Blag
I did not misspell "blog." This is my blag which you can find on my wobsite.
In general, I cannot imagine anyone reading my blag regularly but I would like to have a place to put some advice for students and answers to common questions and other thoughts.
Why a blag?
13 feb 2021All the cool kids are doing it.
True, but that’s not why. I often find myself writing an e-mail to one student that will take hours and wonder if others (specially those who may be unwilling, afraid, etc, to ask) would benefit from my responses. I thought that the most efficient way to reach them was to post them here. That being said, just because I wrote a blag post about something does not mean that students interested in talking to me need to have read it or that I am not happy to have a conversation about similar things again one-on-one. I figure it is mostly a place where I would like to store things for myself and collect my thoughts.
Most mathematicians that make blogs write about actual math. I doubt that I will ever really do that. There are often more important things to say that have no other venue. That is what I would like to post here.
Black Lives Matter
18 feb 2021This is not a controversial statement but is meant to say I know that the experience of Black mathematicians (and Americans) is very different from the experience of white ones. I recognize that it is difficult to do math (or anything else you may enjoy) when your safety and well-being are threatened.
Every time I enter a mathematical space and am the only woman I am painfully aware of my own presence. My mind goes blank and my breath becomes shallow. I worry that my thoughts or ideas will be dismissed or (worse) perceived as representative of those of everyone of my gender. I know that my male colleagues don’t see this. I do not mean to compare this to the experience of Black mathematicians but only to say because of this, I know that there are experiences that are obvious, exhausting, exploitative, unfair, painful... (the list goes on) to my Black colleagues and students that may be imperceivable to me.
I am trying to open my eyes and ears. I am seeking out different voices and perspectives and attempting to amplify them where appropriate.
I will fail. Please tell me when I do. I will embarrass myself but I will keep trying for my students and for the next generation of mathematicians.
I also know that mathematics itself has been and can be used to harm, ignore and exploit Black bodies. Mathematics is not neutral. Mathematics is done by humans. There is no mathematics without us and we give it that power to hurt others. We do so sometimes by malice, sometimes by incompetence but often by ignorance.
Advice for Grad Students: Things that I wish someone had told me sooner
24 feb 2021This list is aimed at graduate students. I tried to put in a mix of both big and very small things as well as some actionable items. I also tied to include only the advice that you don't hear very often.
Sign up to receive e-mails from the arXiv (there is a “subscribe” button way down at the bottom of the screen).
This is about the easiest thing you can and should do. Someone (I think my husband) told me to do this and I wish I had done it sooner. You can subscribe only to the lists that are of interest to you and I, at minimum, read every title and author that comes through my inbox every day. I usually scan most of the abstracts and one or two of the papers that I find interesting as well. When I started, I had no idea what most of the words were but this inspired me to find out more, helped me see what people were doing, who was doing it, and even gauge my progress in learning new areas/research questions.
Go to conferences.
I personally hate big meetings like Sectionals and the JMM but I love going to smaller subject specific conferences. For number theory, in particular, I try to regularly check numbertheory.org. Every once in a while, my advisor would send me a conference announcement but I was never urged by him to go and instead I just told him after the fact what I was doing.
I spoke at my first conference in the spring of my 3rd year (I took 6 to graduate) and I think that is the perfect time. Conferences light a fire under your butt to get work done (both in preparation to speak and after seeing what everyone else is doing/has done). I went to as many as I could after that (minimum 3 a year) I also learned so much about what other mathematicians were up to and where my research fit into number theory at large. Without going to conferences, it is really easy to misrepresent what people do at your institution as “the norm” or “the only thing that is important.” What you and your advisor do may very well be important, but if you cannot put it into the context of the rest of mathematics/what everyone else understands, it is essentially useless.
Finally, speaking at conferences early and often gave me practice and confidence for when I was ready to go on the job market. I knew how to give a good talk, I knew how to talk to other mathematicians and a lot of the silly, seemingly insignificant (but often paralyzing) aspects of giving a job talk can be prepared for.
OH! And! Most conferences will pay for (or at least supplement) travel expenses for grad students! So you may get to go somewhere really cool for free! ...Maybe I should have led with that...
Talk to your peers about your/their research.
