Happy 3rd birthday, blog!

26 Nov

I missed Baking and Math’s 2nd birthday because I had a new human baby at the time.  But for the blog’s 1st birthday I googled “birthday celebration women” and got this fantastic picture:

And then I googled it again just now, two years later.  Same card appeared, but so did this remarkably ugly design:

17th bday present comes in t-shirt, tank top, tote, or thong: http://www.cafepress.com/mf/25934971/17th-birthday-math_tank-top?productId=235581471

17th bday present comes in t-shirt, tank top, tote, or thong: http://www.cafepress.com/mf/25934971/17th-birthday-math_tank-top?productId=235581471

As a birthday present, here are some stats about this modest little blog:

Most visitors in a month: October 2014 (that’s when Ian was born!) 3,578

Highest average visitors per day: November 2015 (that’s right now!) 127

Most visitors in one day: May 1, 2014 (for this post which was tweeted and facebooked by MoMath) 754

Most popular day to visit: Tuesdays (19%) and most popular hour: 3 p.m. (7%)

Most popular post (this doesn’t count people who just go to the home page): my mom’s thit kho  with 14,993 views

And a few of my favorite things from each category:


I love these cute pictures in posts about serious math: Apollonian circle packings from a lecture by Hee Oh, and Kissing Numbers from a talk by Federica Fanoni

I also like the open problems series: geometric group theory, combinatorics, and group theory.

I’ve received compliments/been told that the curve complex series ( I, II, III, IV) and the fundamental theorem of geometric group theory series (I, II) were also helpful for current/beginning graduate students.  I’d love to do more series, so if you have any ideas/requests let me know!  My last series was suggested to me by the postdoc whose work I showcased, so that’s awesome if you want that too.

Unrelatedly: I noticed I have a slight bias toward writing about the work of female mathematicians.  I don’t see this as a bad thing and it might even be a good thing if I do it consciously instead of unconsciously biasing myself toward tribalism.  And obviously I’ve written about male contributions to math as well.  Just a random observation.


I still stand by my breastfeeding post (in case you were wondering, I did end up breastfeeding for several months and loving it, and stopping was bittersweet, but I still don’t advocate relentlessly pushing it on women even if I understand that is a method for societal change).  Writing this list just reminds me that I’m really rather proud of all the math and life posts.  The podcast list has been useful for friends.  Everything about being a woman in math is my life and who I am, and there are often pictures of cute animals or my baby.


Pavlova is still one of my favorite things.

I also love that easy lime pie.

Savory: we’ve been into eggplant lasagna lately, and when I was pregnant I ate so many delicious burgers.  Also all the Vietnamese food.

Semi-homemade: those super easy cinnamon rolls, the rum cake, the Hull banana pudding, and the oreo balls are all hits every time

Things that are more work but so tasty: Moosewood ricotta cake, olive oil cake, and chia pudding with coconut milk and mango


Anyways, this has been a great ride and I really love having my little corner of the internet where y’all come visit me.  Feel free to drop me a line (email is in the About page), comment, tweet (@yenergy), facebook (Baking and Math); I’d love to hear from you.  Also, happily, this week I got my 100th WordPress.com follower, so thanks to Stuart Perkins for that and to all the people who follow me.  Happy Thanksgiving, also!  I’m so thankful that I’ve had this incredible three years: moved to Chicago alone to start a Ph.D. program, traveled all over the world with that program, moved to Austin a few years later with a husband and child in tow for the end of said program, all piecemeal documented on this blog.  Thank you to you, and I hope you stick with me for whatever’s coming next.

Current research: lifting geodesics to embedded loops (and quantification)

19 Nov

Last week we learned about covering spaces, and I made a promise about what we’d talk about in this post.  For those who are more advanced, this all has to do with Scott’s separability criterion, so you can take a look back at that post for a schematic.  I’ll put the picture in right here so this post isn’t all words:

Left side is an infinite cover, the real numbers covering the circle.  Middle is a happy finite cover, three circles triple covering the circle.  Right is a happy finite cover, boundary of the Mobius strip double covering the circle.

Left side is an infinite cover, the real numbers covering the circle. Middle is a happy finite cover, three circles triple covering the circle. Right is a happy finite cover, boundary of the Mobius strip double covering the circle.

In my friend Priyam Patel’s thesis, she has this main theorem:

Theorem (Patel): For any closed geodesic g on a compact hyperbolic surface \Sigma of finite type with no cusps, there exists a cover \tilde{\Sigma}\to\Sigma such that g lifts to a simple closed geodesic, and the degree of this cover is less than C_{\rho}\ell_{\rho}(g), where C_{\rho} is a constant depending on the hyperbolic structure \rho.

We know what geodesics are, and we say they’re closed if the beginning and end are the same point (so it’s some sort of loop, which might intersect itself a bunch).  But wait, Yen, I thought that geodesics were the shortest line between two points!  The shortest path from a point to itself is not leaving that point, so how could you have a closed geodesic?  Nice catch, rhetorical device!  A closed geodesic is still going to be a loop, but it won’t be the shortest path between endpoints because there are no endpoints.  Instead, just think locally: if a closed geodesic has length l, then if you look at any two points x and y less than l/2 apart from each other, the closed geodesic will describe an actual geodesic segment between x and y.  It’s locally geodesic.

What about hyperbolic surfaces of finite type with no cusps?  Well, we say a surface \Sigma is of type (g, b, n) if it has genus (that’s the number of holes like a donut), boundary components, and punctures or cusps.

Pink: (4,0,0) Orange: (3,0,2) Green: (1,2,1) Ignore the eyes they're just for decoration

Pink: (4,0,0)
Orange: (3,0,2)
Green: (1,2,1)
Ignore the eyes they’re just for decoration

Boundary components are sort of like the horizontal x-axis for the half plane: you’re living your life, totally happy up in your two-dimensional looking space, and then suddenly it stops.  This is also what a boundary of a manifold is: where the manifold locally looks like a half-space instead of all of \mathbb{R}^n.  Surfaces are 2-manifolds.

