I am a 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.

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

Radin, C., & Yin, M. (2013). Phase transitions in exponential random graphs. Annals of Applied Probability, 23, 2458-2471.

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

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

Yin, M., Rinaldo, A., & Fadnavis, S. (2016). Asymptotic quantization of exponential random graphs. Annals of Applied Probability, 26, 3251-3285.

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

Presentations

Yin, M., Rinaldo, A., Fadnavis, S., & Kenyon, R. (2014). Phase transitions in the edge-triangle exponential random graph model. International Congress of Mathematicians. Seoul, Korea.

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

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

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

Yin, M. (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

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