This is something that I did do a bit in grad school but wish I would have done more of. I wish I would have tried harder to understand what my colleagues were doing in number theory and how it related to what I was doing. It would have been really nice to have found a side project that I could have started with my friends in grad school while we were there.
Talk to the postdocs.
Generally, at each step of your career it is really good to make friends with people that are a stage ahead. This will get you thinking about and understanding the next phase well before you are thrown into it.
However, specifically as a grad student, there were a number of postdocs at UMN that I wish I would have talked about math with. I now try to reach out to grad students more because I know that I personally was too intimidated to talk to the postdocs about math. A postdoc may be able to “advise” you on a side project or be a good person to bounce your own ideas off of.
Apply for fellowships.
This one is harder than it sounds. It can take weeks of work to and odds are that you will not get the award. At this point most people say “but if you do it’s so worth it!” And that is true. Many are worth far more than a weeks worth of work, but I think the real value is elsewhere:
They get easier and easier to apply for (since you have a draft already and maybe know what is required).
You get better and better at writing them. Basically you write the first one and you are like “this is great!” then you look at it a year later and say “wow, that was crap!” and then write an even better one!
It gives you drafts of your job documents and practice writing them.
Imagine if your first proposal was the most important one -- say for your dream job… do you really want to submit the thing you will look back on a year later and called “crap”?
It is part of your job! Many academic positions require (in some sense) you to write grant proposals very regularly so why not practice now while there is nothing to lose!
Don’t stress about grades and classes.
Literally no one looks at your transcripts. You just need to graduate.
Write every day.
By “write” I mean “.tex”. It doesn’t matter if you are really only copying down some definitions or Theorems into (what at least for now is) a notes file. The number of times have found myself using that .tex’d up information later is always surprising. Furthermore, I find if I go a day without .tex-ing, I likely did not make any real progress. Even if I think I did get some math/research done, I will often find it was wrong, I have forgotten it or I lost that paper by the time I do go type it up. I find typing up my work immediately and looking at it written out in the clearest possible way gets me catching my mistakes far faster and allows me to keep forward momentum. Plus, as my advisor told me, it is far easier to fix mistakes in .tex than on a piece of paper. Finally, I have found that many mathematicians (grad students in particular) get a fear of writing that compounds with time away and lack of practice.
Your advisor is very knowledgeable but may not be thinking about you (or your career) all the time.
This probably sounds odd but bear with me… A lot of grad students wait for their advisor to tell them to do something before doing it. For instance, many only go to a conference only if their advisor specifically tells them to. (I have even asked students why they did not go to a particular conference and only to have them respond “My advisor didn’t tell me to.”) I guess that is fine, but, like, did your advisor tell you to brush your teeth this morning or turn in your homework? Clearly your advisor is not your mom (or maybe she is but I think it is safe to assume she is not) but more importantly, it has not occurred to some students that their advisor is just not thinking about them all the time. Sure, maybe they had a good reason for you not to go to a particular conference or publish that paper you have finished (not sure what one could be but I imagine it is possible) but more likely than not they have too many students, projects and priorities to be constantly thinking about what is best for your career at each moment. If you are in doubt about a particular thing, ask them, but it is not their job to bring every single opportunity that may benefit you up immediately. That being said, some advisors do more of this than others, and that is OK too but soon you will leave the nest and it is good to creatively think about what actions take now and how they will benefit you in the future. It is your responsibility to find out what actions you can take now to get you where you want to be when (and after!) you graduate.
Q & A: Academic job market out of grad school
19 apr 2021The following are my responses to questions posed by Louis Gaudet and Brooke Logan Ogrodnik for a panel in the Rutgers Graduates Students Number Theory Seminar. Note RS = research statement , TS = teaching statement and TT = tenure-track. Please feel free to email me if you have any questions. (You can find a copy of my old RS and other documents on my old website.)
Disclaimer: I am just a postdoc and have never served on a hiring committee so please take my advice with a grain of salt. However, I do think it is more important than ever to get insight from those who were recently on the market.
How many postdocs did you apply to, and how did you decide where to apply?
