Once you pass your prelim exams, it’s time to start finding an advisor. The process of finding an advisor can be difficult, since there are many factors that need to be considered. Below are some tips that may help you through this process, based on a Career Transitions talk given by Sara Billey.

- Make a list of possible advisors (right now!). A list of some of the professors in the department and their fields of research is included below to help you with this first step. While doing so, ask yourself the following questions.
- What fields are you interested in?
- Who specializes in these areas?
- What other fields of math are related?
- Which professors work in these areas?

- Do some research on your prospective advisors.
- Take a class with one of the professors you wrote down in step 1. Go to their office hours.
- Ask them to do a reading course. If you don’t know what to read, ask them if they have any good books in mind.
- Go to their website and look at their papers. Look them up on Mathscinet, arXiv, and/or Google Scholar.
- Set up a meeting with the professor and ask them about their research. Ask them if there are any interesting extensions of their work.
- Go to their Current Topics talk if they are giving one.
- Talk to their grad students. Ask them questions like:
- How much time do they give to their students?
- Do they look closely at their students’ work?
- Do they have good problems?
- Where are their former students now? Do they have jobs? Are they in academia or industry? If academia, do they have tenure?
- Does the advisor have tenure?
- Do they provide research assistantships to their students?
- Do they give good career advice?

- Don’t be too picky about the topic. Having a good working relationship with them matters more.
- Make sure the professor’s style of advising works well for you. If you need regular deadlines and lots of facetime to stay focused, find an advisor who is more hands-on. If you like to be more independent, find an advisor who will give you more freedom to explore on your own

- Start working on a project.
- To reiterate: ask them if there are any interesting extensions of their work. Or, ask them if there are any papers they have been meaning to read that might be accessible to you.
- Read a paper. Write code. Ask questions.

General advice suitable for all graduate students:

- Go to seminars and colloquium talks, even if they are not exactly in your area (that is, if you know your area already).
- Go to Current Topics talks. It's a great way to see what kind of research is going on in the department.

For more advice on other aspects of earning a PhD, see Sara Billey’s advice page.

*The following data was collected in the Winter of 2020. This list only includes professors who responded to our survey and it is organized by last name in alphabetical order.

Professor |
Research Area |
Suggested classes to take |

Jarod Alper |
Algebraic Geometry |
Modern Algebra, Algebraic Structures, Algebraic Geometry, Topology and Geometry of Manifolds, any topics course in Algebra. |

Jayadev Athreya |
Geometry and Dynamical Systems |
Complex Analysis, Real Analysis, Manifolds. |

Sara Billey |
Algebraic Combinatorics |
Combinatorics, Modern Algebra, Algebraic Structures, Manifolds, Probability, Algebraic Geometry, Algebraic Topology, Complex Analysis, Optimization, some Computer Science theory. |

Krzysztof Burdzy |
Probability Theory |
Probability, Real Analysis. |

Dmitriy Drusvyatskiy |
Optimization |
Optimization sequence, basic graduate courses in Probability and Differentiable Manifolds. |

Chris Hoffman |
Probability Theory |
The Advanced Probability sequence. The Combinatorics sequence is also helpful. |

Sándor Kovács |
Algebraic Geometry: moduli theory, singularities, birational geometry |
Modern Algebra, Algebraic Structures, Algebraic Geometry. |

Max Lieblich |
Algebraic Geometry |
The Algebra and Algebraic Geometry sequences |

Monty McGovern |
Representations of Lie Groups, in particular their geometric and combinatorial aspects. |
The Lie Algebras term of the Algebraic Structures sequence. Students should have a good background in Algebra and Combinatorics. |

Isabella Novik |
Geometric and Algebraic Combinatorics |
The core Algebra sequence, the Commutative Algebra part of the Algebraic Structures sequence, the first quarter of Manifolds, a quarter or two of Algebraic Topology, Combinatorics. |

Soumik Pal |
Probability Theory, mostly related to Stochastic Processes, with applications in Optimal Transport and Mathematical Finance. |
Graduate Analysis and Advanced Probability sequences. |

John Palmieri |
Algebraic Topology and Homotopy Theory |
Algebraic structures, in particular the quarter on homological algebra; and Algebraic Topology. |

Julia Pevtsova |
Representation Theory, Homological Algebra, categorical aspects |
Modern Algebra, Algebraic Structures, Algebraic Geometry. |

Farbod Shokrieh |
Non-archimedean Analytic and Tropical Geometry, Number Theory, Algebraic Geometry, Combinatorics. |
Algebra, Algebraic Geometry, and Combinatorics sequences. Topics classes in Arithmetic/Algebraic Geometry. |

Tatiana Toro |
PDE, Geometric Measure Theory, and Harmonic Analysis |
Reals and Complex Analysis, PDE, topics classes in Analysis. Basic knowledge of Geometry, e.g., Manifolds and Geometric Structures is also very useful. |

Gunther Uhlmann |
Inverse Problems |
Real Analysis. Depending on the interest of the student I recommend courses in PDE, Differential Geometry, Optimization, Statistics etc. |

Bianca Viray |
Arithmetic Geometry and Number Theory |
Algebra sequence, Algebraic Geometry sequence, Introduction to Algebraic Number Theory. Topics classes in Number Theory, Arithmetic Geometry, and Algebraic Geometry. |

Yu Yuan |
PDE and Differential Geometry |
Complex/Real Analysis, Manifolds, Algebra; or good handling of multivariable calculus and mathematical maturity. |