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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
Courses
- CICalculus I
- TSTheory of Statistics
- PMProbability Math
- TPTheory of Probability
- TAMTopics in Applied Mathematics
- RAReal Analysis
- ISBIntroduction to Statistics and Biostatistics
- IARIntroduction to Applied Regression and Generalized Linear Models
- RAOReal Analysis of One Variable
- ASPApplied Stochastic Processes
- SPStochastic Processes
Grants
- Seminar on Stochastic Processes 2023
Co-Investigator (COI)
2023
$49.9KActive - 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 Grouat Low Temperatures: Discontinuity Fixed Point
2022
- Absence of renormalization groupathologies 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
- Self-avoiding walks in a rectangle
2013
- Conformal invariance of the 3D self-avoiding walk
2013
- Simulating self-avoiding walks in bounded domains
2012
- Efficient SLE algorithms and numerical pitfalls of the method
2012
- Transforming Fixed-Length Self-avoiding Walks into Radial SLE sub 8/3 sub
2012
- The Self-avoiding Walk Spanning a Strip
2011
- Renormalization groumaps for ising models in lattice-gas variables
2010
- Numerical computations for the schramm-loewner evolution
2009
- Conditioning schramm-loewner evolutions and looerased random walks
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
- Expansions for one quasiparticle states in spin 1/2 systems
2002
- 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
- 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 groupathologies near the critical temperature. Two examples
1996
- Non-positive matrix elements for Hamiltonians of spin-1 chains
1994
- Ballistic behavior in a 1D weakly self-avoiding walk with decaying energy penalty
1994
- Some rigorous results on the ground states of the Falicov-Kimball model
1994
- Some rigorous results on majority rule renormalization groutransformations near the critical point
1993
- Hidden Z2xZ2 symmetry breaking in Haldane-gaantiferromagnets
1992
- Hidden symmetry breaking and the Haldane phase in S=1 quantum spin chains
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
- A fixed-point equation for the high-temperature phase of discrete lattice spin systems
1990
- Exact diagonalisations of open spin-1 chains
1990
- Spin-Peierls transitions in S 1/2 Heisenberg chains
1990
- 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
- Valence bond ground states in isotropic quantum antiferromagnets
1988
- Existence of Néel order in some spin-1/2 Heisenberg antiferromagnets
1988
- Mayer expansions and the Hamilton-Jacobi equation
1987
- Proof of the Peierls instability in one dimension
1987
- Rigorous results on valence-bond ground states in antiferromagnets
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
- Long range order in the anisotropic quantum ferromagnetic Heisenberg model
1985
- Surface effects in Debye screening
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
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