Graduate Students' Guide to Generals

A database of the general examinations taken by graduate
students in the Princeton University Mathematics Department.

Standard Questions
Updated Fall 2013!

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Indexed by student examiner special topics

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A
	Anshul Adve	Sarnak Ionescu Zemke	Harmonic Analysis Analaytic Number Theory	2022
	Spyros Alexakis	Fefferman Schlag Kollár	Harmonic Analysis Partial Differential Equations
	Levent Alpoge	Bhargava Sarnak Dafermos	Analytic Number Theory Representation Theory of Compact Lie Groups
	Ali Altug	Sarnak Mirzakhani Sorensen	Algebraic Number Theory Representation Theory of Compact Lie Groups
	Ryan Alweiss	Alon Dvir Sarnak	Combinatorics Computational Complexity	2019
	Jared Anderson	MacPherson Hsiang Stalker	Representation Theory Algebraic Topology
	John Anderson	Klainerman Yang Gunning	Partial Differential Equations Differential Geometry	2017
	Carolina Araujo	Kollár Kochen Nelson	Algebraic Geometry Model Theory
	Aravind Asok	Katz Aizenman Gan	Representation Theory Algebraic Geometry
B
	Pavel Bachurin	Sinai Mather Oh	Dynamical Systems Stochastic Processes
	Shaoyun Bai	Pardon Fefferman Di Cerbo	Partial Differential Equations Symplectic Topology	2018
	Adrian Banner	Fefferman Sarnak Ram	Singular Integrals Representation Theory of Lie Groups
	Timothy Barber	Trotter Conway, Kohn Nelson, Darmon	Representations of discrete groups Computational complexity theory
	Michael Barz	Bhatt Venkatesh Bringmann	Algebraic Geometry Representation Theory of Compact Lie Groups	2025
	Manjul Bhargava	Conway Wiles Fefferman	Representation Theory Algebraic Number Theory
	Bhargav Bhatt	Wiles Pandharipande Gunning	Algebraic Number Theory Commutative Algebra
	Ryan Bissell-Siders	Conway Trotter Burchard	Set Theory Number Theory
	Andy Booker	Sarnak Fefferman Stalker	Analytic Number Theory Singular Integrals
	Ian Budden	Hsiang Christodoulou Conway	Algebraic Topology Differential Geometry
	Alexander Bufetov	Sinai Mather Gan	Representation Theory Ergodic Theory
	Boris Bukh	Sudakov Sarnak Kohn	Probabilistic Combinatorics Analytic Number Theory
C
	Emma Carberry	Gunning Fefferman Conway	Compact Riemann Surfaces Several Complex Variables
	Will Cavendish	Gabai Yang Katz	Algebraic topology Riemannian Geometry
	Francesco Cellarosi	Sinai Mather Oblomkov	Probability Theory Ergodic Theory and Dynamical Systems
	Melody Chan	Seymour Lindenstrauss Grushevsky	Graph Theory and Combinatorial Optimization Additive Number Theory
	Su Han Chan	Shimura Faltings Nelson	Algebraic Number Theory Algebraic Geometry
	Ming-Yuan Chang	De Lellis Constantin Hanselman	Partial Differential Equations Singular Integrals	2025
	Eric Chen	Chang Constantin Patakfalvi	Riemannian Geometry Partial Differential Equations
	Szu-yu Chen	Yang Fefferman Gunning	Differential Geometry Partial Differential Equations
	Zhiyuan Chen	Xu, C. Pan Menezes	Algebraic Geometry Commutative Algebra	2022
	Cheewhye Chin	de Jong Pappas Trotter	Algebraic Geometry Algebraic Number Theory
	Matei Coiculescu	De Lellis Klainerman Hanselman	Navier-Stoke Equations Riemannian Geometry	2022
	Dan Collins	Skinner Kollár Chen	Algebraic Number Theory Algebraic Geometry
	Brian Conrad	Wiles Aizenman Faltings	Algebraic Geometry Algebraic Number Theory
