Research

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    Papers

  • Tensor representations of discrete data
    In preparation, with Shaowei Lin, Luca Weihs, and Piotr Zwiernik.
    • Description
    • We represent discrete random variables as tensors in a way that allows us to treat any discrete random vector essentially like a binary vector. This enables us to generalize certain known results on the geometry of binary models for arbitrary discrete models.
  • Polynomial constraints on representing entangled qubits as matrix product states
    with Jason Morton (2012).
    • BibTeX
    • arXiv
    • pdf
    • @misc{CM12,
author="Andrew J. Critch and Jason Morton",
title = "{Polynomial constraints on representing entangled qubits as matrix product states}",
year = {2012},
howpublished = "{arXiv:1210.2812}",
}
  • Binary hidden Markov models and varieties
    (2012), in the Journal of Algebraic Statistics, Vol . 4, No. 1, 2013.
    • BibTeX
    • arXiv
    • pdf
    • @misc{Cri12,
author="{Andrew J. Critch}",
title = "{Binary hidden Markov models and varieties}",
year = {2012},
howpublished = "{arXiv:1206.0500}",
}
  • A note on the proportionality between some consistency indices in the AHP
    with Matteo Brunelli and Michele Fedrizzi (2010), in Applied Mathematics and Computation.
    • BibTeX
    • arXiv
    • pdf
    • ScienceDirect 
    • @misc{BCF10,
author="Matteo Brunelli and Andrew J. Critch and Michele Fedrizzi",
title = "{A note on the proportionality between some consistency indices in the AHP}",
year = {2010},
howpublished = "{arXiv:1203.6431v1}",
}
  • Pushing the limit (generalized limits and limit extrema in topology)
    in the Atlantic Electronic Journal of Mathematics, vol. 1, iss. 1 (2006), pp. 47-55.
    • BibTeX
    • AEJM
    • pdf
    • @article{Cri06a,
author="{Andrew J. Critch}",
title="{Generalized limits and limit extrema}",
journal="Atlantic Electronic Journal of Mathematics",
year={2006},
volume={1},
number={1},
pages={47 - 55},
}
  • Resolving the Banach-Tarski paradox: inseparability of rigid bodies
    B.Sc. Honors thesis, Memorial University of Newfoundland (2006).
    • BibTeX
    • pdf
    • @misc{Cri06b,
author="{Andrew J. Critch}",
title = "{Resolving the Banach-Tarski paradox: inseparability of rigid bodies}",
year = {2006},
howpublished = "{B.Sc. Honors thesis, Memorial University of Newfoundland}",
}
 

    Software

  • Tensors.m2 – a Macaulay2 package for studying varieties of tensors and tensor networks.
    with Claudiu Raicu (2012), began at the WFU2012 Macaulay2 developers workshop.
    • Webpage
    • Download v0.1
  • Credence – a game using information-theoretic scoring to calibrate players' subjective belief strengths to more accurately match their success rates.
    with Alexei Andreev and Zachary Alethia (2012).
    • Webpage
    • Download
 

    Selected talks

  • Algebraic constraints on MPS-entangled qubits
    (September, 2012) in the RTG workshop on Tensors and their Geometry in High Dimensions at UC Berkeley
    • Abstract
    • Slides
  • Causality and algebraic geometry
    (September, 2012) in the Queen's Algebraic Geometry Seminar
    • Abstract
    • Slides
  • A new parametrization for binary hidden Markov models
    (June, 2012) at Algebraic Statistics in the Alleghenies, Pennsylvania State University
    • Abstract
    • Slides
  • Computing examples in algebraic geometry
    (January, 2012) in the Student Algebraic Geometry Seminar, UC Berkeley
    • Abstract
  • What causality is (stats for mathematicians)
    (August, 2011) in the Berkeley Algebraic Statistics Seminar
    • Abstract
    • Slides
  • Picard group of the moduli stack of elliptic curves
    (an introduction to stacks by example)
    (March, 2011) in the Student Algebraic Geometry Seminar, UC Berkeley
    • Abstract
 

    Activities

  • Berkeley Student Algebraic Geometry Seminar
    (Spring 2011 - Spring 2012) Co-organized the seminar, first with Charley Crissman, and later with Andrew Dudzik.
    • Webpage
  • COGS Causal Inference Symposium
    (February, 2012) Co-organized the symposium with Mike Pacer.
    • Webpage
  • Berkeley Algebraic Statistics Seminar
    (Fall 2011) Co-organized the seminar with Shaowei Lin.
    • Webpage