Curriculum Vitae

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Citizenship

Costa Rica, Chile, United States

Appointments

  • Visiting Assistant Professor, Colby College, 2015 - 2018
  • Visiting Assistant Professor, Claremont McKenna College, 2013 - 2015

Professional Preparation

  • Ph.D. Mathematics, University of Georgia, 2013
  • M.S. Mathematics, Georgia Institute of Technology, 2008
  • B.S. Mathematics, University of Costa Rica, 2005

Research areas

Arithmetic dynamics, diophantine geometry, algebraic number theory

Doctoral dissertation

Quadratic points on modular curves (Advisor: Dino Lorenzini)

Publications

  1. Galois groups over rational function fields and explicit Hilbert irreducibility, with Nicole Sutherland.
    Submitted. arXiv preprint.
  2. Galois groups in a family of dynatomic polynomials
    J. Number Theory, to appear.
  3. A local-global principle in the dynamics of quadratic polynomials
    Int. J. Number Theory 12 (2016), no. 8, 2265-2297.
  4. Squarefree parts of polynomial values
    J. Théor. Nombres Bordeaux 28 (2016), 699-724.
  5. Computing points of bounded height in projective space over a number field
    Math. Comp. 85 (2016), 423-447.
  6. Computing algebraic numbers of bounded height, with John Doyle.
    Math. Comp. 84 (2015), 2867-2891.
  7. Preperiodic points for quadratic polynomials over quadratic fields, with John Doyle and Xander Faber.
    New York J. Math. 20 (2014), 507-605.

Awards, Fellowships, Grants

  • AMS grant for travel to the ICM, 2014
  • AMS-Simons Travel Grant, 2013-2015
  • University of Georgia Outstanding Teaching Assistant Award, 2013
  • William Armor Wills Memorial Scholarship Award, 2013
  • AMS Graduate Student Travel Grant, 2012
  • University of Georgia Dissertation Completion Award, 2012
  • National Science Foundation VIGRE Fellowship, 2008 and 2010
  • Goizueta Foundation Fellowship, 2007

Teaching Experience

  • Colby College, 2015-2018
    • Complex Analysis: Fall 2017 (taught in IBL format)
    • Cryptography: Spring 2017
    • Number Theory: Spring 2016
    • Calculus II: Fall 2016, Spring 2017, Fall 2017
    • Calculus I: Fall 2015, Spring 2016, Fall 2016, Spring 2018
  • Claremont McKenna College, 2013-2015
    • Abstract Algebra: Spring 2015
    • Number Theory: Spring 2014
    • Linear Algebra: Fall 2014
    • Calculus II: Spring 2014, Fall 2014, Spring 2015
    • Calculus I: Fall 2013
  • University of Georgia, 2008-2012
    • Calculus for Science & Engineering: Fall 2011, Spring 2012
    • Calculus I: Spring 2010
    • Precalculus: Fall 2009
  • Georgia Institute of Technology, 2008 (instructor)
    • Calculus III: Spring 2008
    • Calculus II: Summer 2008
  • Georgia Institute of Technology, 2006-2007 (graduate teaching assistant)
    • Finite Mathematics
    • Calculus II
    • Survey of Calculus

