Fields Medalists and Topology and Thesis Research and…

Today, I spent the day at IAS, listening to Alex Eskin talk about Teichmuller dynamics.

I don’t know why, but I somehow struggle on some deeper level when it comes to that topic. These talks always start relatively similarly with billiards and the (non-)existence(?) of periodic orbits thereof before providing a dictionary between billiards and Riemann surface theory, an introduction to basic notions in ergodic theory (Ergodic, Uniquely Ergodic…), and then – apparently at some point when my brain shuts down – there’s really deep stuff including conjectures by Fields medalists, etc. etc. Somehow, I understand all the pieces before brain shut-down, but even so, the shut down always seems to happen and leave me scratching my head and wondering wtf happened during.

Maybe it’s a tumor.

I’ve been focusing  more on stuff about universal circles. In particular, I’ve found some other documents online that summarize the Calegari-Dunfield paper a bit, and I’ve been using Calegari’s wonderful book to help get new views on things. It’s slow, but it’s progressing way better than it ever has.

Last week, there were three Minerva lectures at Princeton University by Maryam Mirzakhani. The creative ways in which she applies and broadens the scope of hyperbolic geometry is staggering, and as much as I’d like to say I understood a lot of things, I understood very small fragments of a handful of things. It was an amazing experience that I’ll cherish for a long time, but man – I was so tangibly outclassed during that it was almost embarrassing. Wonderful, but (almost) embarrassing.

Besides that, I’ve been working: Mostly boring monotonous things for Wolfram with the exception of breaking Wolfram|Alpha today, and then finally some progress on fixing the very badly-done FSU Financial Math pages. It’s a lot happening, but it’s all mostly enjoyable and I like being kept busy, etc. Always good.

Unfortunately (or perhaps fortunately for my progress on things that matter), I haven’t typed up any more interesting proofs or anything. At some point, I hope I can blog regularly without feeling like I’m missing out on more important things but honestly? Now is not that time.

I hope this finds everyone well, and if I don’t see you again first: Happy holidays!

Had a great first week at IAS. Their math library is fucking unreal and it gave me a chance to read about tons of stuff I should have already read about but haven’t.

The end result is that I did very little in terms of wage earning, and in particular that our savings is down to approximately $0 and if I don’t start earning pay soon we’re going to starve. Even so, the math library here…?

Tomorrow is the first day of the year’s first directed workshop-thing on 3-manifolds (http://www.math.ias.edu/wgso3m/agenda) and I’m indescribably excited about that. I’ve also gotten to a point where I have a schedule in place to earn a livable wage between all that (yay no starvation!) and will hopefully be able to parlay some of the awesome math I’ve been absorbing into things to post here…

…but today is not that day. ::wink::

Yours in math….

Update

I’ve fallen into a bit of mathematical stagnancy since the first week or so of living here but after much ado, I’ve finally become regimented enough to start doing work and doing math and juggling other obligations, etc. etc.

What can I say? Moving is hard business!

Since falling off the mathematical (and career) wagon, I have managed to buy some new math books (uber sale; it’s my weakness) and to completely build a 95%-ish complete version of a new professional homepage which I hope to deploy within a week or so. As of a few days ago, I also managed to climb back on to the career (sans math) wagon, and as of today (well, yesterday; it’s 4:30am “tomorrow” for me right now), I also managed to do some low-key math with my BFF L. Hoping that pans out.

Later today, I’m going to head to IAS and spend the day doing math things and listening to postdocs talk about stuff I’ll likely never be mature enough to comprehend. Hoping this is day 1 of a lot of consecutive days of doing that and/or things like it. We’ll see.

Mathly yours…

Update since the update

The last time I posted something meaningful here (not counting the 2014 year-in-review and the most recent claim of attempting necromancy), it was June 2014 and I was about to embark on a summer of traveling. Around that same time, my son was 21 months old, I was working part-time at Wolfram, and I was a pre-doctoral candidate whose academic situation had gone (apparently without being blogged about) from two doctoral advisors with two separate projects to a single advisor plus a second non-advisor faculty colleague.

Typing that out makes me realize how much has changed.

For those of you keeping score, it’s now August 2015, and 13 months after the last update, lots and lots of things have changed. For example, my son is now one month away from being three years old. There’s also a lot of professional stuff, too. Let’s go somewhat chronologically.