	Baris Coskunuzer	Yang Gabai Ellenberg	Differential Geometry Algebraic Topology
D
	Michael C. Dafermos	Christodoulou Browder Ram	Differential Geometry Algebraic Topology
	Matthew de Courcy-Ireland	Sarnak Conway Templier	Functional Analysis Analytic Number Theory
	Colin Defant	Sarnak Skinner Alon	Algebraic Number Theory Ergodic Number Theory	2018
	Margaret Doig	Szabo Tian Grushevsky	Algebraic Topology Differential Geometry
	Dmitri Dolgopiat	Sinai Sarnak Trotter	Stochastic Processes Dynamical Systems
	Brent Doran	MacPherson Chang Kowalski	Algebraic Topology Differential Geometry
	Blair Dowling	Seymour Takloo-Bighash Gunning	Selected Topics in Discrete Mathematics Algebraic Number Theory
	Eduardo Dueñez	Sarnak Christodoulou Hewett	Analytic Number Theory Differential Geometry
E
	Eaman Eftekhary	Kollár Browder Gunning	Algebraic Geometry Algebraic Topology
	Laszlo Erdos	Lieb Mather Nelson	Functional Analysis Ergodic Theory Statistical Mechanics
	Alexandros Eskenazis	Naor Yang Patakfalvi	Functional Analysis Differential Geometry Statistical Mechanics
F
	Sasha Ovetsky Fradkin	Seymour Takloo-Bighash Pavlovic	Topics in Discrete Mathematics (Matroid Theory & Combinatorial Optimization) Algebraic Number Theory
	Dan Fess	Skinner Sarnak Pusateri	Algebraic Number Theory Representation Theory of Compact Lie Groups	2017
	Francis Fung	Browder Conway McNeal	Representation Theory Algebraic Topology
G
	Jiahui Gao	Zhang, S. Tang Zhang, B.	Algebraic Geometry Representation Theory	2021
	Mar Gonzalez	Chang Nelson Trotter	Differential Geometry Functional Analysis
	Bojan Gornik	Oszvath Stein Yang	Algebraic Topology Differential Geometry
	Josh Greene	Sudakov Szabo Pavlovic	Algebraic Combinatorics Algebraic Topology
	Michael Greenblatt	Sinai Okikioulu Washnitzer	Harmonic Analysis Ergodic Theory
	Philip Gressman	Stein Chang Ellenberg	Harmonic Analysis Partial Differential Equations
	Daniel Grossman	Gunning Hewett Mather	Compact Riemann Surfaces Differential Geometry
H
	Chris Hall	Katz Gunning Yu	Algebraic Geometry Algebraic Number Theory
	Trajan Hammonds	Sarnak Skinner Logunov	Analytic Number Theory Representations of Compact Lie Groups	2021
	Gergely Harcos	Sarnak Trotter Luo	Analytic Number Theory Algebraic Number Theory
	Robert Harron	Takloo-Bighash Ellenberg Nelson	Algebraic Number Theory Algebraic Geometry
	Harald Helfgott	Sarnak Szabo Ram	Representation Theory of Lie Groups Analytic Number Theory
	Wei Ho	Bhargava Takloo-Bighash Nelson	Algebraic Number Theory Representation Theory
	Amit Hogadi	Kollár Pandharipande Rodnianski	Algebraic Geometry Algebraic Topology
	Ko Honda	Shimura Katz Nelson	Algebraic Geometry Algebraic Number Theory
	Evan Huang	Oszvath Szabo Haziot	Algebraic Topology Differential Topology	2025
	Peter Humphries	Sarnak Fefferman Templier	Analytic Number Theory Representation Theory of Compact Lie Groups
	Tim Hsu	Browder Mather Prato	Differential Geometry Algebraic Topology
I
	Bogdan Ion	Szabo Browder Ram	Representation Theory of Lie Groups Hopf Algebras
	Phil Isett	Klainerman Sarnak Sorensen	Partial Differential Equations Analytic Number Theory
	Arie Israel	Fefferman Yang Oblomkov	Elliptic PDE Differential Geometry
	Hari Iyer	Venkatesh Zhang Ionescu	Algebraic Geometry Representation Theory of Compact Lie Groups	2025
J
	Lena Ji	Kollár Skinner Gunning	Algebraic Geometry Algebraic Number Theory	2017
