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Joe Chen

Joe Chen

Assistant Professor of Mathematics
Mathematics , 214 McGregory Hall
p 315-228-6557

Degrees

BS, Yale College, 2006; MS, Cornell University, 2010; PhD, Cornell University, 2013.

Professional Experience

Postdoctoral fellow / Visiting Assistant Professor, Department of Mathematics, University of Connecticut, 2013-16.

Visiting research positions and invited lectures:

Research Interests

Particle systems, growth models, and (stochastic) partial differential equations

My research focuses on the analysis of probability models---in particular, interacting particle systems and Laplacian growth models---on state spaces which are bounded in distance determined by electrical resistance. By studying explicit models and taking the right space-time scaling limits, I can rigorously derive (stochasticpartial differential equations or prove limit shape theorems on these spaces. These mathematical results capture various laws of nature, such as heat flow, wave propagation, charged particles in an electromagnetic field, and fluid dynamics. 

Models which I have studied include: Exclusion processesinternal diffusion-limited aggregationrotor-router aggregationabelian sandpiles, and Gaussian free fields. These models are often inspired from, and studied in, probability theory and statistical physics.

While the models I study may seem disparate, my approach is ultimately grounded in the study of analysis on graphsMarkov processes, and potential theory.

More details can be found on my research page.

Select Grants & Awards

Student Research

2018~19: I am on sabbatical leave and not taking on new students.

Below is a list of undergraduate research projects which I have (co-)supervised. While I make no guarantees, many of the projects have resulted in arXiv preprints and then published in good journals.
  • Fall 2017~Spring 2018 (Colgate): Complex-valued graph Laplacians, random spanning forests, and sandpiles on fractal graphs.
  • Spring 2017 (Colgate): Limit shapes of Laplacian growth & sandpile models on fractal graphs.  arXiv:1807.08748
  • Summer 2015 (UConn math REU): Stabilization by noise of a nonlinear coupled system with quadratic nonlinearity. arXiv:1510.09221 (Published in Stoch. Dyn.)
  • Summer 2015 (UConn math REU): Power dissipation in fractal AC circuits. arXiv:1605.03890 (Published in J. Phys. A: Math. Theor.)

List of Publications

(The papers below have been either published or accepted for publication. See my arXiv page for the most up-to-date list of my papers.)

``From non-symmetric particle systems to non-linear PDEs on fractals.''
(with Michael Hinz and Alexander Teplyaev.) To appear in the proceedings for Stochastic PDEs and Related Fields: an international conference in honor of Michael Röckner's 60th birthday. (2018+). arXiv:1702.03376

``Regularized Laplacian determinants of self-similar fractals.''
(with Alexander Teplyaev and Konstantinos Tsougkas.) Lett. Math. Phys. 108 (2018) 1563-1579. arXiv:1610.10062

``The moving particle lemma for the exclusion process on a weighted graph.''
Electron. Commun. Probab. 22 (2017), paper no. 47. arXiv:1606.01577

``Power dissipation in fractal AC circuits.''
(with Luke G. Rogers, Loren Anderson, Ulysses Andrews, Antoni Brzoska, Aubrey Coffey, Hannah Davis, Lee Fisher, Madeline Hansalik, Stephew Loew, and Alexander Teplyaev.). J. Phys. A: Math. Theor. 50 (2017) 325205. arXiv:1605.03890

``Wave equation on one-dimensional fractals with spectral decimation and the complex dynamics of polynomials.''
(with Ulysses Andrews, Grigory Bonik, Richard W. Martin, and Alexander Teplyaev.) 
J. Fourier Anal. Appl. 23 (2017) 994--1027. arXiv:1505.05855

``Stabilization by noise of a $\mathbb{C}^2$-valued coupled system.''
(with Lance Ford, Derek Kielty, Rajeshwari Majumdar, Heather McCain, Dylan O'Connell, and Fan Ny Shum.) Stoch. Dyn. 17 (2017) 1750046. arXiv:1510.09221

``Singularly continuous spectrum of a self-similar Laplacian on the half-line.''
(with Alexander Teplyaev.) J. Math. Phys. 57 (2016) 052104. arXiv:1509.08875

``Spectral dimension and Bohr's formula for Schrodinger operators on unbounded fractal spaces.''
(with Stanislav Molchanov and Alexander Teplyaev.) J. Phys. A: Math. Theor. 48 (2015) 395203. arXiv:1505.03923

``Entropic repulsion of Gaussian free field on high-dimensional Sierpinski carpet graphs."
(with Baris E. Ugurcan.) Stoch. Proc. Appl. 125 (2015) 4632--4673. arXiv:1307.5825

``Periodic billiard orbits of self-similar Sierpinski carpets."
(with Robert G. Niemeyer.) J. Math. Anal. Appl. 416 (2014) 969--994. arXiv:1303.4032

``Quantum theory of cavity-assisted sideband cooling of mechanical motion."
(with Florian Marquardt, Aashish A. Clerk, and Steven M. Girvin.)
Phys. Rev. Lett. 99, 093902 (2007).

Teaching

For a list of classes I have taught, please visit my teaching page.