Curriculum Vitae

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Citizenship

Costa Rica, Chile, United States

Appointments

• Acting Assistant Professor, University of Costa Rica, 2024
• Visiting Assistant Professor, Reed College, 2018 - 2022
• Visiting Assistant Professor, Colby College, 2015 - 2018
• Visiting Assistant Professor, Claremont McKenna College, 2013 - 2015

Professional Preparation

• Ph.D. Mathematics, University of Georgia, 2013. Advisor: Dino Lorenzini
• M.S. Mathematics, Georgia Institute of Technology, 2008. Advisor: Matt Baker
• B.S. Mathematics, University of Costa Rica, 2005

Research areas

Arithmetic geometry, algebraic number theory, arithmetic dynamics

Publications

1. Portraits of quadratic rational maps with a small critical cycle, with Tyler Dunaisky.
   J. Number Theory 275 (2025), 135-159.
2. Algebraic periodic points of transcendental entire functions, with Diego Marques, Carlos Gustavo Moreira, and Pavel Trojovský.
   Int. J. Number Theory. To appear.
3. Dynatomic Galois groups for a family of quadratic rational maps, with Allan Lacy.
   Int. J. Number Theory 20 (2024), no. 7, 1701-1724.
4. Quadratic points on dynamical modular curves, with John Doyle.
   Res. number theory 10,59 (2024)
5. Morikawa’s unsolved problem, with Jan Holly.
   Amer. Math. Monthly 128 (2021), no. 3, 214-237.
6. Twists of hyperelliptic curves by integers in progressions modulo p, with Paul Pollack.
   Acta Arith. 192 (2020), no.1, 63-71.
7. A finiteness theorem for specializations of dynatomic polynomials
   Algebra & Number Theory 13 (2019), no. 4, 963–993.
8. Galois groups over rational function fields and explicit Hilbert irreducibility, with Nicole Sutherland.
   J. Symbolic Comput. 103 (2021), 108-126.
9. Galois groups in a family of dynatomic polynomials
   J. Number Theory 187 (2018), 469-511.
10. A local-global principle in the dynamics of quadratic polynomials
    Int. J. Number Theory 12 (2016), no. 8, 2265-2297.
11. Squarefree parts of polynomial values
    J. Théor. Nombres Bordeaux 28 (2016), 699-724.
12. Computing points of bounded height in projective space over a number field
    Math. Comp. 85 (2016), 423-447.
13. Computing algebraic numbers of bounded height, with John Doyle.
    Math. Comp. 84 (2015), 2867-2891.
14. Preperiodic points for quadratic polynomials over quadratic fields, with John Doyle and Xander Faber.
    New York J. Math. 20 (2014), 507-605.

Teaching Experience

• University of Costa Rica, 2024
  • Linear Algebra II: Spring 2024
  • Intro to algebraic curves: Fall 2024
• Reed College, 2018 - 2022
  • Galois theory: Fall 2021
  • Topology: Spring 2022
  • Complex analysis: Spring 2022
  • Abstract algebra: Spring 2020
  • Real analysis: Fall 2020
  • Number theory: Spring 2021
  • Vector calculus: Spring 2020
  • Discrete structures: Fall 2021
  • Introduction to Analysis: Spring 2019, Fall 2019, Spring 2021
  • Linear Algebra: Fall 2018
  • Calculus I: Fall 2018, Fall 2020
• Colby College, 2015 - 2018
  • Complex Analysis: Fall 2017
  • 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
  • Calculus III: Spring 2008
  • Calculus II: Summer 2008

