**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"

Mentors: Joe Harris & Anand Patel - The Harker School, San Jose, CA

**Research Publications**

- Inflectionary invariants for plane curve singularities (with Anand Patel), 2017.
- Hyperelliptic curves with maximal Galois action on the torsion points of their jacobians (with Aaron Landesman, James Tao, and Yujie Xu), 2017.
- Surjectivity of Galois representations in rational families of abelian varieties (with Aaron Landesman, James Tao, and Yujie Xu), submitted, 2016.
- Lifting subgroups of symplectic groups over Z/
*l*Z (with Aaron Landesman, James Tao, and Yujie Xu),*Research in Number Theory*, to appear, 2017. - 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. - Permutations that destroy arithmetic progressions in elementary
*p*-groups (with Noam D. Elkies),*Electronic Journal of Combinatorics*,**24**(1) (2017), 1-10. (arXiv) - On logarithmically Benford sequences (with Evan Chen and Peter Park),
*Proceedings of the American Mathematical Society*,**144**(11) (2016), 4599-4608. (arXiv) - On arboreal Galois representations of rational functions,
*Journal of Algebra*,**448**(2016), 104-126. (arXiv) - 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) - Analysis on surreal numbers (with Simon Rubinstein-Salzedo),
*Journal of Logic and Analysis*,**6**(5) (2014), 1-39. (arXiv)

**Expository Articles**

- Inflection points of linear systems on families of curves (Harvard senior thesis), 2017.
- Lie algebras and Ado's Theorem, 2016.
- An introduction to the theory of valued fields (Harvard junior paper), 2015.
- On the Selberg-Erdős proof of the Prime Number Theorem, 2014.
- 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)

- Summer 2016: Worked in
- Duluth REU, Department of Mathematics, University of Minnesota Duluth
- Summer 2015: Worked in
*combinatorial number theory*(mentors: - Summer 2014: Worked in
*Galois representations*(mentor: Joseph Gallian)

- Summer 2015: Worked in
- Independent study, Department of Mathematics, Stanford University
- 2011–2014: Worked in
*logic & analysis*with Simon Rubinstein–Salzedo

- 2011–2014: Worked in

**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 137] Introduction to algebraic geometry (Peter Kronheimer), 2017.

**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
- 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**

**Classical Music**

- Music Review on Matthew Aucoin's "Its Own Accord," 2016
- Letter from Susanna: Handel's
*Messiah*as a universal vehicle of deliverance, 2016 - 2013–2014: Violinist, Harvard–Radcliffe Orchestra (Conductor: Federico Cortese)
- Program Annotator for Dvorak's Violin Concerto, Beethoven's Symphony No. 3 (
*Eroica*), and Verdi's*Requiem* - 2013: John Near Grant Recipient, The Harker School
- Authored research paper on Copland's
*El Salon Mexico*& Bernstein's*West Side Story* - 2010–2013: Violinist, San Francisco Symphony Youth Orchestra (Conductor: Donato Cabrera)
- 2006, 2008, 2009: Violinist, Music@Menlo Summer Chamber Music Festival and Institute (Directors: Wu Han & David Finckel)

Last updated: May 26, 2017