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United States, Costa Rica, and Chile
- Visiting Assistant Professor, Claremont McKenna College, 2013 - Present
- Ph.D. Mathematics, University of Georgia 2013
- M.S. Mathematics, Georgia Institute of Technology 2008
- B.S. Mathematics, University of Costa Rica 2005
Diophantine geometry, arithmetic dynamics, algebraic number theory, geometry of numbers
Quadratic points on modular curves
(Advisor: Dino Lorenzini
- “Computing points of bounded height in projective space over a number field”. (22 pages)
To appear in Mathematics of Computation.
- “Preperiodic points for quadratic polynomials over quadratic fields”, with John Doyle and Xander Faber.
New York J. Math. 20 (2014) pp. 507-605.
- “Computing algebraic numbers of bounded height”, with John Doyle. (22 pages)
To appear in Mathematics of Computation.
- “Squarefree parts of polynomial values”. (20 pages) Submitted.
view on arXiv
- Claremont McKenna College, 2013-2015: Instructor
- 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: Instructor
- 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
- University of Costa Rica, 2002-2005: Undergraduate teaching assistant
- Point-Set Topology
- Calculus II
- Calculus I
Undergraduate research supervision
- Advisor for senior thesis student Jonathan Star (Claremont McKenna College, B.A. May 2015)
- Thesis title: The congruent number problem
- Advisor for senior thesis student Arvind Suresh (Claremont McKenna College, B.A. May 2015)
- Thesis title: On the characterization of prime sets of polynomials by congruence conditions
- Reader for senior thesis student John Shaughnessy (Claremont McKenna College, B.A. May 2014)
- 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.
- 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)
Awards, Fellowships, Grants
- 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
Last updated: Dec. 5, 2014
- Co-organizer (with L. Fukshansky) of the AMS Special Session on Heights, Diophantine Problems, and Lattices at UC Riverside, November 2-3, 2013
- Leader of a working seminar on rational points on curves (Claremont McKenna College, 2013)