# Mei Yin

## Associate Professor

303-871-2130 (Office)

Clarence M. Knudson Hall, 2390 S. York St. Denver, CO 80210

### What I do

I am an associate professor of mathematics here at DU, dedicated to discovering mathematics and teaching mathematics!### Specialization(s)

statistical physics, probability, combinatorics

### Professional Biography

I received my PhD in Mathematics (with a minor in Statistics) from the University of Arizona in August 2010. I then held the Bing Instructor position at the University of Texas at Austin for three years, from August 2010 till June 2013. I joined DU as an Assistant Professor of Mathematics in September 2013, with the 2013-2014 academic year on leave at Brown University as a Tamarkin Assistant Professor. My main research interests lie in statistical physics, probability, and combinatorics.

### Degree(s)

- Ph.D., Mathematics, University of Arizona, 2010

### Professional Affiliations

- American Mathematical Society
- Association for Women in Mathematics
- International Association of Mathematical Physics

### Research

Of particular interest in my work are phase transitions, abrupt changes in the state of a system. Examples include the freezing of liquid water or the temperature at which a molten metal becomes magnetic. The math involved in modeling systems like these is quite difficult, requiring mathematical techniques for dealing with the immense quantities involved. One of those models — and my current research focus — is called exponential random graphs. They are used to model networks in the real world — social networks, power grids, and the Internet are examples. The models can also be used in statistical physics, which is what initially interested me.

Like real-world systems they represent, exponential random graph models undergo phase transitions. Imagine a graph model of a power grid. Sprinkle a broken power line here or there on the graph, and at some point large portions of the network go dark. That’s a phase transition! Simply put, a small change in some local quantity in the graph may lead to some abrupt, large-scale change in a global quantity. Such an insight would have broad application, from understanding social interaction to modeling of disease outbreaks. I received a grant from the National Science Foundation to develop a quantitative theory of those kinds of phase transitions in exponential random graph models from 2013-2017.

Like real-world systems they represent, exponential random graph models undergo phase transitions. Imagine a graph model of a power grid. Sprinkle a broken power line here or there on the graph, and at some point large portions of the network go dark. That’s a phase transition! Simply put, a small change in some local quantity in the graph may lead to some abrupt, large-scale change in a global quantity. Such an insight would have broad application, from understanding social interaction to modeling of disease outbreaks. I received a grant from the National Science Foundation to develop a quantitative theory of those kinds of phase transitions in exponential random graph models from 2013-2017.

#### Areas of Research

phase transitions

random graphs

lattice spin systems

#### Key Projects

- Random Graphs: A Mathematical Physics Perspective
- Collaborative Research: Rocky Mountains-Great Plains Graduate Research Workshops in Combinatorics
- Collaborative Research: Rocky Mountains-Great Plains Graduate Research Workshops in Combinatorics

### Featured Publications

(2013). Phase transitions in exponential random graphs. Annals of Applied Probability, 23, 2458-2471.

. (2013). Critical phenomena in exponential random graphs. Journal of Statistical Physics, 153, 1008-1021.

. (2016). A detailed investigation into near degenerate exponential random graphs. Journal of Statistical Physics, 164, 241-253.

. (2016). Asymptotic quantization of exponential random graphs. Annals of Applied Probability, 26, 3251-3285.

. (2017). On the asymptotics of constrained exponential random graphs. Journal of Applied Probability , 54, 165-180.

. ### Presentations

(2014). Phase transitions in the edge-triangle exponential random graph model. International Congress of Mathematicians. Seoul, Korea.

. (2015). Asymptotics for sparse exponential random graph models. Semester Program in Phase Transitions and Emergent Properties. Institute for Computational and Experimental Research in Mathematics.

. (2016). Phase transitions in (generalized) exponential random graphs. Melbourne-Singapore Probability and Statistics Forum. Singapore, Singapore.

. (2017). Statistical physics of exponential random graphs. Cluster Expansions: From Combinatorics to Analysis through Probability. Mathematisches Forschungsinstitut Oberwolfach.

. (2018). Perspectives on exponential random graphs. Recent Progress on Dimer Model and Statistical Mechanics. Avery Point, CT.

. ### Awards

- Best Poster Award, International Congress of Women Mathematicians
- Outstanding Junior Faculty, University of Denver
- US Junior Oberwolfach Fellow, National Science Foundation