Curriculum Vitae

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Citizenship

Costa Rica, Chile, United States

Appointments

• Acting Assistant Professor, University of Costa Rica, 2024 - Present
• 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.
   Submitted.
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 - Present
  • 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)