Finally, I drew punctures or cusps suggestively- these are points where you head toward them but you never get there, no matter how long you walk.  These points are infinitely far from the rest of the surface.

I think we know all the rest of the word’s in Priyam’s theorem *(hyperbolic structure is a hyperbolic metric).  The important thing to take from it is that she bounds the degree of the cover above by a constant times the length of the curve.  This means that she finds a cover with degree smaller than her bound (you can always take covers with higher degree in which the curve still embeds, but the one she builds has this bound on it).

Just looking at this old picture again so you can have a sort of idea of what we're thinking about

Just looking at this old picture again so you can have a sort of idea of what we’re thinking about

She’s looking for a minimum degree cover and finds an upper bound for it in terms of length of the curve.  Let’s write that as a function, and say f_{\rho}(L) gives you the minimum degree of a cover in which curves of length embed (using the hyperbolic structure \rho).   What about a lower bound?

Here’s where a theorem (C in that paper) by another friend of mine, Neha Gupta, and her advisor come in:

Theorem (Gupta, Kapovitch): If \Sigma is a connected surface of genus at least 2, there exists a c=c(\rho, \Sigma)>0 such that for every L\geq sys(\Sigma), f_{\rho}(L)\geq c(\log(L))^{1/3}.

So they came up with a lower bound, which uses a constant that depends on both the surface and the structure.  But it looks like it only works on curves that are long enough (longer than the systole length, which we’ve seen before in Fanoni and Parlier’s research: the length of the shortest closed geodesic on the surface).  Aha!  If you’re a closed geodesic, you’d better be longer than or equal to the shortest closed geodesic.  So there isn’t really a restriction in this theorem.  Also, that paper is almost exactly 1 year old (put up on arxiv on 11/20/2014).

Now we have c_{\rho,\Sigma}(\log(L))^{1/3}\leq f_{\rho}(L) \leq C_{\rho}L.

This is where it gets exciting.  We know from Scott in 1978 that this all can be done, and then Patel kickstarts the conversation in 2012 about quantification, and then two years later Gupta and Kapovich do the other bound, and boom! in January 2015, just three months after Gupta-Kapovich is uploaded to the internet, my buddy Jonah Gaster  improves their bound to get \frac{1}{c}L\leq f_{\rho}(L), where his constant doesn’t even depend on \rho.  He does this in a very short paper, where he uses specific curves that are super hard to lift and says hey, you need at least this much space for them to not run into each other in the cover.

Here’s a schematic of the curves that are hard to lift (which another mathematician used to prove another thing [this whole post should show you that the mathematical community is tight]):

This curve in the surface goes around one part of the surface 4 times, and then heads over to a different part and circles that.  This schematic is a flattened pair of pants, which we've seen before (so the surface keeps going, attached to this thing at three different boundary components)

This curve in the surface goes around one part of the surface 4 times, and then heads over to a different part and circles that. This schematic is a flattened pair of pants, which we’ve seen before (so the surface keeps going, attached to this thing at three different boundary components).  I did not make this picture it is clearly from Jonah’s paper, page 4.

So that’s the story… for now!  From Liverpool (Peter Scott) to Rutgers in New Jersey (Priyam) to Urbana/Champaign in Illinois (Gupta and Kapovitch) to Boston (Jonah), with some quick nods to a ton of other places (see all of their references in their papers).  And the story keeps going.  For instance, if you have a lower bound in terms of length of a curve, you automatically get a lower bound in terms of the number of times it intersects itself (K\sqrt{i(g,g)}\leq \ell(g), same mathematician who came up with the curves).  So an open question is: can you get an upper bound in terms of self-intersection number, not length?

What is a covering space?

14 Nov

We’ve briefly covered fundamental groups before, and also I’ve talked about what geometric group theory is (using spaces to explore groups and vice versa). One way to connect a group to a space is to look at a covering space associated to that group. So in this post, we’ll come up with some covering spaces and talk about their properties. This is in preparation for talking about separability (we already have an advanced post about that).

Aside: you might catch me slipping into the royal we during my math posts.  This is standard practice in math papers and posts, even if a paper is written by a single author.  Instead of saying “I will show” and proving stuff to you the reader, we say “we will show” and we go on a journey together.  I’m sure that’s not why mathematicians do this, but I like to think of it that way.

Also, sometimes I say “group” when I’m obviously referring to a space, and then I mean the Cayley graph of that group (which changes depending on generating set, but if it’s a finite generating set then all Cayley graphs are quasi-isometric).

Let’s start with an example, and then we’ll go on to the definition.  Here’s an old picture to get us in the mood:

This blue curve goes around the circle three times.

This blue curve goes around the circle three times.

This picture was from the short fundamental groups post: you’re supposed to see that the blue spiral up above represents a curve going three times around the circle below.  Now consider this next picture:

Blue line covering the happy circle below

Blue line covering the happy circle below

Here the blue spiral goes on forever in both directions.  If you unwound it, you’d get a line stretching on forever in both directions, which we’ll call the real line (the same number line you’re used to, with real numbers along it).  This picture sums up the intuition that the real line covers the circle: for any point on the circle, there are a bunch of points on the real line directly above it that project down to that point.  In fact, it does more than that:

Pink parts of blue line cover the pink part of the cirlce

Pink parts of blue line cover the pink part of the circle

For any point on the circle, there’s a neighborhood (the pink part) so that up in the real line, there are a bunch of neighborhoods that map down to that pink part.  And those neighborhoods aren’t next to each other nor all up in each other’s business: they’re disjoint.  So here’s the definition:

A covering space X of a space Y is a space with a map p: X->Y such that any point in Y has a neighborhood N whose preimage in p^{-1}(N)\subset X is a collection of disjoint sets which are homeomorphic to N.