107, I believe. Here was my spreadsheet: Job Spreadsheet
The only jobs I got on my first time around were the ones I did not apply for. Namely, I was offered a lecturer position at Stanford and my postdoc at KSU which was a spousal hire. The next year I only applied for NSF and got it.
Did you have publications already when applying to postdocs? Is that necessary?
I had one publication (already in print) and one thing submitted/on the arXiv. It is not strictly necessary. However, the way the job market is leaning, it is more like it is “not necessary” if you graduated from Princeton; however, it is one of the most impactful things you can do to put you in the running at more places. Basically, if you can at least put something on the arXiv, do it (with your advisor’s consent) but if you cannot, don’t have a panic attack over it.
How much did you tailor your application materials to the specific institution you were applying to?
I edited every single cover letter to, at very least, change the name of the university and mention some people in the department that I was interested in working with.
I also had two major drafts of both my TS and my RS: one for SLAC (Small Liberal Arts Colleges) i.e. TT jobs there and one for postdocs.
Do you have tips for writing a “future work” section on a research statement?
If it is early enough in your academic career, I recommend getting involved in mentoring undergrad research. This was how I was able to write about a variety of future directions (as opposed to just the one obvious extension of my thesis). Undergrad research gives you the excuse to learn about topics tangential to your dissertation, explore possible new research questions and do some mentoring while you are at it. It is truly win-win.
If it is too late to start something like that, ask your advisor about future directions for your thesis if you do not know. You also really do not need much at this point in your career. It is good to have more than one potential future project but they do not all have to be super well explored. You do not need conjectures or anything. It just should be clear that you know how to ask relevant questions and are thinking about future work.
Is there anything you didn’t anticipate about applying?
My very best friend/officemate and other members of my cohort getting amazing offers while I waited to hear anything. Watching my husband do many round of the job market, I thought I was prepared for everything, but I did not thing about the fact that none of his good friends were applying for jobs at the same time as he was. Don’t get me wrong, these people 1000% deserved everything they were offered and I was and am SUPER happy and excited for them. But when you are 6 months pregnant, your hormones are all out of wack and my struggle on the market was amplified by constantly having to congratulate my friends. I just couldn’t get away from it, it was suffocating and led me to one of the worst bouts of anxiety and depression I had ever had.
Also, I did not think about drafting a Diversity Statement before my applications started. More and more school are looking for them for various positions. I highly recommended drafting one.
What do you like most about your current position? What do you like least?
I love basically everything about it. I am surprised how much I miss teaching but I think that is mostly due to being isolated during the pandemic.
Any general advice you wish you had received?
Just because you are not getting everything you think you want and worked for right now does not mean you will not get it eventually. The pathway to success is not always linear. Take care of yourself and find spaces where you have the support you need.
ALSO flag all the jobs that you cannot apply to on mathjobs.org. They take WAY more time.
How did you handle applying within the US vs. internationally? Any specific issues to be aware of?
Most non-US jobs are not on mathjobs.org OR if they are advertised there but you cannot apply through the site. It sounds insignificant but when you apply for 40 jobs in a month, taking the time to register in a new platform, input all your info, change the documents, etc makes a huge difference.
Did you email postdoc advisors or department chairs ahead of time? How does one do that effectively?
I emailed potential advisors (no chairs -- I think that would be weird). I did this at any school where I thought there was someone whose worked aligned decently with mine (i.e they did automorphic forms) or that I knew personally or may want to work with. At the end is a sample of an email that I sent. (I did have a header -- I just redacted it for privacy. I sent similar things to people I had not officially met. And for real I only introduced myself to this person, we did not have a chance to talk about math or anything.)
From many people (including this person) I got a nice e-mail back thanking me for calling their attention to my application. From some people I heard nothing. No one replied angrily -- no even very important people (or the person whose name I misspelled on a reply :( ).
Did you do FRGs, workshops as a PhD student? Is that an important asset to a postdoc application?
Does the MSRI thing count? If so then yes but it made no impact on my life (except I met Matthew :) ). However, conferences (esp topic specific ones) were very helpful.
Did you consider applying to non-academic jobs? Did you apply to them?
