## Assorted stuff I’ve been reading

4 Mar
• On the insecurity of manliness: Actual title is “Is there anything good about men?”  Interesting speech from 2007 with a couple of good points in it.  It’s a bit long, and parts of it have become outdated, but I still enjoyed the read (Thanks Chris!).  In fact, in 2007 I took an Intro Psych class and first learned about evolutionary psychology, which used evolution to explain differences in men/women and their sex drives.  Since then, I’ve read a few places about how evo psych depends too much on social constructs, and if you measure just physical outputs (e.g. blood flow to genital areas) and ignore what people say (which is constrained by what they’ve been taught growing up), sex drive becomes much more equal.  At one point in this 2007 article the author says

It’s official: men are hornier than women.

I just googled “are men hornier than women?” and came up with this 2013 book saying the opposite.  (Now I want to read this book!)

• On challenging the status quo with lots of vocabulary words I don’t know: Actual title is “Feminism and Programming Languages.”  I’m not a usual Hacker News reader (believe it or not I don’t like spending a lot of time on the computer in general), but Jeremy Kun pointed me to this a few months ago and asked for my thoughts- the article itself has lots of vocab words, but the comments are interesting.  One summed up the article well:

This article raises the question: ‘where do our ideas about what programming languages should be like come from?

I’ve done some, but minimal programming in my life.  This isn’t really my field, but I find the above question intriguing because you can replace ‘programming language’ with ‘mathematics’ or really anything.  Or as Jeremy asked me:

Do you feel like the direction of mathematics, what questions are asked or believed to be important, what’s relevant and irrelevant, is shaped by male dominance of the field?

In other words, are there other paths in mathematical inquiry that you feel ought to be taken but aren’t, and that this could be linked to the fact that all the leading researchers are male?
Short answer to question one: yes, absolutely, completely.  Mathematics doesn’t care about us humans, but we certainly care about it.  The directions of research, grant money, what gets published in top journals: everything follows trends that we as a mathematical community create and enforce.  And we are dominated by males, so yes, the male perspective does shape where we’re going and what we’re doing.
Question two is more complicated and not the same as question one.  What “should” we be doing as mathematicians?  What is the goal of mathematics?  I can’t pretend to know the answers to these questions, or even if satisfactory answers exist.  We do what we do, we pursue what we find interesting and are either rewarded by our peers who also think it’s interesting, or not, and we have to find something else to keep the money and publications coming in.  If we were living in the world of Y: The Last Man, would mathematics be different?  Probably.  Better, worse?  Who can say?
That said, stereotypes aren’t so much about people totally projecting things that completely aren’t there but about people having a framework with which they interpret things that actually are there. It’s not that racism causes people to see (for example) belligerent teenage boys where there are none, but that a white belligerent teenage boy is just seen as himself while a black belligerent teenage boy is part of a pattern, a script, and when people blindly follow the scripts in their head that leads to discrimination and prejudice.

Look, we all know that there’s a trope in the movies where someone of a minority race is flattened out into just being “good at X” and that the white protagonist is the one we root for because unlike the guy who’s just “good at X” the protagonist has human depth, human relationships, a human point of view—and this somehow makes him more worthy of success than the antagonist who seems to exist just to be good at X.

So we root for Rocky against black guys who, by all appearances, really are better boxers than he is, because unlike them Rocky isn’t JUST a boxer, he has a girlfriend, he has hopes, he has dreams, etc. This comes up over and over again in movies where the athletic black competitor is set up as the “heel”—look at the black chick in Million Dollar Baby and how much we’re pushed to hate her. Look at all this “Great White Hope” stuff, historically, with Joe Louis.

So is it any surprise that this trope comes into play with Asians? That the Asian character in the movie is the robotic, heartless, genius mastermind who is only pure intellect and whom we’re crying out to be defeated by some white guy who may not be as brainy but has more pluck, more heart, more humanity? It’s not just Flash Gordon vs. Ming the Merciless, it’s stuff like how in the pilot episode of Girls Hannah gets fired in favor of an overachieving Asian girl who’s genuinely better at her job than she is (the Asian girl knows Photoshop and she doesn’t) and we’re supposed to sympathize with Hannah.

