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I am a professor in the Mathematics Department at the University of Arizona with a joint appointment in the Physics Department. I am also a member of the Graduate Interdisciplinary Program in Applied Mathematics and an associate member of the Graduate Interdisciplinary Program in Statistics. My research interests are in mathematical physics and probability.Show Less
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Courses
- IARGLMIntroduction to Applied Regression and Generalized Linear Models
- ASPApplied Stochastic Processes
- SPStochastic Processes
- RAOVReal Analysis of One Variable
- PMProbability Math
- ISBIntroduction to Statistics and Biostatistics
- TSTheory of Statistics
- RAReal Analysis
- CICalculus I
- TPTheory of Probability
- TAMTopics in Applied Mathematics
Grants
- Seminar on Stochastic Processes 2023
Co-Investigator (COI)
2023
$49.9K
Active - Conformal Invariance and the Renormalization Group in Some Critical Systems
Principal Investigator (PI)
2015
$361.4K
- Alliance for Building Faculty Diversity in the Mathematical Sciences
Principal Investigator (PI)
2014
$181.4K
- Critical and Near Critical Systems in Statistical Mathematics
Principal Investigator (PI)
2008
$306.6K
- Increasing the Number of highly Qualified Mathematical Scientists in the Workforce
Co-Investigator (COI)
2007
$551.9K
- Enhancing the Mathematical Sciences Workforce (EMSW21-VIGRE)
Co-Investigator (COI)
2006
$3.5M
News
- Regents Approve College of Science Master's Degree Program
2000
Publications (59)
Recent
- Tensor RG approach to high-temperature fixed point
2022
- Tensor Renormalization Group at Low Temperatures: Discontinuity Fixed Point
2022
- Absence of renormalization group pathologies in some critical Dyson-Ising ferromagnets
2020
- A Non-intersecting Random Walk on the Manhattan Lattice and {SLE} 6
2019
- Conformal invariance of the loop-erased percolation explorer
2019
- A non-intersecting random walk on the Manhattan lattice and SLE_6
2018
- The difference between a discrete and continuous harmonic measure
2017
- The First Order Correction to the Exit Distribution for Some Random Walks
2016
- The Smart Kinetic Self-Avoiding Walk and Schramm Loewner Evolution
2015
- Conformal Invariance Predictions for the Three-Dimensional Self-Avoiding Walk
2015
- Conformal invariance of the 3D self-avoiding walk
2013
- Self-avoiding walks in a rectangle
2013
- Transforming Fixed-Length Self-avoiding Walks into Radial SLE sub 8/3 /sub
2012
- Simulating self-avoiding walks in bounded domains
2012
- Efficient SLE algorithms and numerical pitfalls of the method
2012
- The Self-avoiding Walk Spanning a Strip
2011
- Renormalization group maps for ising models in lattice-gas variables
2010
- Conditioning schramm-loewner evolutions and loop erased random walks
2009
- Numerical computations for the schramm-loewner evolution
2009
- Computing the loewner driving process of random curves in the half plane
2008
- A fast algorithm for simulating the chordal Schramm-Loewner Evolution
2007
- The length of an SLE-Monte Carlo studies
2007
- Compact packings of the plane with two sizes of discs
2006
- Conformal invariance and stochastic Loewner evolution predictions for the 2D self-avoiding walk - Monte Carlo tests
2004
- Instability of interfaces in the antiferromagnetic XXZ chain at zero temperature
2003
- A faster implementation of the pivot algorithm for self-avoiding walks
2002
- Monte Carlo tests of stochastic Loewner evolution predictions for the 2D self-avoiding walk
2002
- Expansions for one quasiparticle states in spin 1/2 systems
2002
- Periodic ground states in the neutral Falicov-Kimball model in two dimensions
2001
- Phase separation in the neutral Falicov-Kimball model
1998
- Majority rule at low temperatures on the square and triangular lattices
1997
- Absence of renormalization group pathologies near the critical temperature. Two examples
1996
- Some rigorous results on the ground states of the Falicov-Kimball model
1994
- Ballistic behavior in a 1D weakly self-avoiding walk with decaying energy penalty
1994
- Non-positive matrix elements for Hamiltonians of spin-1 chains
1994
- Some rigorous results on majority rule renormalization group transformations near the critical point
1993
- Hidden symmetry breaking and the Haldane phase in S=1 quantum spin chains
1992
- Hidden Z2xZ2 symmetry breaking in Haldane-gap antiferromagnets
1992
- Solutions of the Yang-Baxter equation for isotropic quantum spin chains
1992
- Spin-Peierls transitions in S 1 2 Heisenberg chains
1991
- Ornstein-Zernike decay in the ground state of the quantum Ising model in a strong transverse field
1991
- Exact diagonalisations of open spin-1 chains
1990
- A fixed-point equation for the high-temperature phase of discrete lattice spin systems
1990
- Spin-Peierls transitions in S 1/2 Heisenberg chains
1990
- Valence bond ground states in isotropic quantum antiferromagnets
1988
- Existence of Néel order in some spin-1/2 Heisenberg antiferromagnets
1988
- The XY model has long-range order for all spins and all dimensions greater than one
1988
- A two-dimensional isotropic quantum antiferromagnet with unique disordered ground state
1988
- Rigorous results on valence-bond ground states in antiferromagnets
1987
- Mayer expansions and the Hamilton-Jacobi equation
1987
- Proof of the Peierls instability in one dimension
1987
- An itinerant electron model with crystalline or magnetic long range order
1986
- Spontaneous symmetry breakdown in the abelian Higgs model
1986
- Symmetry Breaking in the Lattice Abelian Higgs Model
1985
- Surface effects in Debye screening
1985
- Long range order in the anisotropic quantum ferromagnetic Heisenberg model
1985
- Mean field theory for Coulomb systems
1984
- Debye-Hückel theory for charge symmetric Coulomb systems
1983
- A lower bound on the partition function for a classical charge symmetric system
1982