Welcome! I am a Mathematics Ph.D. student studying Interacting Particle Systems with Dr. Nicolas Lanchier at Arizona State University.
My research involves creating and analyzing mathematical models governed by probabilistic local interactions. Using contemporary techniques, the goal is to prove qualitative results about the long-term behavior of these models.
We have studied the impact of decoupling individuals who are infected with a disease into asymptomatic and symptomatic groups through the lens of a multi-type contact process. Additionally, we proved conjectured and new results about a process modeling Allelopathy in space, created by Rick Durrett and Simon Levin. We have also developed two new models: an extension of the Deffuant model of opinion dynamics which accommodates polarizing interactions, and the Kindness model, which models the relationship between experiencing and exhibiting kindness.
Books and Publications
Peer-reviewed articles:
Nicolas Lanchier and Max Mercer. Durrett-Levin spatial model of allelopathy. ALEA Lat. Am. J. Probab. Math. Stat. 21 (2024) 321-343.
Belhadji, Lamia, Nicolas Lanchier, and Max Mercer. "The contact process with an asymptomatic state." Stochastic Processes and their Applications (2024): 104417.
Articles in review:
Nicolas Lanchier and Max Mercer. Deffuant opinion dynamics with attraction and repulsion. Available as arXiv:2310.19073.
Nicolas Lanchier and Max Mercer. Limiting behavior of a kindness model. Available as arXiv:2402.02579.
Jonas Köppl, Nicolas Lanchier and Max Mercer. Survival and extinction for a contact process with a density-dependent birth rate. Available as arXiv:2404.09944.
Degrees Earned
B.S. Applied Mathematics
Arizona State University, 2021
M.A. Applied Mathematics
Arizona State University, 2023
In Progress: Ph.D Applied Mathematics
Arizona State University, Anticipated 2025
Licenses and Certifications
Master Class for Teaching Online – EdPlus, Arizona State University
Data Science: Visualization (PH125.2x), Harvard
Data Science: Probability (PH125.3x), Harvard
Data Science: Inference and Modeling (PH125.4x), Harvard
Seal of Bi-literacy in Spanish, AAPPL
Scholarships and Awards
New American University - President's Award, Fall 2018-Spring 2022 - $40,000
Block Grant, Summer 2023 - $5,922
ARCS Krepper Family Trust Scholar, Fall 2024-Spring 2025 - $8,500
Dean’s List (All Semesters)
Moeur Award, May 2022
Special Projects
ARCS Poster Presentation - The Contact Process with an Asymptomatic State
This is the culmination of a semester of research with one of my wonderful professors, Dr. Hala King, at Arizona State University. We explored the usage of different numeral systems across the world and the implications of those numeral systems on calendars and other social constructions.
MATLAB Projects Authored
Sudoku Generator
(Sudoku.mlx)
Fractal Generator
(ChaosGameFractalMaker.mlx)
Diffusion Visualizer
(DiffusionPDE.mlx)
Rule Of 72 Accuracy
(72test.mlx)
Teaching Experience
I have had the honor and privilege of serving as a Teaching Assistant at Arizona State University Tempe Campus for three years, and before that, serving as a lead mathematics tutor at the ASU West Campus. I have been an instructor of record for Calculus courses, and a teaching assistant for many graduate-level courses.
My kind and wonderful students gave me reviews, both on the official ASU survey and on Rate My Professor. I believe that my students are the best possible source to ask about my teaching, so I have included their statements below.