Survey of Grad Schools in the Northwest US

date: 2017-10-18
revised: 2018-01-15
status: finished

My notes on grad schools (all but one in the Northwest US) and their faculty’s research. I aim to get a feel for each school’s academic environment, then narrow down a list of people I would like to work with. I’ve focused on folks involved in computational topology, algebraic topology, and numerical analysis.

CU Boulder

Finished speaking with Nikki Sanderson. Here’s the bullet list.

People

University of Utah

Here’s their research group overview.

My prospective applied research goals could include reducing contaminant dispersion, designing sustainable industrial processes, or promoting biomimicry in architecture.

The Multiscale Analysis and Computations (MAC) research group contains smaller projects (I assume which depend on funding, faculty and student interest).

Depending on the culture, I could code PDE solvers (scientific computing).

It seems the math dept works interdisciplinary with computer science and biology.

On the other hand, my abstract research goals could include a better understanding of algebraic geometry (e.g., Dynamics, geometry, and the moduli space of Riemann surfaces). See both the Algebraic Geometry seminar (organized by Katrina Honigs) and the math department colloquium.

From Alex Wright’s colloquium talk

The moduli space of Riemann surfaces of fixed genus is one of the hubs of modern mathematics and physics. We will tell the story of how simple sounding problems about polygons, some of which arose as toy models in physics, became intertwined with problems about the geometry of moduli space, and how the study of these problems in Teichmuller dynamics lead to connections with homogeneous spaces, algebraic geometry, dynamics, and other areas. The talk will mention joint works with Alex Eskin, Simion Filip, Curtis McMullen, Maryam Mirzakhani, and Ronen Mukamel.

See quora what are the differences between … ? for distinctions between algebraic topology and algebraic geometry. (Note: I loathe quora’s material design. The personal bios on that site freak me out.)

At the most basic level, algebraic geometry is the study of algebraic varieties—sets of solutions to polynomial equations. Modern algebraic geometry, however, is much wider than this innocent statement seems to imply. It is notoriously complex and requires a very deep understanding of a wide variety of disciplines and domains.

However you choose to learn algebraic geometry, you would want to have some very, very good grounding in commutative algebra, Galois theory, some number theory (especially algebraic number theory), complex function theory, category theory, and a serving of algebraic topology wouldn’t hurt. General topology is sort-of required; algebraic geometry uses the notion of “Zariski topology” but, honestly, this topology is so different from the things most analysts and topologists talk about that it’s hard for me to see how a basic course in topology would be of any help.

Don’t let this deter you. Algebraic Geometry is awe-inspiringly beautiful, and there do exist more gentle approaches to it than Hartshorne or Shafarevich. Fulton’s Algebraic Curves (Page on Umich) is a great starting point.

Drew Johnson studied at Utah under Aaron Betram. Drew recommends Ravi Vakil’s The Rising Sea: Foundations of Algebraic Geometry for introductory notes. Also see the student algebraic geometry seminar.

The Park City Mathematics Institute is nearby, with relevance to both applied & pure math.

People

Here’re the applied faculty

Here’re the algebraic geometry faculty

And the interdisciplinary folks.

Washington State University

WSU has two campuses, in Pullman and in Vancouver.

NSF grant DBI-1661348 funds an interdepartmental project to study (tda)phenomics. The “deluge” of data associated with corn crops motivates “find[ing] possible hypotheses out of a large amount of data, and conduct[ing] tests in a more targeted fashion.”

Not that I love corn.

Seems like Vancouver has the computational topology classes. I might need to travel to Pullman to start/finish the degree.

Krishnamoorthy also works with “landmarks” to speed up computation. For example, from the abstract of Topological Features in Cancer Gene Expression Data,

Our method selects a small relevant subset from tens of thousands of genes while simultaneously identifying nontrivial higher order topological features, i.e., holes, in the data. We first circumvent the problem of high dimensionality by dualizing the data, i.e., by studying genes as points in the sample space. Then we select a small subset of the genes as landmarks to construct topological structures that capture persistent, i.e., topologically significant, features of the data set in its first homology group.

People

University of Rochester

I logged into a question-answer webinar with Jonathan Pakianathan, Professor of Mathematics at the University of Rochester. Here’s the summary.

UR is medium sized private school, 6k undergrad and 4k grad student population. Strengths in optics, music, some film industry. 9 Nobel prizes from alumni/faculty, with Thaler winning the Nobel prize this year for behavioral economics.

The mathematics department has 21 tenure track faculty, with 3 undergrad education permanent staff. It’s a mathematically oriented campus, with 9/10 freshman taking math courses and 1/10 undergrads with a math major. Hence, they offer a full selection of topics in undergrad, which benefits the graduate program in terms of teaching.

Research

Start with the research overview. I’ll focus on Analysis, Probability, and Topology.

Analysis

Probability

Topology (strong in homotopy theory)

Time Line

Most people get a PhD in 5–6 years (4–7 range). There’s support for 5 years at a 18k stipend with full tuition.

There are 8 required courses (completed by end of Year 2).

I should also attend seminars, develop a research interest, and choose an advisor by the end of Year 2.

After the required courses, faculty randomly offer 5 topic courses each semester.

