Education  Publications  Presentations  Research  Teaching  Honors  Music
Background
I am a fifthyear 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, the CohenLenstra heuristics, rational points on varieties, Diophantine equations, and enumerative geometry. I am also quite fond of learning languages and can read French and Latin with intermediate proficiency. In my free time, I play the violin and enjoy listening to classical music.

Princeton University, Princeton, NJ
 M.A. in Mathematics, 2018 (incidental)

Ph.D. in Mathematics, 2022 (expected)
 Thesis: "\(2\)Selmer groups, \(2\)class groups, and the arithmetic of binary forms" in preparation.
 Advisor: Manjul Bhargava

Harvard University, Cambridge, MA
 A.M. in Physics, 2017

A.B. in Mathematics, 2017
 summa cum laude & with highest departmental honors
 Senior thesis: "Inflection points of linear systems on families of curves" (thesis) (talk)
 Advisors: Joe Harris & Anand Patel
 The Harker School, San Jose, CA
Preprints and Publications

The second moment of the size of the \(2\)Selmer group of elliptic curves (with Manjul Bhargava and Arul Shankar), submitted, 49 pages, 2021.

Geometryofnumbers methods in the cusp and applications to class groups (with Arul Shankar, Artane Siad, and Ila Varma), submitted, 38 pages, 2021.

Average \(2\)torsion in class groups of rings associated to binary \(n\)ic forms, submitted, 39 pages, 2020.

Most integral odddegree binary forms fail to properly represent a square, submitted, 42 pages, 2020.

On the EKLdegree of a Weyl cover (with Joseph Knight and Dennis Tseng), Journal of Algebra, 565(1) (2021), 6481. (arXiv)

Inflectionary invariants for isolated complete intersection curve singularities (with Anand Patel), to appear in Memoirs of the American Mathematical Society, 100 pages, 2020.

Appendix to: An arithmetic count of the lines meeting four lines in \(\mathbb{P}^3\) (with Borys Kadets, Padmavathi Srinivasan, Libby Taylor, and Dennis Tseng), Transactions of the American Mathematical Society, 374(5) (2021), 34473448. (arXiv)

Hyperelliptic curves with maximal Galois action on the torsion points of their Jacobians (with Aaron Landesman, James Tao, and Yujie Xu), Indiana University Mathematics Journal, 69(7) (2020), 24612492. (arXiv)

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 \(\mathbb{Z}/\ell\mathbb{Z}\) (with Aaron Landesman, James Tao, and Yujie Xu), Research in Number Theory, 3(14) (2017), 112. (arXiv)

Permutations that destroy arithmetic progressions in elementary \(p\)groups (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)
Research Articles in Preparation

\(2\)Selmer groups of evendegree hyperelliptic curves, and \(2\)class groups of evendegree number fields (with Manjul Bhargava and Arul Shankar), in preparation, 2021.

Failure of monogenicity in sextic number fields, in preparation, 2021.
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.

TBA, Number Theory Seminar, Princeton University/IAS, 2021.

"\(2\)Selmer groups, \(2\)class groups, and the arithmetic of binary forms," Palmetto Joint Arithmetic and Modularity Series (PAJAMAS) III, Invited Graduate Speaker, 2021

"The second moment of the size of the \(2\)Selmer group of elliptic curves," Workshop on Explicit Methods in Number Theory, Mathematisches Forschungsinstitut Oberwolfach, 2021.

"Average \(2\)torsion in the class groups of rings associated to binary \(n\)ic forms," Bhargava Seminar, Princeton University, 2020.

"Average \(2\)torsion in the class groups of rings associated to binary \(n\)ic forms," Number/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, 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, JMM, 2016.

"Surreal analysis: an analogue of real analysis for surreal numbers," Siemens Competition Regional Finals, California Institute of Technology, 2012.
Contributed Talks
 "Counting lattice points in cusps of fundamental domains," Number Theory Tea, Princeton University, 2020.
 "Three lectures on the average size of \(2\)Selmer groups of elliptic curves," Bhargava Seminar, Stanford University, 2020.
 "On the paucity of soluble superelliptic equations," Bhargava Seminar, Stanford University, 2020.

"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," JMM, 2017.

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

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

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

"On arboreal Galois representations of rational functions," 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.

PhD Thesis, Department of Mathematics, Princeton University

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


Arizona Winter School, University of Arizona

2020: Worked in classical Chabauty (advisor: David ZureickBrown)

2019: Worked in \(\mathbb{A}^1\)enumerative geometry (advisor: Kirsten Wickelgren)


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

20112014: Worked in logic & analysis (advisor: Simon Rubinstein–Salzedo)

20112013: Worked in analytic number theory (advisor: Daniel M. Kane)


Course Instructor, Department of Mathematics, Princeton University

[Math 202] Linear algebra with applications, 2020.


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 CristofaroGardiner), 2015. Qscore: 4.9/5.0

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

[Math 55a] Honors abstract algebra (Dennis Gaitsgory), 2014. Q:score 4.6/5.0


Princeton Engineering Council Teaching Award (Math 202), 2021

Frank and Brennie Morgan Prize, 2017

David B. Mumford Prize, 2017

Paul and Daisy Soros Fellowship for New Americans, 20172019

NSF Graduate Research Fellowship, 20172022

Hertz Fellowship  Finalist, 2017

Centennial Fellowship, Princeton University, 20172021

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 114, 123, 131)

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

Robert Fletcher Rogers Prize, 2016

Phi Beta Kappa  Junior 24, 2016

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

Detur Book Prize for Academic Excellence, 2014

Only student in the world with perfect score on both AP Micro and Macroeconomics tests, 2013

Siemens Competition in Math, Science, and Technology  Regional Finalist, 2013

Siemens AP Science Award  National Winner, 2013
Journal Refereeing

Research in Number Theory

Research in the Mathematical Sciences

Proceedings of the American Mathematical Society

Mathematical Proceedings of the Cambridge Philosophical Society

Involve, a Journal of Mathematics

Music Review on Matthew Aucoin's "Its Own Accord," 2016

Letter from Susanna: Handel's Messiah as a universal vehicle of deliverance, 2016

Violinist, Harvard–Radcliffe Orchestra (Conductor: Federico Cortese), 2013  2014

Program Annotator for Dvorak's Violin Concerto, Beethoven's Symphony No. 3 (Eroica), and Verdi's Requiem


John Near Grant Recipient, The Harker School, 2013

Authored research paper on Copland's El Salon Mexico & Bernstein's West Side Story


Violinist, San Francisco Symphony Youth Orchestra (Conductor: Donato Cabrera), 2010  2013

Violinist, Music@Menlo Summer Chamber Music Festival and Institute (Directors: Wu Han & David Finckel), 2006, 2008, 2009
Last updated: October 18, 2021