Undergraduate research supervision

Talks

  • Galois groups in a family of dynatomic polynomials. Mathematical Congress of the Americas, special session on arithmetic dynamics. Montréal, Canada, July 2017.
  • Galois groups in a family of dynatomic polynomials. University of Georgia, March 2017.
  • The global dynamics of quadratic maps on the projective line. University of Maine mathematics colloquium, December 2016.
  • Explicit Hilbert Irreducibility. University of Georgia number theory seminar, November 2016.
  • Explicit Hilbert Irreducibility. Maine-Québec Number Theory Conference. Laval University, October 2016.
  • Explicit Hilbert Irreducibility. University of Costa Rica mathematics colloquium, August 2016.
  • A local obstruction for periodic points under iteration of quadratic polynomials. RTG Workshop on Arithmetic Dynamics. University of Michigan, December 2015.
  • The global dynamics of quadratic maps on the projective line. Colby-Bates-Bowdoin Mathematics Seminar. Bates College, October 2015.
  • A local-global principle in the dynamics of quadratic polynomials. Maine-Québec Number Theory Conference. University of Maine, Orono, October 2015.
  • A local-global principle in the dynamics of polynomial maps. AMS Western Sectional Meeting, special session on Arithmetic Geometry. University of Nevada, Las Vegas, April 2015.
  • Squarefree parts of polynomial values. MAA MathFest, General contributed paper session on number theory. Portland, Oregon, August 2014.
  • Squarefree parts of polynomial values. Michigan State University algebra seminar, April 2014.
  • Squarefree parts of polynomial values. UC San Diego number theory seminar, March 2014.
  • Computing points of bounded height in P^N over a number field. Sage Days 55: Arithmetic and Complex Dynamics. Florida Institute of Technology, November 2013.
  • Preperiodic points for quadratic polynomials, I. AMS Western Sectional Meeting, special session on heights, Diophantine problems, and lattices. University of California, Riverside, November 2013.
  • Quadratic points on dynamical modular curves. Canadian Mathematical Society Summer Meeting, special session on experimental methods in number theory. Dalhousie University, June 2013.
  • Quadratic points on dynamical modular curves. Center for Communications Research, San Diego, California, April 2013.
  • Preperiodic points for quadratic polynomials. Advances in number theory and dynamical systems. University of Bristol, April 2013.
  • Preperiodic points for quadratic polynomials. Johns Hopkins University algebraic geometry & number theory seminar, February 2013.
  • Computing algebraic numbers of bounded height. AMS Special Session on Mathematics of Computation, Joint Mathematics Meetings, San Diego, California, January 2013.
  • Preperiodic points for quadratic polynomials. Clemson University number theory seminar, December 2012.
  • Preperiodic points for quadratic polynomials. Duke University algebraic geometry seminar, November 2012.
  • Preperiodic points for quadratic polynomials. Georgia Institute of Technology algebra seminar, November 2012.
  • Computation of preperiodic structures of quadratic polynomials over number fields. Canadian Number Theory Association XII Meeting. University of Lethbridge, June 2012.
  • Computing numbers of bounded height. Palmetto Number Theory Series XVI. Emory University, September 2011.
  • The BSD conjecture and related questions. University of Costa Rica, May 2011.
  • Stable reduction of curves of genus 2. University of Georgia number theory seminar, November 2010.

Conferences Attended

  • Mathematical Congress of the Americas (Montréal, Canada July 2017)
  • Inquiry Based Learning Workshop (San Luis Obispo, California June 2017)
  • Potential Theory and Arithmetic Dynamics (Athens, Georgia March 2017)
  • Maine-Québec Number Theory Conference (Québec City, Québec 2016)
  • RTG Workshop on Arithmetic Dynamics (Ann Arbor, Michigan 2015)
  • Maine-Québec Number Theory Conference (Orono, Maine 2015)
  • AMS Western Sectional Meeting (Las Vegas, Nevada 2015)
  • International Congress of Mathematicians (Seoul, Korea 2014)
  • MAA MathFest (Portland, Oregon 2014)
  • Southern California Number Theory Day (Pasadena, California 2014)
  • Sage Days 55: Arithmetic and Complex Dynamics (Melbourne, Florida 2013)
  • AMS Western Sectional Meeting (Riverside, California 2013)
  • Canadian Mathematical Society Summer Meeting (Halifax, Nova Scotia 2013)
  • Advances in number theory and dynamical systems (Bristol, UK 2013)
  • Joint Mathematics Meetings (San Diego, California 2013)
  • Canadian Number Theory Association XII Meeting (Lethbridge, Alberta 2012)
  • Summer School on Contemporary Methods for Solving Diophantine Equations (Banff, Alberta 2012)
  • Palmetto Number Theory Series XVI (Atlanta, Georgia 2011)
  • Summer School Program in Arithmetic Dynamics (Athens, Georgia 2011)
  • Second Summer School UCR & CSU (San José, Costa Rica 2011)
  • Canadian Number Theory Association XI Meeting (Wolfville, Nova Scotia 2010)
  • AMS Southeastern Section Meeting (Boca Raton, Florida 2009)
  • Palmetto Number Theory Series X (Savannah, Georgia 2009)
  • Doctoral Program on Diophantine Geometry (Rennes, France 2009)
  • Arizona Winter School in Mathematics (Tucson, Arizona 2007)