On the gendering of toys, or the free market.  Also videos here, which I highly recommend.  IF YOU CLICK A LINK IN THIS POST CLICK ON THIS ONE.  My fiance suggested there’s no malice in the Lego Corp., just a desire for more sales- gendering the legos may have caused an uptick in sales.  This is the hard part about the free market: of course Monsanto is going to trademark its crap, it wants more money.  Obviously Lego is going to divide the market and embrace stereotypes: they see what Barbie is doing and they want a piece of that money too.  At some level, corporations have a responsibility to society, but that seems totally unenforceable without governmental regulation (part of the point of government).  We just watched the Lego movie and loved it, but we’re also keenly aware of the Bechdel test and female characters in everything =(

I just want my kids to not feel like there’s a monster in them for being female, or half-Asian, or whatever.  Quoting myself

This particular little monster is the one that says boys save the day and overcome obstacles and girls get rescued, even when they try to save the day.  Or the one that sees the handwriting on the exam and braces itself for a bad proof.  The one that thinks you’re more like Amy and not like Penny at all (from Big Bang Theory, a show I actively hate for reasons I’ll go into later if ever), but that wants to be “normal.”  It’s the monster that says you don’t know what you’re talking about and you don’t know what’s going on so why even try.

Wow really long post!  In honor of my officemate, here are a bunch of red panda pics.

Click on photos for links to original sites

## An open problem in group theory

25 Feb

My last post was about Hee Oh‘s talk at CIRM from that conference I went to last month-it actually covered the first third or so of the first of four lectures she gave.  Étienne Ghys gave seven short talks on his favorite groups, which was a huge blast, so I thought I’d try to share some highlights.  This post is a surprisingly simple open problem in group theory, which talks about functions on a circle.  A circle!  Who would’ve thought we still don’t understand everything there is to know about circles?

Who knew? This guy! This is me attempting to draw a smug circle.

If you don’t know what a group is, check out my quick intro post for some examples.  Wikipedia also has a significantly more exhaustive page.

You may remember that I once did a series of posts 1, 2, 4, on the homeomorphisms of the torus.  You don’t need to read all the posts to get this post, I just wanted to point out that at one point I used the notation $Homeo_0(T)$ to indicate the homeomorphisms (continuous functions with continuous inverses) of the torus which are isotopic (wiggle-able) to the identity.  In fact, $Homeo_0(T)$ is a group, very related to the group we’re discussing today.

Instead of homeomorphisms, we can also talk about diffeomorphisms: these are homeomorphisms which are differentiable, whose inverses are also differentiable. Rather than dive into a definition of differentiable here, I’m just going to give you an intuitive definition: differentiable functions are “smooth” instead of chunky.

Top is smooth and a differentiable. Bottom isn’t; there are weird kinks in its frown

Some functions are differentiable, and some aren’t (see illustration above).  You can also take second and third and n-th derivatives, and we say functions are n-differentiable if it’s possible to take derivatives.  So in the above example, the red rectangle function is at least 1-differentiable (maybe 2 or 3 or more), but the blue function isn’t differentiable at all.

Notation time: we call a circle $S^1$, the sphere in one dimension.  So a hollow ball would be $S^2$, and so on.  In this post, we’ll be talking about twice-differentiable diffeomorphisms of the circle that preserve the orientation of the circle: so if a point is clockwise from y is clockwise from z, then f(x), f(y), and f(z) are also in clockwise order.  This group is written $Diff^2_+(S^1)$.

Great, now we know the group we’re talking about.  Now let’s get into the nitty-gritty of the problem.  First, a subgroup is a subset of a group which is itself a group.  For instance, a subgroup of the integers, $\mathbb{Z}$ under the operation of addition, is the even integers, $2\mathbb{Z}$.  This is because adding two even numbers gives you an even number (2+2=4).  In contrast, the odd integers are not a subgroup of $\mathbb{Z}$, since adding two odd numbers gives you an even number (3+5=8), which doesn’t lie in the set of odd integers.

