KMap
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.

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Courses
  • IARGLM
    Introduction to Applied Regression and Generalized Linear Models

  • ASP
    Applied Stochastic Processes

  • SP
    Stochastic Processes

  • RAOV
    Real Analysis of One Variable

  • PM
    Probability Math

  • ISB
    Introduction to Statistics and Biostatistics

  • TS
    Theory of Statistics

  • RA
    Real Analysis

  • CI
    Calculus I

  • TP
    Theory of Probability

  • TAM
    Topics in Applied Mathematics

Grants
  • Funding agency logo
    Seminar on Stochastic Processes 2023

    Co-Investigator (COI)

    2023

    $49.9K
    Active
  • Funding agency logo
    Conformal Invariance and the Renormalization Group in Some Critical Systems

    Principal Investigator (PI)

    2015

    $361.4K
  • Funding agency logo
    Alliance for Building Faculty Diversity in the Mathematical Sciences

    Principal Investigator (PI)

    2014

    $181.4K
  • Funding agency logo
    Critical and Near Critical Systems in Statistical Mathematics

    Principal Investigator (PI)

    2008

    $306.6K
  • Funding agency logo
    Increasing the Number of highly Qualified Mathematical Scientists in the Workforce

    Co-Investigator (COI)

    2007

    $551.9K
  • Funding agency logo
    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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