Curriculum Vitae

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Citizenship

United States, Costa Rica, and Chile

Appointments

  • Visiting Assistant Professor, Claremont McKenna College, 2013 - Present

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

Dissertation

Quadratic points on modular curves (Advisor: Dino Lorenzini)

Awards and Fellowships

  • AMS grant for travel to the ICM, 2014
  • AMS-Simons Travel Grant, 2013
  • 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

Research interests

Arithmetic geometry, arithmetic dynamics, algebraic number theory, geometry of numbers

Publications

  1. “Preperiodic points for quadratic polynomials over quadratic fields”, with John Doyle and Xander Faber.
    New York J. Math. 20 (2014) pp. 507-605.
  2. “Computing algebraic numbers of bounded height”, with John Doyle. (22 pages)
    To appear in Mathematics of Computation.
  3. “Computing points of bounded height in projective space over a number field”. (22 pages)
    To appear in Mathematics of Computation.

Preprints

  • “Squarefree parts of polynomial values”. (20 pages) Submitted. view on arXiv

Teaching Experience

  • Claremont McKenna College, 2013-2014
    • Instructor for the courses Calculus I, Calculus II, Linear Algebra, and Number Theory
  • University of Georgia, 2008-2012
    • Instructor for the courses Precalculus, Calculus I, and Calculus for Science & Engineering
  • Georgia Institute of Technology, 2006-2008
    • Instructor for the courses Calculus II and Calculus III
    • Graduate teaching assistant for the courses Calculus II, Finite Mathematics, and Survey of Calculus
  • University of Costa Rica, 2002-2005
    • Undergraduate teaching assistant for the courses Calculus I, Calculus II, Analysis, and General Topology

Talks

  • 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.
  • Roth's (big) theorem. University of Georgia graduate student seminar, July 2009.
  • Computing the Hilbert function of a complete intersection. University of Georgia graduate student seminar, January 2009.

Undergraduate research supervision

  • Advisor for senior thesis student Jonathan Star (Claremont McKenna College, 2014)
  • Advisor for senior thesis student Arvind Suresh (Claremont McKenna College, 2014-2015)
  • Reader for senior thesis student John Shaughnessy (Claremont McKenna College, B.A. May 2014)

Service

  • Co-organizer (with L. Fukshansky) of the AMS Special Session on Heights, Diophantine Problems, and Lattices at UC Riverside, November 2-3, 2013

Other activities

  • Leader of a working seminar on rational points on curves (Claremont McKenna College, 2013)

Conferences Attended

  • 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)
Last updated: September 2014