Next, we need the concept of a normal subgroup.  FYI, mathematicians really care about normal subgroups: they give us lots of insights about the structure of groups, and they help us cut up groups into smaller, more manageable chunks- lots of times we’ll prove things about normal subgroups in order to say something about the larger group.  We start with a subgroup, call it N.  Then N is normal if for every group elements and in N, $xyx^{-1}$ is also in N.  The $x^{-1}$ means the inverse of with respect to the group operation.  So in the integers under addition, the inverse of 2 is -2, because 2 + (-2) =0.  In the real numbers under multiplication, the inverse of 2 is $\frac{1}{2}$, since $2 \cdot \frac{1}{2} = 1$.

In our example, the even integers is a normal subgroup of the integers (you can convince yourself of this).  It’s pretty easy to find subgroups of most groups, but finding normal subgroups (which aren’t just the identity element or the whole group) can be a little harder.  We say a group is simple if it has no non-trivial normal subgroups.

So here’s the open problem I promised at the beginning: Is $Diff_+^2(S^1)$ simple?

And if you want, here’s another one: is $Homeo (D^2, \partial D^2, area)$ simple?  Those are homeomorphisms of the disk that fix the boundary circle and respect area.

I just find it crazy that we don’t understand everything there is to know about functions of a circle or of a disk!  It’s amazing!

In terms of personal blog time, I did in fact bake last weekend, a lot (we were at a vacation rental house full of bakeware), but I didn’t take photos.  Mostly I baked the cookies, plopped them down in front of our awake and lively friends, and went to bed every night- turns out I’m not great at adjusting to living at 9000 feet.  Day one was those awesome salty shortbread cookies, day two were 3-ingredient peanut butter cookies with added peanuts and chocolate chips, and day three were double chocolate bacon cookies which I totally screwed up on but were still delicious.  Ten people made it through a pound and a half of butter in three days, which is glorious.

## Introduction to Apollonian circle packings (tangent)

17 Feb

This is not my area of research at all, but I think it’s super cool.  The first time I heard of Apollonian circle packings was at that conference I went to in Marseille last month, during the first lecture of Hee Oh’s minicourse.  So here’s a quick write up  background of the first third of that lecture.

These packings and all this theory come from one dude, Apollonius of Perga, who wrote a bunch of math books back around 200 BC.  Literally this math has been around for 2200 years.  Here’s a paper submitted a month ago which is a generalization of Apollonius’s problem from circles to spheres.  Math is so amazing!  We live in history!

To understand the problem, we’ll have to do a quick geometry brush up.  We say that two shapes or curves or lines in the plane are tangent if they touch at exactly one point.

Left: tangent; line hits circle at exactly one point.
Center: not tangent, line hits circle at two points
Right: not tangent, line doesn’t hit circle

So, here’s a theorem of Apollonius: Given three mutually tangent circles (so each one is tangent to the other two) in the plane, there exist exactly two circles tangent to all three of them.  Remember, this theorem is from 200 BC or so.  Here’s a picture representing the problem:

We’re so sad! We want more mutually tangent circles!

Woohoo! Found two! (there’s a little hot pink one in the middle)

A few other ideas that immediately come to mind if you see this theorem: what if the circles aren’t mutually tangent, but just lying around the plane? (per Wikipedia this is the actual Problem of Apollonius)  What if you use spheres in the three dimensions instead?    What if instead of circles you use other shapes?  Can we tell, given the radii of our first three circles, how big the other two will be?  These are all big problems in math that many people have thought about (but I have not).

Here’s a cool thing that can happen: if you take three mutually tangent circles, per the above theorem we can draw two more that are mutually tangent to them.  Now if you take one of these new circles, and two of the other ones, per the theorem again we can draw two more mutually tangent to those three.  See picture below.