So why is this helpful?  Well, in our example we can say that the real line covers the circle, from the pink pictures.  We could also say that the circle wound around itself three times covers the circle, from the first picture in this post:

The three highlighted parts up above are homeomorphic to the the pink part on the bottom circle's chin

The three highlighted parts up above are homeomorphic to the the pink part on the bottom circle’s chin

The picture I just drew might not convince you, because every point on the bottom space needs to have a neighborhood that lifts up to the top space, and what about the left most point of the circle?  Well, up above that neighborhood just winds around between the top and bottom copies:

Still a cover: each of those pink things up above are homeomorphic to the bottom cheek

Still a cover: each of those pink things up above are homeomorphic to the bottom cheek

The fundamental group of the circle is the integers, so maybe using geometric group theory (or algebraic topology, really) we can come up with conclusions about the integers using facts about the circle or the line, and vice versa.  In fact, there’s a correspondence between group structures and covering spaces!  With some conditions, covering spaces correspond to subgroups of fundamental group.

Let’s see how this correspondence works in our example with the integers.  We know that the even integers are a subgroup of the integers, and so are 3\mathbb{Z}, 4\mathbb{Z}, etc.  In fact, these are all of the subgroups (and the trivial subgroup, which is just the element {0}).  Above, we drew two covering spaces of the circle: the real line, where each neighborhood of the circle has infinitely many homeomorphic copies hanging out in the real line, and the circle wound around itself three times, where each neighborhood has three copies.  The number of copies is called the degree of the cover, and sometimes one says the cover is an n-fold covering.  You can wind the circle around itself times for any n, which will correspond to the n\mathbb{Z} subgroup.  How does this correspondence work?  Well, looking at the degree three/3-fold picture again, if you go around the covering circle once, you’ll project down to going around the base circle three times.  So if you go around the covering circle and count, you’ll get 0, 3, 6, 9… In contrast, the real line corresponds to the trivial subgroup (and is an infinite degree cover), and it’s called the universal cover of the circle.  Every space has a unique universal cover, which is a covering space with trivial fundamental group.

Now a preview of why we’ll like this.  Sometimes spaces are tricky and not fun and it’s easier to look upstairs at a cover, and then go back downstairs.  Let’s let the downstairs space be two circles pinched together at a point.

Pink and green above correspond to copies of neighborhoods downstairs

First, you should get convinced that the picture above is a cover; I colored the homeomorphic copies in order to highlight what’s happening.  Also, pretend the branching part goes on forever, a la the Cayley graph of the free group on 2 generators:

from wikipedia

So here’s an example: let’s say we have a path downstairs that goes around the green circle several times.  And maybe we don’t want this path to hit itself over and over again, so we look at a cover upstairs so it turns into a line instead.  So instead of just being immersed (locally injective), the path is embedded (injective) in the cover upstairs.

The orange scribble downstairs goes around the green loop over and over again, hitting itself.  Upstairs, it's a line and doesn't it itself

The orange scribble downstairs goes around the green loop over and over again, hitting itself. Upstairs, it’s a line and doesn’t hit itself

Next time I write about current math research, I’ll be using covering spaces a lot!  In fact, one of the main questions is this: if you have a path downstairs that hits itself (is immersed), what’s the minimum degree cover you need to ensure that the path is embedded in the cover?  This question isn’t explicitly answered yet for loops on surfaces, but the research I’ll blog about gives some bounds on the degree.

Controversy at Yale

10 Nov

I graduated from Yale in 2010.  There’s a fairly sized controversy going on at Yale right now, and I wanted to write down some thoughts and link to some articles about it.  Regular math post coming later this week.

I. News and background.  Gawker has a notably good and unbiased summary of what’s been going on over the past two weeks.  The New York Times has more details, but is more editorial (word choice matters; here’s an article unrelated to this topic that really says why).  If you don’t feel like clicking, the short story is that a committee of Yale people from all over the school (athletics, LGBT coop, various cultural organizations, various religious organizations) sent out a pre-Halloween email suggesting that students be considerate of others when choosing their costumes.  Quick excerpt:

Yale is a community that values free expression as well as inclusivity. And while students, undergraduate and graduate, definitely have a right to express themselves, we would hope that people would actively avoid those circumstances that threaten our sense of community or disrespects, alienates or ridicules segments of our population based on race, nationality, religious belief or gender expression.

