##### KMap

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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

#### VOSviewer

##### 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

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