Education | Publications | Presentations | Research | Teaching | Honors | Music

Background

I am currently a first-year PhD student in mathematics at Princeton University. My primary research interests lie in number theory and algebraic geometry. I am also quite interested in the classics and can read/speak Latin with moderate proficiency. In my free time, I play the violin and enjoy listening to classical music.

Education

  • Princeton University, Princeton, NJ
    • PhD in Mathematics, 2021 (expected)
  • Harvard University, Cambridge, MA
    • AM in Physics, 2017
    • AB in Mathematics, 2017
               summa cum laude & with highest departmental honors
    • Senior thesis: "Inflection points of linear systems on families of curves" (thesis) (talk)
               Mentors: Joe Harris & Anand Patel
  • The Harker School, San Jose, CA
    • High school diploma, 2013
              Class valedictorian (video) (text)

Research Publications

  1. Inflectionary invariants for plane curve singularities (with Anand Patel), 2017.
  2. Hyperelliptic curves with maximal Galois action on the torsion points of their jacobians (with Aaron Landesman, James Tao, and Yujie Xu), 2017.
  3. Surjectivity of Galois representations in rational families of abelian varieties (with Aaron Landesman, James Tao, and Yujie Xu), submitted, 2016.
  4. Lifting subgroups of symplectic groups over Z/lZ (with Aaron Landesman, James Tao, and Yujie Xu), Research in Number Theory, to appear, 2017.
  5. Elliptic curve variants of the least quadratic nonresidue problem and Linnik's Theorem (with Evan Chen and Peter Park), International Journal of Number Theory, to appear, 2017.
  6. Permutations that destroy arithmetic progressions in elementary p-groups (with Noam D. Elkies),  Electronic Journal of Combinatorics, 24(1) (2017), 1-10. (arXiv)
  7. On logarithmically Benford sequences (with Evan Chen and Peter Park), Proceedings of the American Mathematical Society, 144(11) (2016), 4599-4608. (arXiv)
  8. On arboreal Galois representations of rational functions, Journal of Algebra, 448 (2016), 104-126. (arXiv)
  9. Linnik's theorem for Sato-Tate laws on elliptic curves with complex multiplication (with Evan Chen and Peter Park), Research in Number Theory, 1(1) (2015), 1-11. (arXiv)
  10. Analysis on surreal numbers (with Simon Rubinstein-Salzedo), Journal of Logic and Analysis, 6(5) (2014), 1-39. (arXiv)

Expository Articles

  1. Inflection points of linear systems on families of curves (Harvard senior thesis), 2017.
  2. Lie algebras and Ado's Theorem, 2016.
  3. An introduction to the theory of valued fields (Harvard junior paper), 2015.
  4. On the Selberg-Erdős proof of the Prime Number Theorem, 2014.
  5. Arrow's impossibility theorem on social choice systems, 2013.
Presentations
  • Invited Talks
    • "Surjectivity of Galois representations in rational families of abelian varieties," Algebra, Geometry, and Number Theory Seminar, Tufts University, 2017.
    • "Inflection points of linear systems on families of curves," Algebraic Geometry Seminar, Stanford University, 2017.
    • "Analysis on surreal numbers: functions and integration," ASL Special Session, MAA-AMS JMM, 2016.
    • "Surreal analysis: an analogue of real analysis for surreal numbers," Siemens Competition Regional Finals, California Institute of Technology, 2012.
  • Contributed Talks
    • "Surjectivity of Galois representations in rational families of abelian varieties," MAA-AMS JMM, 2017.
    • "Permutations that destroy arithmetic progressions in elementary p-groups," MAA-AMS JMM, 2017.
    • "Elliptic curve variants of the least quadratic nonresidue problem and Linnik's Theorem," MAA-AMS JMM, 2016.
    • "Permutations that destroy arithmetic progressions," Harvard Math Table, 2016.
    • "On arboreal Galois representations of rational functions," MAA-AMS JMM 2015.
    • "How small is that prime?," Harvard Math Table, 2015.
    • "Arboreal Galois representations of rational functions," Harvard Math Table, 2014.
    • "Surreal analysis: an analogue of real analysis for surreal numbers," Harvard Math Table, 2013.
    • "Surreal analysis: an analogue of real analysis for surreal numbers," CMS Summer Meeting, 2013.