 The culturally unaware or insensitive choices made by some members of our community in the past, have not just been directed toward a cultural group, but have impacted religious beliefs, Native American/Indigenous people, Socio-economic strata, Asians, Hispanic/Latino, Women, Muslims, etc. In many cases the student wearing the costume has not intended to offend, but their actions or lack of forethought have sent a far greater message than any apology could after the fact…
In response to this, an associate master (wife of the sort of head of student life) of one of the residential colleges (super-dorms) sent out an email to all the students of that college.  Another quick excerpt from that one, though I’d like it if you’d read both of these emails in full (they aren’t that long).
As a former preschool teacher, for example, it is hard for me to give credence to a claim that there is something objectionably “appropriative” about a blonde-haired child’s wanting to be Mulan for a day. Pretend play is the foundation of most cognitive tasks, and it seems to me that we want to be in the business of encouraging the exercise of imagination, not constraining it. I suppose we could agree that there is a difference between fantasizing about an individual character vs. appropriating a culture, wholesale, the latter of which could be seen as (tacky)(offensive)(jejeune)(hurtful), take your pick. But, then, I wonder what is the statute of limitations on dreaming of dressing as Tiana the Frog Princess if you aren’t a black girl from New Orleans? Is it okay if you are eight, but not 18? I don’t know the answer to these questions; they seem unanswerable. Or at the least, they put us on slippery terrain that I, for one, prefer not to cross.
Nicholas says, if you don’t like a costume someone is wearing, look away, or tell them you are offended. Talk to each other. Free speech and the ability to tolerate offence are the hallmarks of a free and open society.
Also (though I won’t discuss this here), an undergraduate was turned away from a frat party where the brothers said “white girls only.”  It’s funny how the story sounds completely different with the same quotes: Daily Beast doubts it and wants a 19 year old to remember exactly what happened when she was a drunk 18 year old, USA TODAY gives the headline to SAE denies claims… instead of giving active voice to the accusers (another instance of grammar mattering), and WaPo gives the headline to the accusing students (also significantly more in-depth article than the other two).
And of course people are in a huge tizzy about this.  You can read articles for hours representing “both sides” of the issue, which is either “safe spaces vs. freedom of speech” or “systemic oppression.”
II. My personal intellectual thoughts- the gist of this is that people are very upset about two separate issues.  So I’ll just try to articulate those two issues.
First, a September article from the Atlantic, “The Coddling of the American Mind,” really primed the stage for one issue- the idea that creating overly safe, even unrealistically sheltered, spaces for discourse on college campuses in fact ruins the chance for an open discourse because it stifles what people can or can’t say.  An example of a reasonable-sounding article on this side is from Katy Waldman at Slate, who also graduated from Yale in 2010.  Here’s the last op-edy paragraph of her mostly news article:
But horrified emotional responses aside, it’s troubling to see the Christakises scapegoated for defending the crucial liberal tradition of free speech. That’s not to dismiss the pain of students of color; I’m sure Yale proves far less hospitable to them than to the wealthy white scions it was founded to serve. Nor should anyone mourn the days of good old college fun, when wearing a racist Halloween costume was considered a harmless bit of white wing-spreading. But in censuring the Christakises for wanting to create “an intellectual space,” students are vociferously exercising the very rights—to speak out against people and practices they find objectionable—that the Christakises seem to want to protect.
But no one asserted that students should not be questioned about offensive costumes––only that fellow Yale students, not meddling administrators, should do the questioning, conduct the conversations, and shape the norms for themselves.
So in both the Slate and Atlantic pieces, the authors are defending the right of intellectual discussion and the right of Christakis to send an email with her thoughts on meddlesome administrators.  They think that a safe intellectual space is one where students can speak freely to each other and engage in meaningful dialogue, rather than one where all controversial words have been edited out.
 A further branch of issue 1 is the infantilization of Yale students (the meddlesome administrators, the coddlers).  So there have also been a few articles suggesting that Yale students need to learn to be adults to figure out issues amongst themselves, which is in line with Christakis’s email.  Not gonna lie, these articles are really long and I only skimmed.  Also they come from the same publication, and I’m clearly trying to post a diversity of articles.
My thought on issue 1 (not the further branch): sure, it’s an issue.  But it’s not the issue at hand, as much as it may appear to be.  People talking about this issue are talking about something entirely different from the people they’re supposedly reacting to.  Also, snarky facebook post sums up my feelings on issue 1.
The second issue is related to the first, but requires more context than I’ve given so far.  This rather powerful piece on medium written by a Yale senior gives a good feeling (if not specific examples) of this second issue-systemic and chronic racism.  Excerpt:
The reality is that students at Yale have been speaking up about serious racial issues on campus for many, many years — long before Erika Christakis even set foot here. But chronic racism isn’t newsworthy. It quietly whittles away at the hearts and minds of people who feel like they’re not being heard.
This second issue is what protesters are actually protesting about, rather than just the email (so more along the lines of the party).  If you read the email above by itself, great.  Now read the annotated version of it, by a Yale alumna of color.  Regardless of if you agree with her reading or not, you can, I’m sure, believe that she and others do in fact read the email in that manner.
There’s been a fair amount of back and forth between the people talking about the two issues.  In response to issue 1 saying that students should self-regulate, an article about whose burden education is (not the non-white people).  Excerpt:
And while there are many students of color willing to actively engage with their white peers on issues of race, there are many for whom this is little more than unpaid and emotionally taxing labor. Ethnic and racial minorities have every reason to believe that white peers will be hostile to the idea that they’re behaving in racist ways.
III. So Yen, where do you stand?
If you’ve been keeping up with my blog the previous excerpt might sound familiar to you- I’ve said before that it’s not my job as a woman to represent all women and help men figure out how to deal with women.  I’m going to use an anecdote to let you know where I stand.
On Nextdoor a neighbor was upset that two separate women he had passed had not said hello back to him, and he thought they were being rude.  Several people agreed that the neighborhood is going down the tubes (ha!).  A woman responded with a thoughtful and long post about what it’s like being a woman walking down streets- a lifetime of catcalls, propositions, harassment, and the occasional kind hello.  Suppose these passerby women had, like me, just moved to these suburbs from a major city and constant harassment.  We are taught (by experience) to not engage men who try to engage us on the street.  [Fun fact I have been mugged with a knife!]  This is obviously different in my sleepy suburban neighborhood, where the offended man lives.  Anyways, the point is that we engaged in some useful dialogue and most people were understanding of different cultures once they listened/asked questioned/mostly listened.  And also, that a woman chose to compose a long post to explain this to someone.  And also, this comment thread ended up being 46 comments long and, being in Texas, guns showed up.  And it was long and difficult and people got really pissed, but the end result was good.
Here’s where I stand: depending on if you’re an issue 1 or issue 2 person, you’ll read my previous anecdote differently.  But hopefully you’ll agree that at least one person changed his mind on something.  Yes, there’s a lot of crazy going on.  But this is how change happens (hasn’t everyone at Yale taken an amazing history class?)- through discourse and dialogue and, yes, conflict.  And yes, people will disagree on the method of discourse/protest, and spend a long time dissecting the “right” way to engage instead of actually engaging.  But change is happening at Yale, and it’s thanks to these protests and discussions and crazy articles.
Sigh.  I realize that the previous paragraph does not actually tell you where I stand.  Bill Clinton was our amazing commencement speaker for graduation, and I still remember him saying this:

The only place where we’re bigoted now is we only want to be around people who agree with us. You think about it. And in our media habits, we go to the television stuff, we go to the radio talk shows, we go to the blog sites that agree with us. And it can have very bizarre consequences. Hawaii, the State where President Obama was born, has done everything they can to debunk this myth that he wasn’t born in America. They’ve done everything but blow up his birth certificate, put it in neon lights and hang it on the dome of the Capital. But 45% of registered Republicans still believe that he is serving unconstitutionally. Why? Because they’ve been told that by the only place they go to get information.

