Today’s #loveyourmath topic: What inspired you to get into mathematics?

Math was definitely not my plan when going (back*) to college. The plan, which worked out tremendously, was to major in French and Econ and then go work for the World Bank or something. In Paris. Because, you know, Paris. But when I went to Colorado College, the block plan (one class at a time) made it very easy to start in Calc 3, then go on to DEs, then Linear Algebra, then… a year of math. And so I became a math major. I don’t know if this would or would not surprise my K-12 math teachers. In preschool, I had an existential crisis over counting (what if I keep counting? Is there an end to numbers, or no end, and which is worse?!) In 3rd-grade, I was hung up on fractions, decimals, and percents (why bother with three different ways of writing down the same thing?). I flunked 7th-grade pre-algebra (ask me about my recurring back-to-school nightmare) but then started liking math again in high school (I skipped a year of history to catch up and end my HS with Calculus). At that point, I figured I was done with math because what else is left after calculus? Anyway, I owe a huge debt to Patty Parsons and Ken Oliver who made math at Amity High School exciting to this nerd. I’m delighted to have been so thoroughly nurtured (nerd-tured?) at Colorado College by then-visiting professor Travis Kowalski; professors Marlow Anderson, David Brown, and Jane MacDougall; and former professor Amelia Taylor who overlapped with me the year I worked as paraprofessional. And I never would have gotten a PhD without the University of Nebraska–Lincoln faculty, staff (thanks Marilyn and Liz!!), and fellow grad students (shout out to Ashley, Amanda, Lauren, Mike, Ben, Nora, Anisah, Sara, and so many more). Not to mention the huge amounts of coffee and beer in Lincoln; I have a spot in my heart reserved for all the baristas and bartenders that kept me hydrated.

*Yep, back. I dropped out of college the first time. I also dropped out of 1st- and 7th-grades. I like to think I was preparing for the sabbatical cycle.

So far, sabbatical has been busy, busy, busy with research and travel. I managed to get one paper (which you might remember from last summer’s REU posts) retooled and submitted before the end of the summer. Yes! Check one off the to-do list. I spent a week at the Algebraic Statistics MRC and learned that commutative algebra has a lot of applications…and I have a lot to learn about them. The group I was in (led by Serkan Hosten from SFSU) was productive and friendly. The algebraic statistics community, by the way, is one of the most open and welcoming mathematical communities out there. I really appreciate how friendly everyone was even though I’m so new to the field. It was awesome to reconnect with some math folks I haven’t seen since graduate school and to see how they’ve shaped this relatively young field. I’m excited to keep working in this area!

The Big Project, which I think of as my dissertation plus “postdoctoral” work (if I’d had a postdoc, this is what I would have worked on!) with my dissertation advisors, has become a magnificent and enormous piece of mathematics. I’m so lucky to have learned so much through both of my advisors, and it’s been exceptional to collaborate with them and keep learning as junior faculty. I think I would have felt cut off from the larger research world without this project to keep me connected. I had a chance to talk to both Lucho and Roger about it within the same week — now *that’s* a luxury!

Toward the very end of summer, I attended the International Conference on Representations of Algebra (ICRA) at Syracuse University. There was a star-studded lineup, and I left with ideas, questions, and a better understanding of lots of math I was exposed to in graduate school (but not since). It was a fantastic conference! First time in the US, too — huge congrats to SU for such a wonderful job hosting. I got a chance to talk math with my math-brother Frank Moore, and that’s always a delight. Look for a paper from us (+Andy Conner) soonish, I think.

I got to spend a long weekend down at Adelphi University working with my coauthor Branden Stone. We both advised senior research that was based on a paper we’d written together, and we’re souping it up and putting it into a paper. It’s a lot of fun — more complete intersection Betti diagram stuff, which I do really enjoy working on! If we wrap this up by the end of the semester, which seems very possible, I will feel like it’s been a good fall semester research-wise.

Later, my mathematical half-brother Nick Baeth came to visit, and we started working on a project that we’d both looked at once upon a time (thanks to Roger Wiegand). It’s a semigroup project, which happens to dovetail nicely with some semigroups stuff I’ve been thinking about turning into a student research project for the coming summer.

We’ll cross paths again in a few weeks at the Second International Workshop and Conference on Commutative Algebra at Tribhuvan University in Kathmandu, Nepal. Guess who’s organizing a conference in a location with good trekking and climbing…? If you said Roger and Sylvia Wiegand, you know your stuff. It was a pleasure to be able to celebrate their 50th wedding anniversary at one of their numerous parties; it will be great to see them and the other speakers (from a dozen countries!) in Nepal.

The last travel I have set up for the semester (as of now) is to visit Williams College to speak at their faculty research seminar. My goal is to lay out some of the overlap between my interests and Pamela Harris’s interests to set up future collaborations. Pamela is a rock star, and I look forward to talking representation theory with her!

