Education  Publications  Presentations  Research  Teaching  Honors  Music
Background
I am currently a thirdyear PhD student in mathematics at Princeton University, working with Manjul Bhargava. My general research interests lie in number theory and algebraic geometry; more specifically, I am interested in arithmetic statistics, invariant theory, rational points on varieties, and enumerative geometry. I am also quite fond of learning languages and can read/speak French and 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, 2022 (expected)
Advisor: Manjul Bhargava

PhD in Mathematics, 2022 (expected)
 Harvard University, Cambridge, MA
 The Harker School, San Jose, CA

Average 2torsion in class groups of rings associated to binary nic forms, in preparation, 2020.

On the paucity of soluble superelliptic equations, submitted for publication, 2019.

Appendix to: An arithmetic count of the lines meeting four lines in P^{3} (with Borys Kadets, Padmavathi Srinivasan, Libby Taylor, and Dennis Tseng), submitted for publication, 2019.

On the A^{1}Degree of a Weyl Cover (with Joseph Knight and Dennis Tseng), submitted for publication, 2019.

Inflectionary invariants for isolated complete intersection curve singularities (with Anand Patel), to appear in Memoirs of the American Mathematical Society, 2020.

Hyperelliptic curves with maximal Galois action on the torsion points of their Jacobians (with Aaron Landesman, James Tao, and Yujie Xu), to appear in Indiana University Mathematics Journal, 2018.

Surjectivity of Galois representations in rational families of abelian varieties (with Aaron Landesman, James Tao, and Yujie Xu), Algebra and Number Theory, 13(5) (2019), 9951038. (arXiv)

Elliptic curve variants of the least quadratic nonresidue problem and Linnik's Theorem (with Evan Chen and Peter Park), International Journal of Number Theory, 14(1) (2018), 255288. (arXiv)

Lifting subgroups of symplectic groups over Z/lZ (with Aaron Landesman, James Tao, and Yujie Xu), Research in Number Theory, 3(14) (2017), 112. (arXiv)

Permutations that destroy arithmetic progressions in elementary pgroups (with Noam D. Elkies), Electronic Journal of Combinatorics, 24(1) (2017), 110. (arXiv)

On logarithmically Benford sequences (with Evan Chen and Peter Park), Proceedings of the American Mathematical Society, 144(11) (2016), 45994608. (arXiv)

On arboreal Galois representations of rational functions, Journal of Algebra, 448 (2016), 104126. (arXiv)

Linnik’s theorem for SatoTate laws on elliptic curves with complex multiplication (with Evan Chen and Peter Park), Research in Number Theory, 1(1) (2015), 111. (arXiv)

Analysis on surreal numbers (with Simon RubinsteinSalzedo), Journal of Logic and Analysis, 6(5) (2014), 139. (arXiv)
Expository Articles

Inflection points of linear systems on families of curves (Harvard senior thesis), 2017.

An introduction to the theory of valued fields (Harvard junior paper), 2015.

On the SelbergErdős proof of the Prime Number Theorem, 2014.

Arrow's impossibility theorem on social choice systems, 2013.

Invited Talks

"On the paucity of soluble superelliptic equations," Number Theory/Representation Theory Seminar, University of Toronto, 2020.

"Most hyperelliptic curves are pointless," Bhargava Seminar, Princeton University, 2019.

"Inflectionary invariants for plane curve singularities," Special Session on Research in Mathematics by Undergraduates, MAAAMS JMM, 2018.

"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, MAAAMS JMM, 2016.

"Surreal analysis: an analogue of real analysis for surreal numbers," Siemens Competition Regional Finals, California Institute of Technology, 2012.


Contributed Talks

"On the paucity of soluble superelliptic equations," Bhargava Seminar, Princeton University, 2019.

"Inflectionary invariants for local complete intersection curve singularities," Graduate Student Seminar, Princeton University, 2018.

"Inflectionary invariants for plane curve singularities," LinkedIn Bangalore, 2018.

"Surjectivity of Galois representations in rational families of abelian varieties," MAAAMS JMM, 2017.

"Permutations that destroy arithmetic progressions in elementary pgroups," MAAAMS JMM, 2017.

"Elliptic curve variants of the least quadratic nonresidue problem and Linnik's Theorem," MAAAMS JMM, 2016.

"Permutations that destroy arithmetic progressions," Harvard Math Table, 2016.

"On arboreal Galois representations of rational functions," MAAAMS 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

PhD Thesis, Department of Mathematics, Princeton University

2017present: Working in arithmetic invariant theory (advisor: Manjul Bhargava)


Senior thesis, Department of Mathematics, Harvard University

20162017: Worked in algebraic geometry (advisors: Joe Harris & Anand Patel)


Emory REU, Department of Mathematics, Emory University

Summer 2016: Worked in arithmetic geometry (advisors: David ZureickBrown & Ken Ono)

Summer 2015: Worked in analytic number theory (advisors: Jesse Thorner & Ken Ono)


Duluth REU, Department of Mathematics, University of Minnesota Duluth

Summer 2015: Worked in combinatorial number theory (advisors: Noam D. Elkies & Joseph Gallian)

Summer 2014: Worked in Galois representations (advisor: Joseph Gallian)


Independent study, Department of Mathematics, Stanford University
Teaching Experience

Course Assistant, Department of Mathematics, Harvard University

[Math 137] Introduction to algebraic geometry (Peter Kronheimer), 2017. Qscore: 5.0/5.0

[Math 131] Topology I: Topological spaces & the fundamental group (Joe Harris), 2016. Qscore: 4.5/5.0

[Math 123] Algebra II: Theory of rings & fields (Arul Shankar), 2016. Qscore: 4.9/5.0

[Math 114] Analysis II: Measure, integration, & Banach spaces (Daniel C.Gardiner), 2015. Qscore: 4.9/5.0

[Math 55b] Honors real & complex analysis (Dennis Gaitsgory), 2015. Qscore: 4.3/5.0

Honors and Awards

Frank and Brennie Morgan Prize

David B. Mumford Prize

Paul and Daisy Soros Fellowship for New Americans

NSF Graduate Research Fellowship

Hertz Fellowship  Finalist

Centennial Fellowship, Princeton University

Declined PhD Fellowship Offers:

Graduate Fellowship, Stanford University

Dean's Fellowship, Columbia University

President's Fellowship, Massachusetts Institute of Technology

Berkeley Fellowship, University of California, Berkeley


Harvard University Certificate of Distinction in Teaching (Math 131, 114, 123)

John Harvard Scholar for Academic Achievement (2016, 2015, 2014)

Robert Fletcher Rogers Prize, 2016

Phi Beta Kappa  Junior 24

Barry M. Goldwater Scholarship (Fellow  2016, Honorable Mention  2015)

Detur Book Prize for Academic Excellence, 2014

Siemens Competition in Math, Science, and Technology  Regional Finalist

Siemens AP Science Award  National Winner

National Merit Scholar

Valedictorian  The Harker School
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: March 30, 2020