Everyone in my life wanted to force feed me non-academic jobs. One my best friends is at Medtronic and I have a bunch of friends in other great industry jobs. I went through a bunch of the motions (internship fairs, classes on applying to industry jobs, talks, etc). I really have nothing against industry, but I honestly think I would be better suited as a high school teacher if this does not work out for me and I think I would honestly be jazzed about that. I think industry is SO great for SO many people but I just really don’t think I am one of them. I love academia so much (modulo the racism/sexism/classism) that I can put my whole soul into having it crush me but I do not have the adequate amount of desire to go through the nontrivial amount of work to get an industry job.
How do you write a teaching statement?
Great question! You sit down and you write a teaching statement. Then, you take that teaching statement and throw it in the trash. It is garbage. I am not kidding. My best friend (the one that got all the offers) went on the market or SLAC (Small Liberal Arts College) TT jobs a year early just to see. She sent me her first TS, and I ripped it apart. She was super upset about it. But the next year she was like, you were so right. Every first draft of a TS I have read is awful -- my own included!
There are some good guidelines here. But to summarize, this should not feel incredibly different from your RS. It should not waft philosophically. It should not inspire. It should not bring tears to your mothers eyes. A good guideline is to describe a typically day in your classroom and why it is structured the way it is. Take about concrete objectives you have, how you achieve those objectives and then how you measure whether your were successful.
For the most part these do not matter much for postdoc but you do not want to embarrass yourself. If want a TT at a SLAC, then they matter a ton and I can talk more about that.
Any tips for preparing an effective CV?
Your teaching experience should always be last. Don't be too creative. Look at a TON of examples. If your CV is publicly available on this internet, I have probably looked at it. Just literally google everyone and look at their CV.
Did you go through any interview processes? Did you give any job talks? Any advice about what to do when visiting a department where you’re applying to?
I had 3 “fly outs” --two for postdocs and 1 for a TT at a SLAC. I legit thought I would not have fly-outs for postdocs-- that is why I decided to have a baby then and not wait (also by the time I have tenure somewhere--IF I ever get tenure-- I will be >40).
The talks I gave ran the gamut: a ~5-10 min research talk, colloquium talk at a research university, colloquium talk at a SLAC, and a “teaching talk”. Did you know that some SLAC fly-out interviews are TWO DAYS?! It is awful.
Advice: drink lots of water, prepare way more questions than you could ever imagine needing (don’t forget to ask about living in the area, etc), pay attention to how you feel being there -- you are checking them out too!
My only piece of non-obvious advice is to have a game plan for how to react for when someone offends you. In one interview I was talked over by an older white gentleman in CS who basically told me that undergraduate analysis was too hard for me to teach since I was not an “analyst” (sidenote: they hired an applied mathematician…). I sort of blacked out at that point and tried to calmly explain my qualifications; however, I am very bad at masking my emotions so I do not think I did a great job. I am not sure how you prepare for this. However, in my research talk the next day I was probably a little to “showy” and quick when I was talking about Sobolev theory and functional analysis just to make that man feel small. Not a high point for me but I have no regrets.
Miscellaneous other advice:
Make a website and a CV. Now. It is so easy but it is something you can do immediately.
Offer to edit your friends' job documents (even well before you plan to go on the market). The more you read, the better it is for you.
Plan to apply for the NSF Postdoc. You should really start thinking about this the spring before you go on the job market, but preparing for this is a really good head start for your other materials. I also have tons of NSF specific advice if anyone would like to hear it.
For a working/editing group with your peers:
The summer before we all went on the job market, a few of my friends and I started meeting weekly. The first half of the summer we had a tight schedule in which each week we would try to complete a draft of our a Research Proposal (i.e. NSF), research statement, teaching statement, CV, cover letter, etc). In the weekly meeting we would sometimes look at drafts or chat about issues or questions that came up. (Most of these drafts took multiple weeks but we would still meet and try to keep our goals ambitious.) The second half of the summer was mainly just editing. We would pair off and trade drafts, permuting the pairs each week. We would usually talk about them all together just so we could all weight in and hear each others' advice.
We also created a Google Drive with an organizations spreadsheet tracking our goals and progress as well as helpful materials and some sample documents that our friends were willing to share with the group.
No one ever talks about this but you should also draft a Diversity Statement.
Make a spreadsheet to keep track of your applications (see mine above for an example).