In Year 3, I should give a qualifying talk about my research interest, then, in Years 4 and 5, complete substantial research towards a dissertation. I’d defend my PhD before a general audience at the end of Year 5.

Webinar Questions

Q: Can you explain more about the collaboration between math and CS?

A: Brownian sheets. Computer networks with various connections, build a network. Propagation of problems in computer network.

Q: What applications are the topology group currently working on? Any topological data analysis?

A: Persistent homology was popular. Faculty no longer interested. Many grad students to do joint work with CompSci for TDA. Lizz Maduer, postdoc. A little in flux. No permanent tenure faculty. All interested. Do a little work. Some courses. It would be joint work. New Data Analysis center ==> Data Analysis. Data science.

Q: You mentioned many people in the department doing mathematical physics. To what degree does the mathematics department seek out people with strong physics backgrounds?

A: Many folks move from Physics to Mathematics. Common transition. Surprisingly large number of analysts have backgrounds in physics. Lee Theory & Lee Algebras. Schrodinger Eqns. String theory. Joint work. Strong Icing model & statistical mechanics. Mathematical Physics seminar. No formal connection.

Q: Enrollment requirements?

A:

Q: Expected background?

A:

Q: Some physical intuition?

A: Topology developed separately, but now comes back. Geometry does come from physics, but feeds back?

Q: How many folks apply? How many accepted?

A: Relatively small, 6–8 students accepted. Sometimes, we accept a larger pool.

Q: How about publications on average per PhD student to make a competitive thesis defense?

A: in areas like alg top or alg geometry, you don’t even need one! It’s excepted that the stuff gets written up in a postdoc. (WHAT? This seems like a horrible idea. No iteration?) … The abstract side of the research takes a f-ing long time to learn. OTOH, with combinatorics, it’s good to have at least 2 or 3 publications. Advisors will help. Alg Top has a very high build up (~0 publications). We want at least one paper submitted regarding thesis material for summer prior to graduation. Then the job search is easier (well, duh!).

Q: How often are outside speakers brought in to give talks for the department as a whole on current research topics?

A: Speakers every 2 weeks. 6 seminars, 1 for each research group. 1 monthly colloquium, for larger topics. The Wing lectures in applied mathematics have 4 major speakers each year. Math in industry. Mathematics in Pixar’s animation industry = 2000 folks in auditorium. General applied math in lectures.

Q: How do you consider industry work experience in a technical industry (software development, biotechnology etc.) vs. mathematical research experience in an REU or similar?

A: Experience is pretty good. Industry experience shows initiative. What math REUs are useful? Well, the REUs are directly corresponding. What’s the weighting factor? We like most all experiences.

Q: What about funding for grad students to go to research conferences?

A: Small fund, but the advisors and students can apply for grants. $500 per student per month.

Q: Do you have an idea of what your PhD students end up doing? I’m thinking primarily academia vs industry.

A: look on alumni page. mostly 50/50.

Q: What computer algebra software is incorporated in the undergraduate curriculum? I’m thinking in terms of a TA-ship. Python? SAGE?

A: With regards to CompSci, the math dept only teaches discrete mathematics. However, WebWork was invented at UR. Some students use MATLAB & Mathematica, basically for free. Perl, Python, and Sage are used as needed. For example, we’ll generate fractals with numerical methods. We tend to concentrate more on the mathematics.

Q: What other schools do you see students most commonly collaborating with, if at all? I ask because RIT, where I currently am, loves to promote their relationships with other schools, especially UoR.

A: usually amongst individual folks.

Q: How close do graduate students tend to live to campus and how do they get around?

A: Eastman school of music downtown. We have a free shuttle from main campus to downtown. Most students live on campus. We also have

Q: What is the average ratio of domestic students to international students?

A: It’s 50/50. It used to be further 70/30 international. Students mostly apply from China, India, Japan and Turkey.

Q: In this train of thought, do you have many students from the Buffalo/Rochester area?

A: a few.

Q: Role teaching and TA-ship?

A: If you have the std tuition waiver, 10 hours work/week as a TA or GA. 3 recitations each week. Some grading of exams. Prep for recitations, grading, and teaching/tutoring should come to about 10 hours/week. Folks who get good TA evals can enter good courses earlier. It’s competitive during the semester. It’s important that every grad student gets some teaching exp. Will be scheduled to teach a course in the summer. Summer courses are paid extra 2,800 per summer course (w00t extra money). We require students to have some teaching experience. We actively set each student up. We want to outline a program so that by the time.

Q: How does already having a math MS affect admission chances?

A: Great. Any mathematical Master’s work up to 30 credits will transfer. BTW, you’ll need 90 credits of course work. 4 credits a course. 8 courses. 32 required credits. The rest are from reading courses & seminars. If you’ve already taken real analysis, we could waive it. Additionally, the final exams of the courses of the req are prelims. The prelims are additionally offered. Students need to complete prelims for the req’d subjects. Welcome to sit in for the courses. 6 main courses. 6 exams for the courses to be passed by the end of the 2nd year.

University of Oregon

People

Meta

  1. They’re the “page owner” for their research group. (I believe anyone who’s updating a website has already made an serious investment of time to recruit new students).  2 3