I force myself to listen to people who disagree with me, and to try to get into a fact-based mode. So I will say again, I think that this is an enormous opportunity for you, but you have to understand just about anything you think is wrong with the world can be categorized as a result of too much inequality, too much instability, or too much unsustainability.

So the mission of every citizen, not just in the United States, but every empowered person in the world in this time has to be to build up the positive and reduce those negative forces of our interdependence. Whenever anybody asks me, what’s your position on x, y or z, I have this little filter that automatically runs the question through and I ask myself will it build up the positive and reduce the negative forces of our interdependence? If it will, I’m for it. If it won’t, I’m against it. And I think it’s really important to think about that.

I try to seek out opinions different from my own, and I want to understand where others come from.  That’s why I have so much written up there for issue 1, and almost none written for issue 2.  My thought: this email/party situation is simply the straw that broke the camel’s back, and people are focused on the straw instead of the camel.

IV. Related topics/keywords: There is so much to unpack here and y’all, I’ve got to get back to math!  But if you’re interested, think about what is cultural appropriation vs. appreciation (Macklemore? Dressing up as Tiana?  Dressing up as Tiana with blackface?), intersectionality of gender and race issues, the whole Calhoun college thing and while you’re at it calling people at Yale “Master”.
V. Personal Yale anecdotes
My first week at Yale, our freshman counselors (some seniors in the college) threw us a welcome party with the theme “Linen and Seersucker.”  You were supposed to wear your linen or seersucker clothes.  I did not know those were clothes terms at the time.  It was uncomfortable.
Before that student-run party was the official Freshman Dinner at our college.  We dressed up, met the Master at his house, and walked through the courtyard to the dining hall.  I should mention that our architecture is Georgian and people have remarked that it looks like a Southern plantation.  [Our rival college with identical architecture was once called the Pierson Slaves.] Once in the dining hall, we sat and were served by the dining staff, who were all black.  Let me underline this for you: we were dressed in our finest, walked from the master’s house to the dining hall in a beautiful plantation-looking building, and then were served by a bunch of black people.  Yeah, it was uncomfortable.
My anecdotes are crappy (I did leave Yale for an entire year and have a remarkably poor memory), so I suggest you go look for more if you are interested.  In fact, I’ll leave you with thoughts from people on the inside, op-eds from the Yale Daily News written by people who obviously love Yale:
(Oh and a facebook post from the Yale Herald, diversity of publications yo!)

Soooo many podcast recommendations

5 Nov

Some housekeeping: I changed all these random feminism/articles/race/other stuff posts to a new “Life” category and un-“Math” tagged them, so that everything tagged with Math is now actual math.  I also put anything that has to do with cooking into “Baking” because that’s the name of the blog even if it’s not factually accurate.  New page for “Life” posts to follow.

Now that I live in Austin, I drive instead of bike to campus.  In total I spend about an hour to an hour and a half per day in my car, so I thought I’d start listening to podcasts.  I highly recommend theget podcast from my friend Ivy, which only has three episodes so far.  Here’s a list of recommendations from my facebook friends so you don’t have to ask your facebook friends for recommendations.  I put the words I didn’t write into italics.  I also feel like this list really reflects the makeup of my facebook friends (sorry E, I cut your classical music podcasts).  Also, I binge-listened to podcasts over the past two weeks to try to put in as many of my own comments as I could.

Instructions for those of us new to podcasts: i-World step by step instructions, Android go find a third party app


  • Welcome to Night Vale “Prairie Home Companion meets Stephen King”, a very weird existentialist scifi podcast with really great indie music, 30 min episodes twice a month. Make sure you start at the beginning so you can follow all of the relevant storylines and have some hope of understanding the in-jokes.  Also there’s now a book.
  • Serial — enough said.  This incredibly popular podcast flew past me when it was being made, but maybe I’ll catch up.  But maybe not because I don’t like tension (I told this to a friend of mine when he asked what TV shows I watch.  I only watch comedies because I get really sweaty and can’t sleep if there’s any tension.  Somehow I make it through Sherlock, but only if I’m holding my husband’s hand, and then he complains about the sweat).
  • Undisclosed —goes more into details about problems with the States case against Adnan Syed. They sometimes pretend that they are unbiased, when they very clearly aren’t, which is a little annoying, but it’s still interesting.


  • The Moth funny story, I had tickets to see this live and was about to get on my bike to head to the bar, but then ended up biking to the ER for a kidney infection instead.  Worst bike ride I’ve ever had (stabbing pain each time I pedaled). So I haven’t heard this live.  But I’ve heard it on the radio and loved it (if you live in Chicago, NYC, or SF, go see Too Much Light Makes the Baby Go Blind; she’s the storyteller I heard on the Moth).
  • Harmontown–by the creator of Community.  I wikipedia’d this and it seems like an asburd, improv-y short show.  I listened to a single 4 minute joke and loved it.
  • Mystery Show- every episode the host solves a new mystery that cannot be solved by googling. For example, one guy found a very unique belt on the ground when he was 10 and wanted to track down the owner after 25 years. Interesting stories but there is only one season so far.  I actually listened to one of the episodes of this and LOVED IT.  I laughed out loud and unexpectedly choked up in the middle of her meandering conversations with strangers.  This was one of the best things I’ve ever heard.
  • Thrilling Adventure Hour– an old-timey radio show that ran for a decade.  A decade!
  • Limetowna fictional narrative in the style of Serial
  • Criminal — stories about crime
  • Strangers-– about meeting strangers (I think this is non-professional people tell stories to the hosts, but I’m not sure)
  • StoryCorps— non-professional people tell stories to/with family members.  I’ve read the transcripts of this and agree with my husband’s analysis-the stories are disappointingly, infuriatingly short.  They’re so interesting and you want it to go deeper, but then it abruptly stops.
  • This American Life — the most popular podcast in ever everyday; everyone loves Ira Glass.  (I tried to link to the website but got a weird error).