Try to get a letter writer from outside your university. Applying for NSF is a great way to do this.
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Q & A: Academic Rejection
25 oct 2021The following are my responses to a Q & A for a panel for Lunch in the Time of Covid.
Have you experienced rejection in your career?
I think my career has been roughly 50% rejection. For every line on my CV I could write a paragraph of the crap I went through to get it. I have been planning for years to make a failure CV (FCV) but have not found the time. I hope to do it soon.
What should you do when your paper is rejected?
You should do what you need to feel best – maybe it is eating ice cream, maybe it is having a beer, maybe it is going for a hike. Make sure you sit with the rejection for a minute and talk about it with someone you trust – take a day or an afternoon if that is what you need. Then I think it is best to do something that empowers and energizes you. For me it is often going for a run or hike or spending time with my family.
How do you reach out to others (personally or professionally) when you’re struggling with something in your career?
I think it is important to have the right “who” first. Don’t just reach out to the first person you think of and dump things on them. I also think it is a good rule of thumb to check in with others first. The person you may want to reach out to may be going through something much worse and unloading on them is unfair or tough. Or that person may have just gotten some great news from themselves so they will not be coming from the most empathetic place. Talk to someone you know will understand and will not judge but that you can trust to help you get to the right place.
Do your departments have open discussions on rejection in academia (from paper rejections, to rejections on the job market, grant rejections, … )? If not, should they? What would you like to see or hear in such a discussion?
I have never been a part of a department that does this. However, to be honest I am not sure that is what I want from my department. I think it is nice to have a friend who is not in your every day circle that you can confide in. I would not want everyone I work with knowing how much I suck all the time. In fact, it often gets me through that they DON’T know about my failures. This is a mental exercise that I work through regularly. I instead try to think about how my coworkers see me. Now it is really important when doing this to only think through the facts that outsiders actually know about you (not how you feel or what you are speculating they must think of your worth). Knowing that there are things that I suck at and my coworkers don’t know often makes me feel better! They probably have just as many things they have messed up but I have not seen.
Personally, what steps do you take after a setback? What about professionally?
First take care of yourself personally before you do anything professionally.
Get through the day – do what I gotta do to survive. I used to overlook this step but it is really important.
Honor the feelings of rejection when I can (talk to a friend, cry, just feel sad because it is OK to be sad sometimes.)
Do something for myself – even if it is small (go on a run, eat ice cream, take the night off and watch Netflix, etc).
Get back on the horse (submit the paper, look for the next grant to apply for, use this as an excuse to prove people wrong).
How can we support graduate students and postdocs when they are facing rejection?
Tell our stories. Students especially only see our stories of success but it is so important that we tell them how many times we failed to get there and how much it hurt. This is especially helpful if we can do this semi publicly so we can get rid of the stigma and shame.
Do you have a beautiful redemption story?
I have so many. The most important ones to tell are the ones I find most shameful. One I plan to make a whole blog post about not getting a job coming out of grad school.
I will say I applied to the math phd program at the UMN first in 2010. I was rejected. Part of the reason I was rejected was because I was in the 11th percentile on the math GRE subject test. (I am SUCH a bad test taker.) I even have a Masters in math. I sat in on classes in the dept and passed their prelims – 2 years later I was accepted. I still took 6 years get through the program – I am very slow but math is not a race.
How to talk about mathematics effectively and respectfully
26 july 2022Assume that the person you are speaking with is as intelligent (if not more intelligent) than you are.
That being said, the person you are speaking with is not you and has not been living in your head.
It does not matter if you spoke to this person yesterday about the same problem, when you start talking about math with someone, give a mini introduction: “Remember yesterday we were talking about X, we agreed that the real sticking point will be at point Y of the argument. Since then I realized that there may in fact be a problem earlier on with this particular assumption.” or “Yesterday we were talking about X, we agreed that the real sticking point will be at point Y of the argument. I think I have an idea of how we can resolve that issue.” It is really important to be as clear and explicit as possible, especially at the beginning.