Adding the pink circle, which is mutually tangent to green, orange, and purple

Then you can do this over and over again: for instance, we’ve still got lots of circles to build which are mutually tangent to three of the circles in this picture (how many did you count?  I count eight on first glance.  Remember that the dark blue and light pink circles, for instance, aren’t tangent, so you wouldn’t count a triplet with those two in them).  And then once you build those new circles, you get more circles.  Do this forever and you have an Apollonian gasket, a type of fractal.

I’m not going to build an Apollonian gasket to show you, but the internet has lots of pictures.

Wikipedia: click on image for link

Fractal Science Kit: click for link

I just wanted to put in the pretty pictures.  Let’s prove Apollonius’ theorem!

Review: the complex plane looks like the real plane, with coordinates (x,y), but the y-axis represents multiples of the imaginary number i, where $i = \sqrt{-1}$.  So if you see a coordinate like (2,3) in the complex plane, it represents the complex number 2+3i.  If you aren’t that familiar with i, you can think of it like a variable.  So in algebra, if you wanted to simplify the expression 3(x+4), you would have 3x+12, not 15x nor 15, because the x lives on its own.  Similarly, we add complex numbers like this: (2+3i) + (5-7i) = (2+5) + (3-7)= 7-4i.

If we add a point at $\infty$ to the complex plane, we’ll get the extended complex plane, $\mathbb{C} \cup \{\infty\}$.  One way to think of the extended complex plane is as a big ball, with the point at infinity at the north pole, and the origin (0,0) at the south pole, the unit circle (the circle with radius 1) lying on the equator, and the rest of the complex plane wrapping around to get closer and closer to infinity.  This way of thinking about the extended complex plane is called the Riemann sphere.  You can drop it back down to the complex plane by drawing a line from a point on the sphere to the point at infinity, and figuring out where the line hits the sphere.  In more concrete terms, imagine putting a tennis ball on a piece of paper.  Use a marker to draw a point on the tennis ball, then use a super high power laser and shine a line from the north pole of the tennis ball to hit that point.  You’ll burn a hole in the paper, which is exactly where the corresponding point on the complex plane lies.

Wikipedia is great.

Circles in the plane might look a little different on the sphere.  Lines can go through the point at infinity, just like any other point.  Here’s a picture of two circles that are tangent at the point at infinity:

The blue and red circles both wrap around the sphere.

If we project these circles down onto the plane as we were saying before, you get parallel lines: the point at infinity heads toward “infinity” in all directions.

So now we have a few new configurations for tangent circles.

Here’s a fact: if you multiply all the points in two tangent circles in the extended complex plane by a matrix $A=\begin{pmatrix} a & b \\ c & d \end{pmatrix}$ so that $A(x+iy) = \frac{a(x+iy) +b}{c(x+iy)+d}$, the resulting circles will still be tangent to each other.  A condition you need is that ad-bc=1 for this to be true, which can be a bit tricky since a,b,c, and d are all complex numbers.  More facts: if you’ve got any two circles, you can always find a matrix that will send one circle to another one.  You can actually do this for any three circles to any other three.

Okay, now we’re going to prove the theorem.  Take your three tangent circles, and choose a matrix A to map them to two parallel lines with a circle in between them.

Where do we put mutually tangent circles?

This makes it pretty clear that there are only two choices for mutually tangent circles.

Adding the blue and green circles!

Now multiply everything by $A^{-1}$ to send the pink circle and parallel lines back to your original three circles.  From our first fact, when we multiply the blue and green circles by $A^{-1}$, they’ll still be parallel to the pink circle and parallel lines.  So that’s all the ways you can find circles mutually tangent to three given, mutually tangent circles.

That’s your introduction to Apollonian circle packings!  I will probably never blog about them again, unless I randomly see another talk on them.  This was the first quarter or so of the first lecture by Hee Oh.  Other references: wikipedia.

P.S. Sorry that I’ve been doing such a bad job over the past few weeks of blogging every week (I think I’m averaging every 9 days).  I moved in with my SO three weeks ago (yay!) and am still trying to figure out how to live with someone with whom I want to hang out all the time.  Also we don’t own lots of baking ware (I just bought a glass pyrex casserole dish, which we didn’t have before.  We don’t have a cookie sheet.  We had to buy some measuring spoons.)  So I haven’t been baking as much.  And I can’t seem to find my camera battery charger!  It’s a little hectic.  Happy winter!

