I am an assistant professor in department of mathematics, University of Connecticut. I am also a researcher in probability theory and mathematical physics.



  1. Local statistics of realizable vertex models, Commun.Math.Phys, 304, 723-763(2011), arxiv
  2. Critical temperature of periodic Ising models, Commun.Math.Phys, 315, 337-381(2012), arxiv
  3. 1-2 model, dimers, and clusters, Electron. J. Probab. 19 (2014), no. 48, 1-28, journal
  4. Self-avoiding walks and the Fisher transformation, with Geoffrey Grimmett, Electron.J.Combin.,20 (2013), Paper P47, 14 pp arxiv
  5. Uniqueness of the infinite homogeneous cluster in the 1-2 model, Electron. Commun. Probab. 19 (2014), no. 23, 1-8 journal
  6. Bounds on connective constants of regular graphs, with Geoffrey Grimmett, Combinatorica, 35 (2015), no. 3, 279-294 arxiv
  7. Strict inequalities for connective constants of transitive graphs, with Geoffrey Grimmett, SIAM J. Discrete Math. 28 (2014), no. 3, 1306–1333, arxiv
  8. Spectral curve of periodic Fisher graphs, Journal of Mathematical Physics 55, 123301 (2014); pdf
  9. Conformal invariance of dimer heights on isoradial double graphs, ANNALES DE L’INSTITUT HENRI POINCARÉ D, vol. 4 (2017), 273-307, pdf
  10. Critical surface of the hexagonal polygon model, with Geoffrey Grimmett, Journal of Statistical Physics 163 (2016), no. 4, 733–753, arxiv
  11. The 1-2 model, with Geoffrey Grimmett, Contemporary Mathematics 696 (2017) , 139-152, arxiv
  12. Connective constants and height functions for Cayley graphs, with Geoffrey Grimmett, Trans. Amer. Math. Soc. 369 (2017), no. 8, 5961–5980, arxiv
  13. Critical surface of the 1-2 model, with Geoffrey Grimmett, Int. Math. Res. Not. IMRN, arxiv
  14. Self-avoiding walks and connective constants, with Geoffrey Grimmett, arxiv, to appear in Festschrifts for Charles Newman’s 70th birthday, edited by Vladas Sidoravicius
  15. Self-avoiding walks and amenability, with Geoffrey Grimmett,  the Electronic Journal of Combinatorics, Volume 24, Issue 4 (2017), Paper #P.4.38, arxiv,
  16. Locality of connective constants, with Geoffrey Grimmett, arxiv, Discrete Mathematics, Volume 341, Issue 12, December 2018, Pages 3483-3497


  1. Constrained percolation in two dimensions, with Alexander Holroyd, arxiv
  2. Cubic graphs and the golden mean, with Geoffrey Grimmett, arxiv
  3. Positive speed self-avoiding walks on graphs with more than one end, arxiv
  4. Mixing time of Markov chains for the uniform 1-2 model, arxiv
  5. Constrained percolation, Ising model and XOR Ising model on planar lattices, arxiv
  6. Limit shape and height fluctuations of random perfect matchings on square-hexagon lattices, with Cédric Boutillier, arxiv
  7. Weighted self-avoiding walks, with Geoffrey Grimmett, arxiv
  8. Schur function at generic points and limit shape of perfect matchings on contracting square hexagon lattices with piecewise boundary conditions, arxiv
  9. Fluctuations of dimer heights on contracting square-hexagon lattices, arxiv, pdf


  1. PI for NSF DMS-1608896 2016-2019 100K USD
  2. PI for Simons Collaboration Grant-351813 2015-2020 35K USD (voluntarily declined after 1st year)
  3. NSF DMS 1643027, PI: Rinat Ridem, 4000 USD, awarded 2017 for participating IHP trimester Combinatorics and Interactions
  4. Co-PI for NSF conference grant DMS-1823060 2018-2019 49998 USD


Education and Employments


  1. 2006-2011, Ph.D student, department of mathematics, Brown University. Advisor: Richard Kenyon


  1. 2011-2014, research fellow, department of pure mathematics and mathematical statistics, University of Cambridge, UK
  2. 2014-present, assistant professor, department of mathematics, University of Connecticut