With this, keep in mind that likely sharing the way you came to an idea or all the thoughts you have had since you last spoke to your partner will make it more difficult to get your point across. Instead, this about what the best way is to present what you have bene thinking about or what you want to say before your conversation. If this turns into a 10+ minute lecture at the other person, they will not be able to follow and sift out the important ideas. It is not because they are intellectually inferior to you, it is only because you have had much more time to ruminate over them. Part of being a good mathematician is identifying what the important ideas are, communicating them clearly and ignoring all the extra stuff that really doesn't matter.
Use as little jargon, notation, etc as possible and when you do use notation you should clearly explain it. Give your partner time to internalize that definition and remind them of the definition periodically. It’s important to ask things like “Am I making any sense?” or “Do you have questions so far?” regularly to give your conversation partner a chance to internalize information and clarify their understanding.
If you think the other person may have made a mistake, you should almost always present it as your own misunderstanding or confusion.
The main reason for this is it really might be your own confusion, but furthermore, it can be quite embarrassing to be told you’re wrong and it is a natural response to be defensive. You want to do what you can to avoid your partner feeling attacked and/or becoming defensive. When I believe someone may have made a mistake, instead of saying “You cannot do that” or “This is wrong”, I usually start by doing two things:
Acknowledging what I believe to be correct and understand about what the other person has done.
Then I say something like “I don’t understand what you have done here, can you explain it to me?” or “How did you account for the fact that __?” or “I am confused about this part?” or “I think I misunderstood something you did, do you mean X?”
It is best if you can phrase your point of concern as a question rather than an accusation. I try to approach the situation with the viewpoint that it is much more likely that I am confused or have made a mistake than that the other person is wrong.
Also try not to assume that the other person is implying you are less intelligent if they point out an error.
In other words you can be wrong about something without it being an implication of your intellectual inferiority. Try not to be dismissive of criticism and listen carefully to what you are being told. Often it is easy to read too much into a small, specific error someone is trying to point out. If you do not understand, try to explain what you have done so far step by step so that they can more clearly point to the issue. Instead of explaining why you are not wrong, try to ask "what if I changed things this way? Would that resolve the issue?" It is important not to get too attached to things like the way something is written or choice of notation that may make sense to you but be confusing even misleading to a reader. One Everyone makes "mistakes" and finding an error should be exciting. Being wrong has nothing to do with intelligence and being wrong about something just tells you that thing is more interesting than you may have originally thought!
It is very natural to become frustrated.
Being confused is frustrating. Explaining something to someone and not having them understand you is frustrating. However, it is important to remember that a situation can be frustrating without it being anyone’s fault or intention. If you feel that you are not being understood or listened to, it may well be that you have not explained yourself clearly. And there is no excuse for taking that frustration out on someone else. If you find yourself getting frustrated, take a deep breath and ask your partner to take a break. Go to the bathroom, get some water, go for a walk, or just wait and continue the conversation the next day. Math becomes much more difficult to discuss once anyone has become overly frustrated.
You should never use the following words or phrases:
“That’s obvious”/“obviously,” “clearly,” “we all know that,” “you didn’t know that?”, “that’s trivial”
That being said, your tone and demeanor often matters just as much as the words coming out of your mouth. It is important to speak clearly but not raise your voice too loudly, roll your eyes, sigh heavily, etc. Speaking clearly but gently is your best bet.
The onus is on the person explaining/presenting/writing something to make their thoughts clear, not on the listener/reader.
While reading and listening to math is active and you must ask pointed questions where you do not understand, the responsibility is on the one presenting the information to do so in a way that is clear and illuminating. If the listener/reader does not understand, it is the responsibility of the presenter to express things more clearly. Take ownership of the fact that possibly you have not explained yourself clearly. Your fellow mathematician is not an undergraduate who just does not want to be doing math right now, they are instead someone who is already actively engaged in the conversation, so if they do not understand what you are saying or writing, you likely have not presented the information clearly and should be open to suggestions on what needs to be clarified.
This Is What Success Feels Like: What I Learned from Applying for the NSF Postdoc Twice
august 2022Read my full article in the Notices here.
CV Templates
20 march 2024Overleaf has a number of very nice templates for CV's that can be found here: https://www.overleaf.com/gallery/tagged/cv.
You can also find the source files for my CV Template here. Note that you will need both the .tex and .cls file in the same folder (on either your computer or Overleaf) in order for it to compile properly.