Research Experience

  • Senior thesis, Department of Mathematics, Harvard University, 2016-2017
    • 2016-2017: Worked in algebraic geometry (mentors: Joe Harris & Anand Patel)
  • Emory REU, Department of Mathematics, Emory University
    • Summer 2016: Worked in arithmetic geometry (mentors: David Zureick-Brown & Ken Ono)
    • Summer 2015: Worked in analytic number theory (mentors: Jesse Thorner & Ken Ono)
  • Duluth REU, Department of Mathematics, University of Minnesota Duluth
    • Summer 2015: Worked in combinatorial number theory (mentors: Noam D. Elkies & Joseph Gallian)
    • Summer 2014: Worked in Galois representations (mentor: Joseph Gallian)
  • Independent study, Department of Mathematics, Stanford University
    • 2011–2014: Worked in logic & analysis with Simon Rubinstein–Salzedo
    • 2011–2013: Worked in analytic number theory with Daniel M. Kane

Teaching Experience

  • Course Assistant, Department of Mathematics, Harvard University
    • [Math 137] Introduction to algebraic geometry (Peter Kronheimer), 2017. Q-score: 5.0/5.0
    • [Math 131] Topology I: Topological spaces & the fundamental group (Joe Harris), 2016. Q-score: 4.5/5.0
    • [Math 123] Algebra II: Theory of rings & fields (Arul Shankar), 2016. Q-score: 4.9/5.0
    • [Math 114] Analysis II: Measure, integration, & Banach spaces (Daniel C.-Gardiner), 2015. Q-score: 4.9/5.0
    • [Math 55b] Honors real & complex analysis (Dennis Gaitsgory), 2015. Q-score: 4.3/5.0
    • [Math 55a] Honors abstract algebra (Dennis Gaitsgory), 2014. Q:-score 4.6/5.0

Honors and Awards

  • 2017
    • David B. Mumford Prize (most promising senior in mathematics at Harvard)
    • Paul and Daisy Soros Fellowship for New Americans -- Fellow
    • NSF Graduate Research Fellowship -- Fellow
    • Hertz Fellowship -- Finalist
    • Centennial Fellowship, Princeton University (highest fellowship for graduate students at Princeton)
    • Declined PhD Fellowship Offers:
      • Berkeley Fellowship, University of California, Berkeley
      • President's Fellowship, Massachusetts Institute of Technology
      • Dean's Fellowship, Columbia University
      • Graduate Fellowship, Stanford University
    • Harvard University Certificate of Distinction in Teaching (Math 131)
  • 2016
    • John Harvard Scholar for Academic Achievement
    • Harvard University Certificate of Distinction in Teaching (Math 123)
    • Robert Fletcher Rogers Prize (best talk at Harvard Math Table)
    • Phi Beta Kappa -- Junior 24 (top 24 juniors in Harvard class)
    • Barry M. Goldwater Scholarship -- Scholar
  • 2015
    • Harvard University Certificate of Distinction in Teaching (Math 114)
    • John Harvard Scholar for Academic Achievement
    • Barry M. Goldwater Scholarship -- Honorable Mention
  • 2014
    • Wendell Scholarship -- Nominee
    • John Harvard Scholar for Academic Achievement
    • Detur Book Prize for Academic Excellence
  • 2010-2013
    • Siemens Competition in Math, Science, and Technology -- Regional Finalist
    • Intel Science Talent Search -- Semifinalist
    • Only one in the world to receive perfect score on both AP Microeconomics & AP Macroeconomics tests
    • One in four in the world to receive a perfect score on two AP tests
    • Siemens AP Science Award -- National Winner (took 17 AP tests & scored 5 in every one, with highest raw score on all science tests)
    • National Merit Scholar
    • Qualified for USAMO and USAPhO

Journal Refereeing

  • Research in Number Theory (9 articles)
  • Research in the Mathematical Sciences (1 article)
  • Proceedings of the American Mathematical Society (1 article)

Classical Music

Last updated: May 26, 2017