## Fractions are hard, or way too many brown butter cookies

8 Feb

Sometimes I have parties at my house.  I enjoy hosting people, and I especially enjoy feeding people.  There usually comes some time between 10 p.m. and 2 a.m. when there’s no more food but still plenty of people, and I get bored of my friends antsy to bake.  I threw a party to celebrate moving out, so of course at some point I stopped what I was doing and made brown butter cookies.

I bet Fall Out Boy would love these cookies. We’re going brown, brown… sugar we’re going brown baking

I love brown butter with some sage leaves, tossed over gnocchi or pasta, so I wondered if brown butter cookies would work out.  I didn’t have a lot of people over, which meant I didn’t want to make 5 dozen cookies, so I decided to divide the recipe by four.  Totally reasonable.

Start by melting your butter: two cups divided by four is half a cup, or one stick.

Foam, foam on the range, where the butter and the pots play, where seldom is heard, a discouraging burn, and the skies are the ceiling all day

It’ll foam up and then die down, and you just let it cook for a few minutes until it turns a beautiful brown.

There used to be some loose tea in this bowl, but it vacated when the butter moved in. If I look into these patterns, can I read how tea leaves?

While the butter is browning, toast up some pecans, either on the stove in a hot pan with nothing in it (stir every thirty seconds or so) or in the oven.  I went with oven.  Takes a few minutes in either case.

Hear hear, a toast! We didn’t think P. could, but yes, P. Can!

Set aside about two tablespoons of the butter for icing, then mix all your ingredients except for flour together with the butter, starting with the brown sugar.

Brown butter-brown sugar. I can’t remember if I used brown eggs- guess I browned out. (This is a double entendre but not a sexual one).

Then add the flour.  Here’s what I did: the original recipe called for 3 cups of flour.  I looked at it and thought, oh, 3/4.  Inexplicably, I then multiplied 3 by 3/4 to get 9/4, or 2 and a 1/4 cups of flour, which I then dumped in.

Hippies need to leave- there’s way too much flour power going on here

“That’s weird…” I thought.  These cookies are WAY too floury to hold together.  It took me another few minutes to figure out what had gone wrong.  Frankly, I was amazed I’d done something so bone-headed.  (This is funny because there’s a really big bone in our heads, and I’d be concerned if someone didn’t have a skull.)

Of course I wasn’t going to give up on these cookies now.  So I halved the recipe and did everything again (because 1/4 + 1/2 = 3/4, a fact that I triple checked before I restarted).

Now the dough was a reasonable texture, and a dropped tablespoon at a time baked for ten minutes resulted in beautiful, buttery, brown cookies.  Mix the set aside butter (now there should be about 6 tablespoons) with some powdered sugar (I used around 3/4 cup) and a dash of vanilla, and use it to frost the cookies.  Apparently you were supposed to mix hot water in there too, which I didn’t realize until now.  Given how well I’d done earlier in the night with reading comprehension, I shouldn’t be surprised I messed up another step.

Anyways.  These cookies are super delicious and ridiculously rich and buttery.

Brown butter cookies, recipe poorly followed but turned out great from all recipes:

3 sticks of butter (1 and 1/2 cups)

1 1/2 cups brown sugar

1 egg

vanilla

1 tsp baking soda

1/4 tsp baking powder

2 1/4 cups flour

handful of chopped pecans (I used the rest of a bag in my freezer)

1 cup confectioners sugar

Melt butter and let foam and die down until it’s a rich brown color, then pour into a big bowl.  Take out 3/4 cup or so and put in a small bowl, set aside.

Preheat oven to 350, toast pecans if you want them.

Mix the butter with the brown sugar, then add the rest of the ingredients except for flour, pecans, and powdered sugar.  I like putting in a liberal amount of vanilla- maybe 1/2 TB.