So there’s the scoop as far as research goes.

]]>**Successes:**

- Got Singular installed *and* got my mac to shut up about “programs from the internet” every time I open it;
- Ran an example in Singular with (almost) the expected output;
- Ran the same example in Macaulay2 with the same output as Singular;
- Installed Bertini and managed to get the Bertini.m2 package to work.
- Installed 4ti2.

**Failures:**

- Can’t get my Aquamacs preferred theme (Solarized Dark) to stick despite hours of googling today and other days;
- Can’t get Aquamacs to find and run Singular;
- No clue what to do with 4ti2 now that it’s installed…

I’ve had a few other successes, though, unrelated to software:

- Tracked down all the references for my homework (with the help of a librarian at Hamilton — thanks Glynis!)
- Managed to remember some statistics.

Moo is arguably the greatest cat in the world. She’s fluffy, she purrs, she talks, she knows tricks. I adore this cat. In grad school, I had a dream that I physically gave birth to her (probably a product of the stress of grad school and the comfort she provided when I got home feeling bad every day). Moo keeps me humble — every once in awhile, she places a hairball right where I’ll step in it. Moo keeps me stylish — I find tasteful accents of cat fluff on every outfit.

For those doing the math, Moo’s about 13 years old. She’s in excellent health; last year, she had a dental surgery to preempt future problems. Other than that, she has never had a major medical procedure (aside from spaying).

Sometimes, things as a pre-tenure professor get a little overwhelming. On the toughest of days, I know I can rely on Moo to sit on me and purr until I get out of my funk.

So, here’s to Moo!

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Cats: Moo, Sophie, and Tipper

Ages: 13, 8, 1.5

Sexes: Female (spayed) × 3

Rescued: 2004 (Colorado), 2008 (Nebraska), 2015 (New York)

Follow the #cats tag for more information. Coming up: Moo’s biography.

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One of my friends called the process “self-irritation inducing.”

And now we wait…

]]>I’m sure everyone has her favorites, but here are my top three:

- Seeing my people!
- Karen Smith’s invited lectures & the associated special session (see below)
- Minicourse 6: Flipping the Classroom

Anyway, I also had a wonderful time with the other speakers in the Concrete Computations in Algebra and Geometry session (organized by Karen and Sarah Mayes-Tang). In case they’re useful, my slides are on the web: View Slides

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It’s been a lot of work to be an REU mentor, but it’s been equally fun.

In the next week, I’ll wrap up a few thoughts about the REU and post a link to our final product. But for now, it’s time to get to the airport and start my trip back to Hamilton.

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I’m lucky to have an REU group that takes my criticism in stride. They realize, I think, that it’s the math that matters. My comments, though critical, are not judgments of the students. Anything that obscures the math (or worse, misrepresents it!) is a problem. Too much detail is as bad as too little detail, but these are subjective norms decided by the mathematical community. Yep, proof is a social construct. What makes a proof *good* is much different than whether it’s a proof.

There are many ways in which I think I’ve been a solid REU mentor, but the place where I give myself the harsh feedback is in my transmission of this sense of style. Partly, this is because every mathematician has a personal aesthetic. One’s criteria for “goodness” comes from reading papers (and liking the style of the papers that he or she finds easiest to understand), from writing papers, from having papers refereed (and then refereeing papers). And there’s a difference between a paper that’s pleasant to referee and a paper that contains useful (again subjective!) mathematics.

So, I’m left with this unresolved question: How do you begin to help students develop their math paper writing skills? It’s much harder than just writing up proofs that happen to be true. I don’t really feel like I’ve been helping the students learn anything except how to use the “todonotes” package in LaTeX. Your comments are welcome. Feel free, too, to rip on my writing.** If I can dish it out…

*At Hamilton, linear algebra is also the “intro to proofs” class. As such, it’s writing intensive. This designation means that I grade proofs assignments once or twice a week. At my lowest point, I’ve written “duh” on a paper (and I won’t do that again in linear algebra; senior theses, however…). I have not yet written “aardvark barf” on a paper, but I do remember that particular biting comment making several appearances on drafts of my dissertation.

** I specifically avoided using my Grammarly plugin and my spell check so you’d have plenty to criticize!

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I left two weeks for writing, anticipating these hiccups, but it still seems too short.

Irena Swanson, of Reed College, is visiting us today. She’ll give a lecture on free resolutions. I’m excited! Irena is much more than a kickass mathematician. She’s also an ideal role model for anyone who hopes to be good at all parts of the profession. She has a robust research career while also being an excellent teacher at an elite liberal arts school. She’s done a ton for the mathematical community, especially commutative algebra. She’s advised more undergraduates that I can count on my hands and feet (along with a handful of Masters and Ph.D. students).

Having the chance to talk to Irena about their research will be an excellent opportunity for my group. And learning about free resolutions and Groebner bases will be super for the other REU participants.

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