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Contact: mamerce1@asu.edu
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. I work with my phenomenal advisor Dr. Nicolas Lanchier at Arizona State University, where I earned an M.A. in 2023 and a Ph.D. in 2025.
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 three new models: an extension of the Deffuant model of opinion dynamics which accommodates polarizing interactions, the Kindness model, which models the relationship between experiencing and exhibiting kindness, and the Teaching Model, which explores the dynamics of knowledge in spatial networks, with the goal of understanding what it takes for knowledge to outlive its keepers.
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. MR4710541.Lamia Belhadji, Nicolas Lanchier and Max Mercer.
The contact process with an asymptomatic state.
Stochastic Process. Appl. 176 (2024) 104417. MR4768390.Nicolas Lanchier and Max Mercer.
Limiting behavior of a kindness model.
Statist. Probab. Lett. 214 (2024) 110205.Nicolas Lanchier and Max Mercer.
Deffuant opinion dynamics with attraction and repulsion.
Electron. Commun. Probab. 29 (2024) no. 45, 12 pp.Jonas Köppl, Nicolas Lanchier and Max Mercer.
Survival and extinction for a contact process with a density-dependent birth rate.
To appear in Electron J. Probab.
Articles in review:
Jonas Köppl, Nicolas Lanchier and Max Mercer.
Evolutionary games on the lattice: multitype contact process with density-dependent birth rates.
Available as arXiv:2412.19957.Nicolas Lanchier, Max Mercer and Hyunsik Yun.
Contact process for the spread of knowledge.
Available as arXiv:2503.17260.
Degrees Earned
Ph.D. Applied Mathematics
Arizona State University, 2025
M.A. Applied Mathematics
Arizona State University, 2023
B.S. Applied Mathematics
Arizona State University, 2021
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
Graduate Research Award, May 2025
Graduate Excellence Award, May 2025
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.
Android App: Simple Calorie
I wanted a simple calorie tracker app with no advertisements or cost, and thanks to MIT, I was able to make one! First, set your daily desired calorie goal and hit "new day".
If you eat, add the amount of calories you ate in the "ATE: " text box and hit the first "LOG IT!" button.
If you exercise, add the amount of calories in the "BURNED: " text box and hit the second "LOG IT!" button.
When you're ready to start a new day, just click "New Day" - No need to put in your daily calorie goal again, it will be saved after the first time (or to the default - 1500 - otherwise).
That's all! If you'd like to download the APK on your device, here is the link
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. In Fall 2025 I became an Assistant Teaching Professor for this wonderful school, and hope to empower my students with the joys of mathematics to improve their lives.
My kind and wonderful students gave me reviews on the official ASU survey. I believe that my students are the best possible source to ask about my teaching, so I have included their statements below.
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