Stir in the flour and pecans.  Drop onto a cookie sheet and bake for 10 minutes to get a slightly crisp outside and soft middle.

Mix the powdered sugar with the set-aside brown butter and another dash of vanilla until frosting-like.  Recipe says to add hot water, which would make it easier to spread and icing-like.  If you need more powdered sugar, do so.  If it’s too sugary, add some water.  Use to frost cooled cookies.

## I actually followed a recipe: banana bread

30 Jan

Well, I made it into muffins, but close enough.  And I liked this recipe so much that I sent it to my brother (he asked for it)!  To make it clear how big a deal this is, I’ve never seen either of my siblings bake something besides a frozen pizza or a box of au gratin potatoes.

Anyways, when visiting my brother’s house in California as a wonderful respite from our polar vortex, I noticed he had three very brown bananas sitting on the counter.  Obviously, time for banana bread!  Always delicious and easy.  And my favorite: one big bowl and a little one only!

Can you SPOT the main difference between this picture and this one? I’ll give you a hint: it’s in all caps in this caption.

Dark brown/spotted bananas are very sweet and mushy, so great for banana baking (I’ve also used mashed bananas to lower the amount of sugar in a recipe).  Plus they’re so easy to mash!

I was going to make a double batch, but Santa Claus came by earlier and I decided to encourage his healthiness by giving him bananas instead of cookies. So you aren’t seeing the FOUR Nick ate. Maybe I just wanted to make a dirty pun.

I invited Bruce Banner to come by and fork these bananas for me. I was just curious if, after the Hulk comes around, he points at everything he did and yells HULK’S MASH!

So you start by mashing the bananas, then mix in some melted butter (melting it takes the small bowl).

BETTY BOTTER IS FROM 1899. In case you’re not aware who Betty Botter is, she’s most famous for putting approximately this amount of a superior version of this product into her batter, hence making it better.

Beat an egg in the now vacant bowl, and add that along with some sugar (I went with less) and a dash of vanilla (I forgot this and the world didn’t explode).

It seems to cost more and more for ingredients these days… guess you could call it a bowl market.

I love that one of the lines from the recipe is “Sprinkle the baking soda and salt over the mixture and mix in.”  Because most times recipes required you to whisk these guys into the flour before you add it, which is such a pain (requires another bowl).  It does avoid pockets of baking soda/salt, but so does sprinkling!

Call me Jean Claude Van DAMN this is a great action shot! (sarcasm) (+pun!)

Mix all that up.  My brother and sister in law own this Pam baking spray stuff.  I’ve never used spray fats (I like my olive oil and butter and lard and I throw them in all my food generously), but this was AMAZING!  WOW!  So easy to grease the pan!  I forgot to take an action picture, but rest assured it was incredible.  I think it’s important, if you go this route, to get the ‘for baking’ one or else your stuff will taste like olive oil or whatnot.  Generally when greasing pans I wipe around a pat of butter, because that is delicious, or some vegetable oil (olive oil has too strong a flavor for greasing, in my opinion).

I put a heaping 2 TB of batter into each mini muffin spot.

I was looking for one of these pans for myself the other day, and searched for “4 x 6.” Then realized that I was in the postcard section of the store.

We devoured most of these very quickly (it’s about three bites) before dinner, but here are some of the survivors from twenty minutes in the oven and an hour outside of it:

And my adorable nephew showing one off!

Quick and easy banana bread recipe from simplyrecipes.  All I did differently was bake mini muffins for 20 minutes instead of an hour for the loaf.  I figured since I did no doctoring I should just link to the original: here it is again.

## Math talk etiquette; also, hello from France!

20 Jan

I’m skipping a poster session right now at this incredible conference  to take some time when there aren’t 100 peoples’ faces around me (does this happen to other people?  I just need to *not* see a face right now), so figured I’d write a quick post while huddling in my room.  Also, I’m in math heaven again (MSRI was the last time I was in math heaven), only this time the rooms are in the building, and they feed us delicious French food for all our meals.  CIRM is pretty amazing and if any mathletes out there are reading this, I highly recommend finding a conference taking place here and going.