Quiz shows:

  • Wait Wait Don’t Tell Me weekly NPR news quiz show, absolutely hilarious, good way to keep up with American news.  This is recorded in Chicago and we watched it live, which was so fun.  We’ve listened whenever we can catch it on Saturdays/Thursdays.  I recommend this one a lot.
  • Ask Me Another — this is another weekly NPR quiz show, with word games and general silliness.  My friend was on this!  Also a fun one (though not as good as WWDTM)
  • You’re the Expert — Possibly about science- comedians trying to guess what professors study.


  • The Rachel Maddow Show — they always have the audio available, for free, of the most recent show. Only if you’re into liberal political news, obviously, but Rachel Maddow’s really super smart, does a really good job of explaining the background of current issues in the news, and her interviews are both really fair and really skilled.  Honestly I doubt I’ll ever listen to this; I’m not into political news.
  • History of English —a bit dry sometimes, but I’ve learned a lot.
  • The Allusionistand anything else in the Radiotopia network because they explore everyday things in a very interesting way.  This seems to be about linguistics.  I am intrigued.
  • A Way WIth Words— seriously it’s all about words!
  • Backstory Podcast —really great American history podcast
  • Stuff You Missed In History Class — Years ago I used to listen… and I really liked it for awhile (but then got tired of it).
  • You Must Remember This I can’t personally vouch, but my boss tells me (focusing on secret/forgotten histories of 20th century Hollywood) is really good
  • Revolutions— about revolutions throughout history.  Basically this entire category is a “doubtful” for me to ever listen.

(Science) Nerds:

  • No Such Thing As A Fish — 30-45 minutes each week, the researchers for a popular British quiz show called “QI” come together and talk about the most awesomely random stuff they learned doing research that week. Most of these researchers, by design or by chance I don’t know, also double as professional stand-up comedians, so the podcast is both super interesting and absolutely hilarious.  We listened to part of this, but it wasn’t as snappy as WWDTM or the podcasts in the next category.  I’ll try again some other time.
  • Meanwhile in the Future: from Gizmodo and one of my favorite science writers Rose Eveleth, it starts with a fictional account of a potential future scenario (what if we started genetically engineering humans to combat climate change, what if we didn’t care about gender any more, what if wind turbines took enough energy from wind that it affected global wind patterns) and then talks to experts about whether it could happen and what would have to lead up to it and happen as a result of it… also Rush Limbaugh thought Meanwhile in the Future was real policy suggestions instead of interesting thought experiments.  I found this one really interesting!  I really liked it and it’s quite well done and I recommend it!  And it’s quite short; 15 minutes or so. 
  • The Story Collider: like the Moth but for stories/storytellers with a connection to science…some really interesting science related stories.
  • Stuff You Should Know: By the HowStuffWorks people- they explain stuff!
  • RadioLab— I should note here that lots of people love RadioLab, but I do not.  This podcast sort of scared me off podcasts a few years ago because there were too many sound effects and I got overwhelmed.
  • TED Radio Hour— TED but in radio format
  • Invisibilia- about the invisible forces than change human nature.  Also has just one season so far, of six hour-long episodes.  I’m listening to it right now.  It’s awesome.  Very well-researched.
  • Hidden Brain— essentially psych experiments/studies on the brain.  I’m interested, haven’t listened yet.

Race, Feminism: (“social justice warrior” actually sounds super badass to me)

  • PostBourgiean excellent podcast where some younger (like our age or a little older) black individuals talk about race, gender, class, media, politics, etc. If you listened to the This American Life about Ferguson schools, they did a follow up interview with the woman who reported that story (Nicole Hanna Jones ?).  This is funny because the first three podcasts I listened to were young black people talking.  And I loved them.
  • Call Your Girlfriend:  is two smart, wonderful, feminist ladies talking about everything from their life updates to pop culture to politics and is by far my favorite podcast of the moment…it feels like you’re in your kitchen listening to your two best friends talk…has me thinking a lot about gender, sexism, and racism lately so it was right on point. The conceit of the podcast is these 2 women who are best friends but living on opposite coasts so they call each other and record it while drinking wine, talking about their period cramps, nyt’s articles, and Kanye West.  Three separate people suggested this podcast to me!  I listened to part of one and it reminded me of the get (so that’s probably a compliment to the get because CYG is huge).  This should probably be in the next category but they make money.
  • Slate’s Double X Gabfestfor covering lady-centric topics in an entertaining, reasoned way, plus the soothing nature of June Thomas’ voice.
  • Show about Race is amazing.  I’m both excited and trepidation-filled about this one.
  • Start Up season 2 follows two young women who are trying to start an online dating company with an interesting concept. Addresses a lot of interesting things like racism in online dating and sexism in silicon valley.

Friends chatting and making a podcast:

  • theget: two black young women talk about politics, pop culture, and whatever they want in a feminist light.  I get a shout out at the end of the second and third hour-long episodes!  (this could also fit in the previous category)
  • Brand New Podcast: My friend Brittani talks with her other friend in her car about stuff
  • Dinner Party Download, a little mix of everything. They describe themselves as “The Dinner Party Download is a fast and funny hour of culture, food and conversation designed to help you win your weekend dinner parties.” and how can you not like a podcast that opens with Dad jokes?
  • Millennial podcast– (a podcast about a woman learning to navigate her twenties).  This is actually one person but it still seems to fit in this category
  • Monkey and the Minotaur — my friend MJ messing around with her fiance: it’s fun to make podcasts!  A designer and a historian discuss philosophy, culture, and design.

Pop Culture:

  • Pop Culture Happy Hourmy favorite pop culture podcast.  I listened to this on the way home today, but wasn’t that into it.  It’s a roundtable discussion and/or an interview about books, TV, music, movies, radio, etc.  It feels more like meandering conversations rather than super-produced stories.
  • Popaganda a feminist pop culture podcast. Their episode on privacy was amazing.  
  • Reply All- a show about the Internet. I promise it’s more interesting than it sounds… it can be both hilarious and thought provoking.  I listened to one episode of this, and it was both interesting and pleasantly short, about half an hour.

