# Faculty

## Ian Alevy

*Visiting Assistant Professor of Mathematics*

1008 Hylan Building

(585) 276-6871

Fax: (585) 273-4655

ian.alevy@rochester.edu

Office Hours: By appointment

### Research Overview

My research interests include statistical mechanics, probability, discrete dynamical systems, and discrete geometry.

### Courses Taught

### Selected Publications

#### Publications and Preprints

- I. Alevy and S. Mkrtchyan,
*The Limit Shape of the Leaky Abelian Sandpile Model*, submitted 2020. We show that the limit shape of the Leaky-ASM is the dual of the amoeba of the associated spectral curve. - I. Alevy, R. Kenyon and R. Yi,
*A Family of Minimal and Renormalizable Rectangle Exchange Maps*, Ergodic Theory and Dynamical Systems, 1-28, doi:10.1017/etds.2019.77, 2019. We study certain rectangle exchange maps using a cut-and-project method. - Regular Polygon Surfaces. How can you build a surface which is topologically a sphere but whose faces are regular Euclidean polygons? Submitted 2018.
- I. Alevy and E. Tsukerman.
*Polygonal Bicycle Paths and the Darboux Transformation*, Involve, 9(1):57–66, 2016. - T. Nagylaki, L. Su, I. Alevy and T. Dupont.
*Clines with Partial Panmixia in an Environmental Pocket*, Theoretical Population Biology, 95:24-32, 2014.

#### Selected Talks

*The Limit Shape of the Leaky Abelian Sandpile Model.*Slides and Recording*Renormalizable Rectangle Exchange Maps.*Slides and Recording*Regular Polygon Surfaces*