	Hadi Jorati	Stein Sinai Katz	Harmonic Analysis Probability Theory and Random Processes
	Andrei Jorza	Wiles Kollár Stein	Algebraic Number Theory Algebraic Geometry
	Andras Juhasz	Szabo Browder Gunning	Algebraic Topology Differential Topology
K
	Kenz Kallal	Venkatesh Skinner Zhang	Algebraic Number Theory Representation Theory of Compact Lie Groups	2023
	Vadim Kaloshin	Sinai Mather de Jong	Dynamical Systems Stochastic Processes
	Kiran Kedlaya	de Jong Katz Nelson	Algebraic Number Theory Algebraic Geometry
	Matthew Kerr	Browder Fefferman Hsiang	Differential Geometry Algebraic Topology
	Dano Kim	Pandharipande Gunning Ozsvath	Algebraic Geometry Algebraic Topology
	Allen Knutson	Trotter McLaughlin Jeffrey	Lie algebras Algebraic Topology
	Denis Kosygin	Sinai Mather Hewett	Dynamical Systems Stochastic Processes
	Cosmas Kravaris	Naor Alon Witaszek	Metric Embeddings Extremal Combinatorics	2023
	Noah Kravitz	Alon Sarnak Tang	Analytic Number Theory Combinatorics	2021
	Joachim Krieger	Fefferman Kohn Oh	Elliptic PDE Representation Theory
L
	Shilin Lai	Skinner Zhang, S. Gunning	Algebraic Number Theory Representation Theory of Compact Lie Groups	2018
	Holden Lee	Dvir Bhargava Dafermos	Computational Complexity Algebraic Number Theory
	Sam Lewallen	Szabo Gunning Conway	Algebraic Topology Compact Riemann Surfaces
	Chi Li	Tian Kollár Kohn	Differential Geometry Algebraic Geometry
	Yuchen Liu	Kollár Tian Pausader	Algebraic Geometry Complex Geometry
	Ben Lowe	Marques Constantin Hanselman	Differential Geometry Partial Differential Equations	2018
	Jonathan Luk	Rodnianski Alexakis Grushevsky	Partial Differential Equations Differential Geometry
	Shiji Lyu	Kollár Morel Shlapentokh-Rothman	Algebraic Geometry Model Theory	2020
M
	Zhao Yu Ma	Sawin Bhargava Shankar	Algebraic Geometry Analytic Number Theory	2025
	Heather Macbeth	Chang Tian Golsefidy	Differential Geometry Elliptic PDE
	Kamal Khuri-Makdisi	Shimura Faltings Nelson	Algebraic Geometry Algebraic Number Theory
	Andy Manion	Szabo Yang Katz	Algebraic Topology Differential Geometry
	Simon Marshall	Sarnak Bhargava Fefferman	Lie Groups and Symmetric Spaces Number Theory
	Thomas Massoni	Pardon Ozsvath Marcus	Symplectic Topology Algebraic Topology	2020
	Andrew Mayer	Hsiang Bien Prato	Differential Geometry Representation Theory
	Michael McBreen	Okounkov Fenley Beliaev	Representation theory Algebraic geometry
	Djordje Milicevic	Wiles Sarnak Fefferman	Analytic Number Theory Algebraic Number Theory
	Alison Miller	Bhargava Okounkov Mather	Algebraic Number Theory Representation Theory
	Maggie Miller	Gabai Yang Bhargava	Algebraic Topology Differential Topology
	Stephen Miller	Browder Aizenman Solovej	Algebraic Topology Functional Analysis
	Steven (J) Miller	Fefferman Sarnak Katz	Singular Integrals/Harmonic Analysis Analytic Number Theory
	Peter Milley	Gabai Szabo Chang	Algebraic Topology Differential Geometry
	Ritabrata Munshi	Wiles Gunning Pandharipande	Algebraic Number Theory Algebraic Geometry
N
	David Nadler	Kochen Christodoulou MacPherson	Algebraic Topology Differential Geometry
	Eric Naslund	Sarnak Fefferman Sarkar	Analytic Number Theory Ergodic Theory
	Ting Fai Ng	Gan Chang Nelson	Representation Theory Differential Geometry
	Yi Ni	Gabai Okounkov Stein	Algebraic Topology Functional Analysis
	Martin Niepel	Szabo Gan Stalker	Representation Theory Algebraic Topology