Work and Money:

  • Open Account: SuChin Pak interviews people about money, but I just listened to the first episode and it was about so much more than money.  Lots of feminism and self-confidence and humor.
  • Working which is a Slate podcast about what people do all day. They basically talk to various people with jobs that are either unusual or unknown and find out what’s involved and how they do them and how they get in to them. Which, put that way, sounds kind of boring but it’s actually fascinating, in large part because the interviewers are really good (although the third season apparently has a new interviewer)
  • Planet Money–Two people suggested this one, about money and economics.  It’s only 15-20 minutes long.
  • Freakonomics— using economic tools in possibly questionable ways to examine questions about daily life
  • Death, Sex, and Money— interviews with people about life

Random But Specific Topics:

  • On Being – philosophy!  You will love it.
  • Song Exploder – musicians taking apart their songs, about 15-20 minutes.  We listened to the Death Cab for Cutie one, but it was a bit drier and self-serious than I expected.  This seems good if you’re really into music/musicians.
  • All Songs Considered – 40 minutes about music.
  • The Longest Shortest Time they are authentic true stories about parenting that I really enjoy even as a non parent.  I love parenting clickbait crap (“best pregnancy Halloween costumes!” was open in my browser a few minutes ago) and I LOVE this podcast.  Listened to the one about accidental gay parents and I was completely enthralled and emotional.
  • Judge John Hodgman because who doesn’t want to listen to John Hodgman, the guy who played the pc in the Mac v. PC commercials, adjudicate disputes and make up fake internet law. He is funny and surprisingly insightful and thoughtful.  Was this the guy in the NYT Magazine?  Or was that Ozzy Osbourne?
  • Rendered which is unfortunately over, but the old episodes are still available. A great podcast about DIY.
  • The Mortified Podcast Adults reading embarrassing things they wrote as kids. Need I say more?  Oh my gosh this was HILARIOUS and we LOVED it.  Definitely recommend this.
  • Futility Closetbecause their tag line explains it all: “An idler’s miscellany of compendious amusements”, 
  • 99% Invisible– Design and architecture
  • Very Bad Wizards- moral psychology and moral philosophy
  • Dear Sugar Radio- advice from Cheryl Strayed and Steve Almond
  • Savage Love— Dan Savage, love and sex advice.
  • You Are Not SO Smart— about self delusion and psychology
  • The Bugle: (if you like John Oliver especially)

Thank you to all my friends who heeded my Facebook cry for help!  They are: Catherine, Erin, Laura (congrats on getting married I did not realize your last name had changed), Ellie, Tom, Jeremy, Lindsay, Evelyn, Andrew, Jessica, Paulina, Megan, Joanne, B, Kate, Jessica, Vivian, Angela, Jackie, MJ, Dinah, Meredith, and David, and they live all over the US (and UK and HK) and all do different things and are overwhelmingly female.  Interesting.  I didn’t notice that until I typed all their names.

International Day of the Girl was October 11th- late is better than never?

27 Oct

This Day of the Girl thing started two years ago.  I remember that Google Chicago was having an event for it, but I did not attend.  I feel like I remember very clearly the things I choose not to do, but I have a remarkably bad memory for the things that I actually do.  For instance, I have a friend I visit every time I go to San Francisco, but I’m not sure how many times I’ve seen him.  At least once, but I probably didn’t nap and sleep and have coffee and have dinner and have breakfast all at the same time.  He remembers each interaction quite clearly though.  So I’m an asshole.

Anyways, this post isn’t supposed to be about me.  I’m a woman now, suckers!  I think I’ve mentioned before that I’ve been incredibly lucky in the educational opportunities I’ve been given: Project PRIME which no longer exists, but is similar to this program for 4th-7th grade girls interested in mathematics in the Twin Cities (I learned about spherical geometry when I was 10, at a Saturday workshop!), UMTYMP where I took the standard high school math curriculum during middle school and was subsidized by the state of Minnesota, great calculus courses at my high school where we got college credit, and the opportunity to take several more college courses across the street at CSUF while I was still in high school (for $3.50 each course, if I remember right).  And of course I won the lottery that is getting into Yale, and I studied abroad for math, and did some undergraduate research, and taught some math, and got into grad school, and was encouraged to go, and the point is that I’ve been very lucky throughout my life.  And very few people are this lucky.  And very, very few girls are this lucky.  That’s my take on Day of the Girl.

Here’s a company’s take on Day of the Girl:

Currently, 36 percent of high school students within the United States are not ready for college-level sciences. Misha Malyshev, CEO of Teza Technologies works with nonprofits to curb that number. International Day of the Girl is a great time to celebrate the women in this field, and every field, and recognize the opportunities allowed to girls.

Day of Girl

I’ll try to follow the suggestions of the infographic (this company randomly emailed me and asked if I wanted to see it, and I said yes, and that’s how it’s on the blog now).  In that whole educational bio paragraph up there I embedded all the math programs I was part of.  Here in Austin, girlstart is pretty amazing and in this department we have a Saturday Morning Math Group as well as an occasional Sunday Math Circle.

So yeah.  Girls are cool.

A few nights ago I went to dinner with a few postdocs and another graduate student.  This was remarkable because we were all women!  We traded war stories and discussed our experiences as women in math, and it was so so nice to interact with people who had similar experiences to mine.  Every school I’ve been to has a women in math-type group which usually is open to men joining in as well.  This sort of supportive community helps lots (not all) women grit our teeth and stick to it.  And we’re women!  When we were girls we were so much less confident and self-assured, and (some of us) needed a guiding hand or supportive push to keep us in math.  I really really appreciate all the help I’ve been given/earned throughout my life, and I think everyone deserves at least a chance to do what they love/figure out what they love.

