I obtained my Bachelor's degree in Applied Mathematics from Boise State University before coming to Utah. Outside of mathematics I enjoy hiking, traveling, baking, and playing/directing handbells. In Spring 2020, I gave a graduate student colloquium talk on the mathematics of handbells, and the slides can be found here.

Research

I am interested in using mathematical models to understand the formation of a fibrin clot within the process of blood clotting. Using a kinetic polymerization framework, I am currently working on how fibrin-fibrinogen interactions affect both clot time and clot structure. In general, I am passionate about using mathematical and computational tools to understand the complex biological and biophysical components in physiological processes. Here I am talking about my research at the AWM Poster session for SIAM AN2020!

At University of Utah, I am an active member of the Physiology group and the Biofluids and Biogels group and present at least twice a semester.



Projects

1. Two-monomer polymerization

Motivated by the interactions of fibrin and fibrinogen during the clotting process, I developed a two-monomer kinetic polymerization model with gelation, consisting of type A and type B monomers with varying functionality. Assuming that reactions between different oligomers occur based on free binding sites having equal probability of reacting with available binding sites on a different oligomer, analytical gel times or bounds are derived for gelation that depend on both the initial amount of each monomer present and functionality of monomer.

2. Fibrinogen-fibrin branching model

The structure of a fibrin gel is often defined by the number of fiber branches present in the resulting clot. Using framework from the previous project, I built a model of fibrin polymerization that incorporates biologically relevant reactions such as branching and fibrinogen binding. The resulting fibrin-fibrinogen branching model characterizes the impact fibrin-fibrinogen interactions have on fibrin gel structure and gel time.





Publications

A. C. Nelson and A. L. Fogelson. "Modeling fibrin polymerization with fibrinogen interactions." In preparation.

A. L. Fogelson, A. C. Nelson, C. Zapata-Allegro, and J. P. Keener. "Development of fibrin branch structure before and after gelation." Submitted to SIAM Journal on Applied Mathematics.

A. C. Nelson, M. A. Kelley, L. M. Haynes, and K. Leiderman. "Using Mathematical Modeling to Understand the Fibrin Polymerization Trifecta: Fibrin(ogen), Thrombin, and FXIII." Submitted to Current Opinion in Biomedical Engineering.

A. C. Nelson, J. P. Keener, and A. L. Fogelson. "Kinetic model of two-monomer polymerization". Physical Review E, 101, 022501 (2020).

J. L. Herlin, A. C. Nelson, and M. Scheepers. "Using ciliate operations to construct chromosome phylogenies". Involve, Vol. 9, No. 1 (2016).



Recent and Upcoming Conferences


Joint Mathematics Meeting

January 6 - 9, 2021

Virtual

AWM Poster Session



Teaching

At University of Utah, I have had the opportunity to teach a wide variety of courses, including several online courses. As instructor, my responsibilites include lecture, writing quizzes and exams, and grading. Links to the course syllabi are below. During 2018-2019, I was a recipient University Teaching Assistantship recipient from the Graduate School with another graduate student, under the project, Graduate Teaching Mentor Program.

I am passionate about teaching pedagogy and training graduate student instructors in teaching best practices. I have been involved with the incoming Math Instructor Training Workshop for 3 years, and have been the lead graduate student facilitator for two years. Aimed at incoming graduate students and postdocs, the eight day long workshop includes practice lectures, workshops on campus-wide resources, and teaching pedagogy workshops.

Current teaching

In Fall 2020, I am not teaching, however I have attended the Math Education/Teaching Seminar.

Past teaching



  • Spring 2017: College Algebra (Math 1050-004)

  • Fall 2016: College Algebra (Math 1050-007)

  • Summer 2016: Intro to Quantative Reasoning Online (Math 1030-090)

  • Spring 2016: Math 1030-090 Intro to Quantative Reasoning(Math 1030-090)

  • Fall 2015: Math 2250-014,015 Differential Equations (Lab Instructor)

Contact

Office

Room 305
LeRoy E. Cowles Building (LCB)

Email

anelson "at" math "dot" utah "dot" edu