By now I’ve been to many math talks (and I hope to go to many more!) and I’ve picked up on some random math etiquette that beginning grad students/undergrads might not realize.  So here’s my list.

ON THE BOARD

• Write Thm: [Last name-last name of people who wrote it] theorem here.
• Names go alphabetically.  Because we’re math!  None of that first authorship/last authorship of other fields.
• Speaking of underlining, underline all words that are defined too.

IN THE TALK

• Always include history.  I didn’t realize this until I got to graduate school.  It gives your talk context and shows respect for those who came before you and made your research possible.  Plus it’s pretty awesome.  Exceptions if it’s a very short talk.
• Always thank the organizers/inviters at the beginning and end.
• One mathematical joke is really great.  Two is okay.  Three gets to be too many.  Zero is also great.  Even if you’re a huge goofball, it seems like mathematical audiences can only stand so many jokes (but we do love them).
• Speaking of jokes, people love cultural in-jokes.  I heard three jokes about the number of saunas in Finland when I was at a conference in Helsinki, and it’s still funny.  If you’re American and reading this, avoid cultural jokes.  If you’re not, have at it!  I especially enjoy when, to skip a long calculation, speakers write “beurk” and explain that that’s French for “yuck”
• Beurk!  It’s better to be too basic than too advanced.

IN THE AUDIENCE

• If you suspect you will fall asleep (some of us are pros at this), don’t sit in the front.  Also, try to avoid that head flopping thing.  Either commit to the sleep if you’re falling asleep, or commit to not falling asleep (I don’t know how to do that).  Everyone has fallen asleep at some point during a talk.  My friend just told me that it was slightly comforting to have me fall asleep beside him just now, as it reminded him of the many classes we’ve taken together over the years.
• Ask questions.  If the speaker doesn’t see your hand, it’s not rude to call out “excuse me” or “sorry” or “can I ask a question?”  Plus if you leave your hand up and the speaker keeps not seeing you, it makes everyone uncomfortable.
• Don’t leave.  If you’re not sure if this talk will hold your interest for the whole time, but are still interested in coming, sit in the back and bring a paper to read or some work to do.  Be discreet.  Exceptions to the don’t leave rule: you or your partner is having a baby or a medical emergency, you really have to use the bathroom.

There’s lots and lots of other resources for this: this page from the Topology Students Workshop (which I attended two years ago) has links to all sorts of do’s and don’ts (I like Dan Margalit’s a lot).

I’ll try to do the thing I did last year when I was at this conference (it was in Haifa, Israel last time) and type up some notes.  I’m really enjoying Hee Oh’s minicourse so far, and Apollonian circle packings are a great and pretty topic for a blog post for non-mathers (and the rest of my notes might be useful for mathers).

## Procrastinating…eggplant lasagna

16 Jan

I can’t find an original source for this but I think it’s funny. Picked up from reddit

I’m giving a talk tomorrow in my advisor’s little seminar and I’m definitely doing that silly thing where I’m too unprepared and panicky about it, and hence rather than preparing I’m procrastinating (because the thought of preparing makes me realize how unprepared I am).  That’s a universal problem.  My specific problem is that this paper by Olshanskii is SO COOL and has all the things I like (functions between graphs, some combinatorics, some algebra, lots of pictures) and yet the talk I’m preparing is SO BORING.  Somehow I sucked all the fun out of the paper and now my talk is joyless, which is exactly what you *don’t* want to do when teaching or talking.  It’s like listing all the ways to integrate functions without ever saying why integration is so awesome.  Giving someone that flowchart above without a picture of an integral.

Inspired by my friend Ellie, I tried to make eggplant lasagna.  It’s nice because my former-Paleo SO likes to avoid pasta, so I have yet to make regular lasagna (which my wonderful mom used to make all the time).

Yknow how to make these beautiful red fruits seem grosser? Say the name aloud with a stress on the first syllable. TOE-mato. Ugh. Just imagine toenailmatoes.

