I am an applied mathematician working in complex and nonlinear systems. I study a variety of social and biological systems with mathematical models. My goal is to create and communicate mathematics in a way that is exciting, relevant, and inclusive.
I am an Assistant Professor of Mathematics at Harvey Mudd College. I earned my Ph.D. in Mathematics from the University of Utah in 2018, where I was advised by Paul Bressloff. Before joining the faculty at Harvey Mudd, I was a CAM postdoc in the Mathematics department at UCLA (under the mentorship of Mason Porter).
I use a combination of analytical and computational techniques to study phenomena in social and biological applications. I pair tools from dynamical systems and differential equations (including linear and weakly nonlinear analysis, perturbation theory, adiabatic reduction, and symmetric bifurcation theory), network theory, and stochastic processes with numerical simulation and data-driven computational techniques (like agent-based models and dynamic mode decomposition). Read more about my projects here.
I am passionate about the teaching and learning of mathematics. I am a Project NExT Fellow (Silver ’19 cohort) and I was a graduate fellow for the Center for Teaching and Learning Excellence at the University of Utah. I strive to create an inclusive environment where my students can engage meaningfully with challenging problems. My teaching portfolio is here.
As a first-generation college student and woman in mathematics, I strive to be an active advocate for historically underserved people in the math community. I am a proud member of AWM and the Spectra Ally List.
I was born in Idaho and raised in Utah. I played classical flute for many years (I was originally a music major!). Outside of math and music, I love climbing, hiking, skiing, rafting, trivia, podcasts, and coffee.
9. Influence of media on opinion dynamics in social networks: HZB and Mason A. Porter. Physical Review Research 2(2): 023041, 2020.
8. How emergent social patterns in allogrooming combat parasitic infections: Shelby N. Wilson, Suzanne S. Sindi, HZB, Maryann E. Hohn, Candice R. Price, Ami E. Radunskaya, Nakeya D. Williams, and Nina H. Fefferman. Frontiers in Ecology and Evolution 8:54, 2020.
7. Bifurcation analysis of pattern formation in a two-dimensional hybrid reaction-transport model: Sam R. Carroll, HZB, and Paul C. Bressloff. Physica D: Nonlinear Phenomena 402:132274, 2020.
6. Mathematical analysis of the impact of social structure on ectoparasite load in allogrooming populations: HZB, Maryann E. Hohn, Candice R. Price, Ami E. Radunskaya, Suzanne S. Sindi, Nakeya D. Williams, Shelby N. Wilson, and Nina H. Fefferman. In Understanding Complex Biological Systems in Mathematics, Springer (2018), pp. 47-62.
5. How disease risks can impact the evolution of social behaviors and emergent population organization: Nakeya D. Williams, HZB, Maryann E. Hohn, Candice R. Price, Ami E. Radunskaya, Suzanne S. Sindi, Shelby N. Wilson, and Nina H. Fefferman. Preprint available at arXiv:1904.09238. In Understanding Complex Biological Systems in Mathematics, Springer (2018), pp. 31-46.
4. Turing mechanism for homeostatic control of synaptic density during C. elegans growth: HZB and Paul C. Bressloff. Physical Review E, 96(1):012413, 2017.
3. A mechanism for Turing pattern formation with active and passive transport: HZB and Paul C. Bressloff. SIAM Journal on Applied Dynamical Systems, 15(4):1823-1843, 2016.
2. Coarse-graining intermittent intracellular transport: two and three-dimensional models: Sean D. Lawley, Marie Tuft, and HZB. Physical Review E, 92(4):042709, 2015.
1. Quasicycles in the stochastic hybrid Morris—Lecar neural model: HZB and Paul C. Bressloff. Physical Review E, 92(1): 012704, 2015.
1. Disease Detectives: Using Mathematics to Forecast the Spread of Infectious Diseases: HZB, Unchitta Kanjanasaratool, Yacoub H. Kureh, and Mason A. Porter. Preprint available at arXiv:2007.05495. Accepted, Frontiers for Young Minds, 2020. (This is an explanatory article for young readers)
In Fall 2020, I’m teaching Math 131: Mathematical Analysis. Further course materials can be found on Sakai.
- Introduction to Networks [Spring 2020, UCLA]
- Mathematical Modeling [Fall 2019, UCLA]
- Reading Course in Nonlinear Dynamics [Spring 2019, UCLA]
- Linear and Nonlinear Systems of Differential Equations [Fall 2018 and Winter 2019, UCLA]
- Vector Calculus and Partial Differential Equations [Spring 2018, U. Utah]
- Calculus I, online course [Fall 2017, U. Utah]
- Linear Algebra [Spring 2017, U. Utah]
- Partial Differential Equations for Engineers [Summer 2016 and Fall 2016, U. Utah]
- Calculus II for Biologists [Spring 2016, U. Utah]
- Calculus I for Biologists [Fall 2015, U. Utah]
- Differential Equations and Linear Algebra for Engineers [Fall 2013, U. Utah]
- College Algebra [Summer 2013, U. Utah]
- Intermediate Algebra [Spring 2013 and Spring 2014, U. Utah]
- Intro to Quantitative Reasoning [Fall 2012, U. Utah]