Related old post.

My mom’s goi cuon (Vietnamese spring rolls)

26 Oct

Apologies for the long delay in blog posts.  I have no excuses, really.  I’ll make up for it by trying to post a lot this week.  This afternoon I’m planning on chatting with a postdoc friend about some math for a blog post!  In the meantime, here’s a cooking post.

I get a lot of compliments on the sauce that accompanies these light, fresh spring rolls.  Peanut, hoisin, onion, garlic are the main players.  Usually I make a bunch of goi cuon as an appetizer for a party, though the other night we ate a bunch of these for dinner and they make a great light dinner.

The end (of the onion) is nigh-fed (pronounced 'knifed' in case you thought that said nigh fed)

The end (of the onion) is nigh-fed (pronounced ‘knifed’ in case you thought that said nigh fed)

It’s also nice because you can throw out all the ingredients on the table and people make their own rolls with whatever they want.

First, you’ll want to boil a piece of pork.  I had a hunk of pork leg leftover in my freezer that I used for this.  Something without too much fat, but with a little bit of fat (so like a tenderloin but with more fat).  If you want to boil the first (so boil just the outside of the pork, then toss out the water and boil it to cooked with new water), you can do that to minimize the smell, or just throw half an onion in the water.

You heat the water. Por que? To cook the pork!

You heat the water. Por que? To cook the pork!

It takes surprisingly long to cook a hunk of pork.  This took about 25 minutes at a low steady boil (not a simmer).  But that’s fine, because I did everything else during that time- prep veggies, make sauce, make noodles and shrimp.

Do you think a group of Irish people in Argentina would be called Garlic?

Do you think a group of Irish people in Argentina would be called Garlic?

Consider putting a pot of water on to boil after putting the pork in, so you’re ready for the noodles/shrimp.  Anyways, minced onion goes in a pan with a bit of oil as long as you can stand in (the more caramelized, the better!), then add minced garlic until fragrant.  Toss in a can of diced tomatoes (I used fresh because I had them), peanut butter, hoisin sauce, and enough water so it can actually simmer down and the tomatoes cook away.

These tomatoes were being really fresh with me so I told them to simmer down

These tomatoes were being really fresh with me so I told them to simmer down

You’re left with a delicious, sweet and salty and umami-sauce for dipping.  I’ve used an immersion blender on this sauce to great effect in the past, but since it was just for us two I let us eat it chunkily.  My mom also likes squeezing a lime into it, for some acid to cut the richness of the peanut butter.

While that’s simmering away, hopefully your secondary pot of water has got to boiling, and you can toss in some noodles (bun tao or whatever kind of rice noodles you want) and cook per package directions.  Shrimp boils for just 2 minutes or so, depending on the size (until it’s opaque).  Rice noodles are very thin and slippery, so I’d recommend getting a metal strainer instead of just a plastic colander.

Making Vietnamese food was a huge strain before I got this piece of kitchen equipment

Making Vietnamese food was a huge strain before I got this piece of kitchen equipment

A colander just coldn't cut it

A colander just coldn’t cut it

You’re almost there!  Time to thinly slice the pork…

Whaddup, homeslice? Not much, I'm about to get eaten. Oh... that doesn't sound great.

Whaddup, homeslice? Not much, I’m about to get eaten.
Oh… that doesn’t sound great.

And peel the shrimp.  My mom likes cutting them in half, which is a lot of work but also looks nice.

To serve, place your proteins, noodles, and veggies on a table along with rice paper and a bowl of WARM water (or one of these cool things).  Also small dishes for the dipping sauce and a plate for rolling for each person.  For veggies: lettuce is a must, also something crunchy like pickled shredded carrots (shred carrots, add some rice vinegar and sugar and salt and water and leave in a bowl for at least an hour), or sliced apples, or sliced cucumber or bean sprouts.  Spearmint, shiso leaf, and cilantro are all good.  If you’re at a Vietnamese grocery store, just get everything that’s labelled “rau sống” and try everything to see what you like.


Apples are snappy and the spoon is saucy, but the noodles are just limp. They are poor conversation partners.

To eat: wet the rice paper.  Some recipes say to leave it in the water for 5-10 seconds, which is way too long in my opinion unless the water isn’t warm.  Just dip it so that every part of the rice paper is wet; it will soften on your place as you assemble the roll.

About 1 inch from a side, make a line of herbs and lettuce.  Put on about a tablespoon of noodles, a few pieces of pork, and whatever else you want.  About one inch above the rectangle, place the peeled shrimp in a line.

Fold the bottom side (the close one) over your rectangle, then fold in the sides and roll it up like a burrito.

They see me rollin'... they hatin'... because they're jealous

They see me rollin’… they hatin’… because they’re jealous

My husband likes putting the sauce directly inside the roll, which makes sense if you’re going to eat it immediately and aren’t making these ahead of time.  I like dipping them.  Either way is fine.



My mom’s goi cuon: this recipe makes about 10 rolls, so dinner for 3 or appetizers for 10.

1 lb Pork leg/shoulder/some cut with a little fat on it

1 onion

1 apple and/or carrot and/or cucumber and/or bean sprout, sliced/shredded

1 can tomatoes

3 TB peanut butter

3 TB hoisin sauce


1/2 lb shrimp

herbs: half a head of lettuce, cilantro, shiso leaf, coriander leaf, spearmint, peppermint…

rice paper

rice noodles

  1. Boil the pork with half the onion and a spoonful of salt and a spoonful of sugar for about half an hour or until cooked.
  2. Make the sauce: dice the onion and saute in some oil until translucent, then add minced garlic until fragrant.  Add tomatoes, hoisin, peanut butter, and enough water to thin, let simmer until tomatoes are cooked down.
  3. Cook the rice noodles according to package directions (boil for 4 minutes, rinse with cool water).  Boil shrimp for 1-2 minutes until just opaque.
  4. Serve noodles, pork, and shrimp with vegetables and rice paper and a bowl of warm water.

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