I don’t buy tomato sauce, though it seems so convenient and I’m all for convenience!  I just know I’ll never finish a jar before it goes bad and I hate throwing food out, while diced tomatoes or whole tomatoes in a can last approximately forever.  So the first thing to do is make some tomato sauce.

Step one: dice up some garlic.  If you have a garlic press, good for you!  We got one for Christmas and I promptly broke it.  I pushed too hard?  Here are some up close photos of how to peel garlic: press the flat side of a blade against the clove, and the peel will pop right off.

Then start to fry up the garlic in a little bit of olive oil until fragrant.  I added some oregano, basil, and red pepper flakes.

It’d probably burn your tongue if you (gar)LICKed this up

Pour in a can of diced tomatoes (I like the fire roasted ones sometimes).

Sauce is hard to apPOURtion out

Though portable, I wouldn’t take this all the way to SAUCE-alito. I mean, it’s probably too much liquid for the airline and CA is far.

Season with some salt and pepper, let it simmer for a bit while you slice up your eggplant.

Have you stopped by the waffle factory lately? I hear there’s a lot of great things coming out of that EGGoPLANT.

Some people recommend salting your eggplant for awhile to leach the bitterness out, but I’ve never had a problem with bitter eggplant.  If you want to do that, slice em all and throw em in a strainer and sprinkle a bunch of salt all over that for half an hour.  I have zero patience so I also skip this step.  Another good step: roast the eggplant ahead of time (see the zero patience thing).  Roasting eggplant here.

I was thinking of a lemon pun BUT THEN I DISCOVERED THAT LEMMINGS ARE SO CUTE. CLICK ON IMAGE.

Now that your sauce is all simmered, give it a taste.  Apparently I added some onion to it at some point (how about that!) and a squeeze of lemon (never hurts).  I also like adding a bit of sugar to combat the acidity/bitterness of tomatoes.

Throw the sauce aside, and soften some diced onions in your pan with some olive oil.  Then throw in some sliced mushrooms (I’m lazy and buy the pre-sliced ones which always say you should wash them, which makes me think that’s beside the point of buying them presliced).  You could also put in whatever veggie here: zucchini, yellow squash, red or green peppers, etc. etc.

What if you built a cross between an RV and a dogsled? Then you’d have a MUSHroom

Once that’s cooked, throw in some spinach.

When spinach goes to a concert in LA, it prefers the WILTern

I grabbed all the cheese-like products in my fridge, which was: half a ball of mozzarella, a pack of cream cheese, some shredded parmesan, and some greek yogurt.  I mixed it except for the mozzarella with two beaten eggs, some olive oil, and a tablespoon of this weird basil paste I bought.

There’s some alright bases out there (10, 2 for binary, 3 for Cantor set proof)… but for sure the most sweet is base ILL

Then mix your cheese mixture with the veggies in the pan.

And layer tomato sauce, eggplant, cheese mix, tomato sauce, eggplant, cheese mix, tomato sauce, and top with sliced fresh tomatoes and mozzarella cheese.

Bake at 350 until cheese is bubbly, 20 minutes or so.

This was so yummy!

Eggplant lasagna:

1-2 eggplants

1 can tomatoes + cloves of garlic + spices OR some spaghetti sauce

1 onion

vegetables: mushrooms, peppers, squash, kale, spinach, whatever…

1-2 fresh tomatoes

some mozzarella

2-3 eggs

ricotta or cream cheese

olive oil

1. If you’re making tomato sauce, make it.  Garlic and onion in olive oil until soft, then add a can of tomatoes, and spices (oregano, basil, red pepper flakes, salt, pepper) to taste.  Let simmer while you do other things.

2. Slice the eggplant.  If you prefer, salt it to eliminate bitterness.

3. Cook the vegetables.

4. Make the cheese mix: beat eggs with some olive oil and cheeses.

5. Layer tomato sauce, eggplant, veggies, cheese, etc.  Top with fresh tomato slices and slices of fresh mozzarella.  Bake at 350 for 20-30 minutes, or until cheese is bubbly and melted.

I’m just going to wake up at 6 tomorrow and write my talk again and make it more exciting.