Undergraduate research supervision

• Advisor for senior thesis student Tyler Dunaisky (Reed College, B.A. May 2021)
  • Thesis title: Dynamics of quadratic rational maps with maximal automorphism group
  • Available through Reed Digital Collections
• Advisor for senior thesis student Liz Prestegaard (Reed College, B.A. May 2021)
  • Thesis title: The lattice of Alexandrov topologies
  • Available through Reed Digital Collections
• Advisor for senior thesis student Peter Marcus (Reed College, B.A. May 2021)
  • Thesis title: Computing the henselization of a valued field
  • Available through Reed Digital Collections
• Advisor for senior thesis student Pallavi Prakash (Reed College, B.A. May 2019)
  • Thesis title: Rational periodic points of quadratic maps
  • Available through Reed Digital Collections
• Advisor for senior thesis student Jonathan Star (Claremont McKenna College, B.A. May 2015)
  • Thesis title: Elliptic curves and the congruent number problem
  • Available at http://scholarship.claremont.edu/cmc_theses/1120/
• 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
  • Available at http://scholarship.claremont.edu/cmc_theses/993/
• Reader for senior thesis student John Shaughnessy (Claremont McKenna College, B.A. May 2014)
  • Thesis title: Finding zeros of rational quadratic forms
  • Available at http://scholarship.claremont.edu/cmc_theses/849/

Research Talks

• Dynamical Galois groups and rational portraits in one-parameter families of arithmetic dynamical systems. Oregon State University number theory seminar, February 2024.
• Algorithmic specialization of Galois groups over function fields. Jornada de Álgebra y Aplicaciones, San José, Costa Rica, December 2023.
• Arithmetic dynamics in families of quadratic rational maps. University of Costa Rica mathematics colloquium, October 2023.
• Classification of pre-periodic portraits for quadratic polynomials over quadratic number fields. Oregon State University number theory seminar, April 2022.
• Classification of pre-periodic portraits for quadratic polynomials over quadratic number fields. SIMMAC XXIII, February 2022.
• Twists of hyperelliptic curves by integers in progressions modulo p. University of Costa Rica mathematics colloquium, May 2021.
• Twists of hyperelliptic curves by integers in progressions modulo p. Oklahoma State University number theory seminar, April 2021.
• Classification of preperiodic portraits for quadratic polynomials over quadratic fields. AMS Special Session on Current Trends in Arithmetic Dynamics, Joint Mathematics Meetings, January 2021.
• Algebraic preperiodic points of entire transcendental functions. AMS Special Session on Arithmetic Dynamics, Joint Mathematics Meetings, Denver, Colorado, January 2020.
• Algebraic preperiodic points of entire transcendental functions. Oregon Number Theory Days, November 2019.
• Algebraic preperiodic points of entire transcendental functions. Maine-Québec Number Theory Conference. University of Maine, Orono, October 2019.
• A family of Galois groups in arithmetic dynamics. Portland State University mathematics colloquium, April 2019.
• A family of Galois groups in arithmetic dynamics. Oregon State University number theory seminar, April 2019.
• Finiteness criteria related to Hilbert's irreducibility theorem. Integers Conference, October 2018.
• Finiteness questions related to Hilbert's irreducibility theorem. University of Costa Rica mathematics colloquium, July 2018.
• A finiteness theorem for specializations of dynatomic polynomials. AMS Special Session on Arithmetic Dynamics, Joint Mathematics Meetings, San Diego, California, January 2018.
• 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.

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

Conferences Attended

• Jornada de Álgebra y Aplicaciones (San José, Costa Rica 2023)
• SIMMAC XXIII (San José, Costa Rica 2022)
• Oregon Number Theory Days (Portland, Oregon 2021)
• Joint Mathematics Meetings 2021
• Joint Mathematics Meetings (Denver, Colorado 2020)
• Oregon Number Theory Days (Eugene, Oregon 2019)
• Maine-Québec Number Theory Conference (Orono, Maine 2019)
• Number Theory in the Americas (Oaxaca, Mexico 2019)
• HINT 2019 (Honolulu, Hawaii)
• Integers Conference (Augusta, Georgia 2018)
• Joint Mathematics Meetings (San Diego, California 2018)
• Mathematical Congress of the Americas (Montréal, Canada 2017)
• Inquiry Based Learning Workshop (San Luis Obispo, California 2017)
• Potential Theory and Arithmetic Dynamics (Athens, Georgia 2017)
• Maine-Québec Number Theory Conference (Québec City, Canada 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)