O
	Evan O'Dorney	Bhargava Zhang, S. Naor	Representation Theory of Compact Lie Groups Algebraic Number Theory	2017
P
	Jonathan Pakianathan	Hsiang Mather Machedon	Functional Analysis Algebraic Topology
	Alessandra Pantano	Sarnak Fefferman Ozsvath	Algebraic Topology Representation Theory
	Seth Patinkin	Nelson Fefferman Stalker	Game Theory Singular Integrals
	Ryan Peckner	Sarnak Skinner Nelson	Algebraic Number Theory Functional Analysis
	Alex Peng	Sarnak Sinai Ellenberg	Theory of Probability Analytic Number Theory
	Paul Pollack	Sarnak Fefferman Ellenberg	Analytic Number Theory Algebraic Number Theory
	Rohil Prasad	Pardon Ozsvath Shlapentokh-Rothman	Differential Topology Symplectic Topology	2019
	Kartik Prasanna	Katz Yu Forni	Algebraic Number Theory Algebraic Geometry
Q
R
	Bela Racz	Szabo Browder Gunning	Algebraic Topology Differential Topology
	Ali Rajaei	Wiles Washnitzer Almgren	Algebraic Number Theory Algebraic Geometry
	Arash Rastegar	Sarnak Washnitzer Okikiolu	Number Theory Algebraic Geometry
	Kevin Ren	Naor Fefferman Zemke	Harmonic Analysis Metric Geometry	2023
	Jose Luis Rodrigo	Fefferman Hagelstein Browder	Harmonic Analysis Partial Differential Equations
	Slava Rychkov	Stein Kohn Trotter	Harmonic Analysis Several Complex Variables
S
	Ricardo Saenz	Stein Fefferman Browder	Harmonic Analysis Partial Differential Equations
	Colin Sandon	Dvir Gunning Kollár	Computational Complexity Compact Riemann Surfaces
	Sucharit Sarkar	Szabo Conway Hang	Algebraic Topology & Differential Topology
	Jeff Schenker	Fefferman Stalker Trotter	Functional Analysis Singular Integrals and Harmonic Analysis on R^n
	Rolfe Schmidt	Stein McNeal Shimura	Harmonic Analysis Several Complex Variables
	William Schneeberger	Nelson Conway Trotter	Logic and Set Theory Quadratic Forms
	Peter Sepanski	Hsiang Aizenman McNeal	Algebraic Topology Functional Analysis
	Iman Setayesh	Pandharipande Szabo Stein	Algebraic Geometry Algebraic Topology
	Arul Shankar	Sarnak Lindenstrauss Golsefidy	Algebraic number theory Representation theory
	Yakov Shlapentokh-Rothman	Rodnianski Yang Sorensen	Partial Differential Equations Riemannian Geometry
	Erico Silva	Marques Dafermos Di Cerbo	Partial Differential Equations Differential Geometry	2020
	Jaydeep Singh	Rodnianski Hanselman Yang	Riemannian Geometry Partial Differential Equations	2020
	Laura Shou	Aizenman Sly Hanselman	Probability Statistical Physics	2018
	Mikhail Smirnov	Kohn Sarnak Bridson	Differential Geometry Several Complex Variables
	Antoine Song	Marques Constantin Katz	Riemannian Geometry Partial Differential Equations
	Alfonso Sorrentino	Mather Chang Kollár	Elliptic PDE Hamiltonian Dynamical Systems
	Phil Sosoe	Aizenman Fefferman Golsefidy	Harmonic Analysis Probability
	Shruthi Sridhar	Gabai Szabo Gomez-Serrano	Algebraic Topology Differential Topology	2019
	Noah Stevenson	Ionescu Constantin Pan	Harmonic Analysis Fluid Dynamics	2022
	John Stogin	Klainerman Warren Gunning	Hyperbolic PDE Riemannian Geometry
	Brian Street	Nelson Aizenman Ellenberg	Stochastic Processes Functional Analysis
	Douglas Stryker	Coda Marques Constantin Di Cerbo	Riemannian Geometry Partial Differential Equations	2021
	Jun Su	Taylor Ionescu Patakfalvi	Algebraic Number Theory Algebraic Geometry
	Hongbin Sun	Gabai Yang Kollár	Differential Geometry Algebraic Topology
	Mohan Swaminathan	Pardon Di Cerbo Shcherbyna	Symplectic Topology Complex Algebraic Geometry	2018
T
	Longke Tang	Bhatt Xu, C. Zhang, R.	Algebraic Number Theory Commutative Algebra
	Terence Tao	Stein Klainerman Rudnick	Harmonic Analysis Analytic Number Theory
	Mohammad Farajzadeh Tehrani	Tian Pandharipande Wienhard	Riemannian Geometry Complex Geometry
	Henry (now Maya) Thackeray	Skinner Sarnak Naor	Algebraic Number Theory Representation Theory
	Ralph Thomas	Browder Stein Hewett	Singular Integrals Algebraic Topology
	Fernando Trejos Suarez	Skinner Zhang Zhang	Algebraic Number Theory Algebraic Geometry	2023
	Jacob Tsimerman	Sarnak Lieblich Okounkov	Algebraic Number Theory Algebraic Geometry
U
V
	Jeffrey Vanderkam	Nelson Flach Sarnak	Analytic Number Theory Functional Analysis
	Peter Varju	Lindenstrauss Klainerman Gunning	Ergodic Theory Harmonic Analysis
	Konstantinos Varvarezos	Szabo Yang Vicol	Algebraic Topology Differential Geometry	2018
	Vinayak Vatsal	Washnitzer Wiles Rudnick	Algebraic Number Theory Algebraic Geometry
	Anibal Velozo	Tian Ozsvath Gunning	Complex Differential Geometry Symplectic Topology
	Sameera Vemulapalli	Bhargava Skinner Gunning	Algebraic Number Theory Algebraic Geometry	2019
	Akshay Venkatesh	Sarnak Fefferman Katz	Algebraic Geometry Representation Theory of Lie Groups
	Marco Antonio Sangiovanni Vicentelli	Skinner Sarnak Shlapentokh-Rothman	Algebraic Number Theory Algebraic Geometry	2020
	Jade Vinson	Daubechies Sinai Hewett	Harmonic Analysis of Wavelets Ergodic Theory
	Daniel Vitek	Ozsvath Tian Pusateri	Algebraic Topology Symplectic Geometry
W
	Victor Wang	Sarnak Zhang, S. Buckmaster	Representation Theory of Compact Lie Groups Algebraic Geometry	2018
	Xin Wan	Skinner Katz Klartag	Algebraic Number Theory Algebraic Geometry
	Yi Wang	Chang Neves Gunning	Partial Differential Equations Differential Geometry
	Zhiren Wang	Lindenstrauss Bhargava Szeftel	Ergodic Theory Representation Theory
	Boya Wen	Zhang, S. Skinner Gomez-Serrano	Algebraic Geometry Algebraic Number Theory	2017
	Katy Woo	Sarnak Zhang, S. Buckmaster	Analytic Number Theory Representations of Compact Lie Groups	2021
	Willie Wong	Klainerman Kollár Gunning	Harmonic Analysis and PDEs
	Conan Wu	Gabai Guth Mather	Metric Geometry Dynamical Systems
	Zhongtao Wu	Szabo Grushevsky Hang	Algebraic Topology Algebraic Geometry
X
	Chris Yang Xiu	Szabo Ozsvath Holzegel	Algebraic Topology Differential Topology
	Chenyang Xu	Kollár Pandharipande Tian	Algebraic Geometry Commutative Algebra
	Guangbo Xu	Tian Neves Golsefidy	Complex Geometry Atiyah-Singer Index Theorem
Y
	Mehdi Yazdi	Szabo Sarkar Gunning	Algebraic Topology Differential Topology
	Nung Kwan Yip	Klainerman Christodoulo Washnitzer	Differential Geometry Functional Analysis
	Hung-Hsun Yu	Alon Dvir Sarnak	Probabilistic Method Discrete Geometry	2023
	Pin Yu	Klainerman	Partial Differential Equations
		Chang	Differential Geometry
	Zhiwei Yun	MacPherson Pandharipande Gunning	Algebraic Geometry Algebraic Topology
	Po-Lam Yung	Stein Yang Takloo-Bighash	Harmonic Analysis Differential Geometry
Z
	Sam Zbarsky	Rodnianski Katz Yang	Riemannian Geometry Partial Differential Equations	2018
	Ruixiang Zhang	Sarnak Fefferman Lie	Harmonic Analysis Analytic Number Theory
	Ruobing Zhang	Yang Constantin Sorensen	Elliptic PDEs of second order Riemannian Geometry
	Runpu Zong	Kollár E Aizenman	Mathematical Physics Algebraic Geometry
	Nina Zubrilina	Sarnak Katz Nestoridi	Analytic Number Theory Algebraic Geometry	2020

Graduate Students' Guide to Generals

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

U

V

W

X

Y

Z

Last updated June 2025