• I spent summer 2014 traveling.
  • I went to an absolutely amazing topology conference at Cornell (and met a Fields medalist).
  • I spent a month learning how to use Mathematica better at a Wolfram summer school.
  • I went to an okay topology conference at CUNY Staten Island.
• Afterwards, I was offered a full-time position at Wolfram as Math Content Developer. I accepted and took the year off from teaching.
• I landed a lead role in a really awesome math-related project at Wolfram.
• I went to a great conference at Yale and really enjoyed New England. New Haven is absolutely incredible.
• I passed my advanced topics exam (ATE) and became a doctoral candidate. My work was on Gabai’s colossal (first) work on Reebless foliations in 3-manifolds, and while I definitely learned more significant math than I’ve ever learned, I feel like there’s so much in that paper than I’m years away from understanding.
• I went to the Tech Topology Conference soon after becoming a candidate.
• Not long after, FSU had a pretty gnarly conference on Clifford analysis.
• I flew up to Baltimore to interview for an NSA gig. I didn’t get chosen.
• I went to the 40th annual spring lecture series at the University of Arkansas and had a complete blast. I ended up slipping on ice, busting my ankle up pretty badly, and having some travel woes near the end but when all was said and done, I met some cool people (Benson Farb, Allen Hatcher) and saw some really great talks. Oh, and great coffee!
• I went to Rhode Island College and gave an invited lecture on limit sets and computer visualization. It was an honor and I couldn’t have hoped for a better first invited lecture experience.
• I finished a pretty uneventful spring semester at FSU. Lots of work. Lots and lots of work.
• Once summer (2015) rolled around, I got accepted to some pretty great things:
  • An MSRI program on Geometric Group Theory. I eventually had to decline this one.
  • Moduli Crossroads Retreat; also had to decline this guy.
  • A Berkeley summer school in diffeomorphism groups. I went there and had an absolute blast.
  • The first annual Chicago summer school in geometry and topology. I can honestly say that this was the best mathematical experience I’ve ever had, and man: What a beautiful city Chicago is!
• I was fortunate enough to be awarded a pair of scholarships from the FSU math department.

And now, here we are! It’s officially September 1 (1:07am now): That means Fall semester has started at FSU (which means I’m now a fourth year doctoral student; eek) and things are back in full swing. It never gets familiar, really, no matter how many times it happens. C’est la vie, I guess.

I’ve got a bunch of stuff going on, professionally:

• I’m still trying to make progress on my dissertation research (3-manifolds and, eventually, foliations).
• I’m studying Dirac operators / spin manifolds / hypercomplex structures / supermanifolds / miscellaneous things that seem to get more and more into the realm of theoretical physics as we progress. This is with my non-advisor faculty colleague.
• I’m trying to get a small research project going with an undergraduate at FSU on topological quantum computing (maybe Microsoft will take interest?).

Non-professionally, things have also happened. I got pretty serious into working out for a bit; later, I lost track due to travels, though I’ve since made some pretty considerable body transformations due to a healthier diet. I’ve also tuned back my Wolfram hours to give me more time to do student things; I’ve upgraded my workstations (desktop and mobile); I’ve made the switch from Windows to Linux (full-time rather than as a hobby)…

…that may actually be about it!

So there! Now we’re caught up! That means that I can pick up next time with an actual update / piece of newness / whatever. And who knows – maybe there will even be some math thrown in here! gasp

Good night, everyone.

PS: Oh! I was also introduced to Mnemosyne by a mathematician considerably better than myself! So far, I’m a pretty big fan.

Random Update, or A Prologue to Travel

Okay, so I’m almost never around these parts anymore. That’s probably obvious to anyone who lands on the home page. Aside from “the random question regarding Hatcher problems” (read: the random pointing out of something very stupid I did when attempting to solve problems from Hatcher), I usually don’t receive many updates regarding this place either. 

Truth be told: This place is essentially a wasteland. That makes me at least mildly sad.

I’d like to attempt to remedy that at least somewhat, and in order to attempt such an endeavor, I’ve brainstormed a plan. Before sharing, perhaps I should preface:

I’m about to be traveling quite a bit.

In particular, I’m going to be leaving on Friday (20 June) for approximately five weeks. My travels will include extensive bus rides that will land me in Ithaca, New York, Boston, Massachusetts, and Newark, New Jersey (en route to Staten Island, NY) and will include a variety of math- and computer science-related things. 

Much excitement is expected on the professional front.

I figure this makes for at least a somewhat worthwhile opportunity to update this thing, though, since I could use it as a sort of travel diary. Truth be told, I’ve never traveled much, so I don’t know what exactly a travel diary entails; I figure I can come here, vomit out some photos and maybe a video diary or two, and hope that the inspiration I get by being surrounded by greatness will provide me the motivation to at least type up a summary entry or two on some fascinating stuff.

Long story short: Ostensibly, I should be able to post without having to rigorously type up mathematics I’m working on (or attempting to work on). That’s a win.

So yea…I’m at T-minus 51(ish) hours before my first bus departs. There’s lots to do, and so I won’t stick around here much longer. I will try to cough up a legitimate update, though; it’d be silly for me to start a travel diary without at least trying to piece together some sort of update on the journey behind the journey.

In the meantime, I hope this finds the internet in good spirits.

Yours in math,

 

C

Foliation Theory Observation I

Observation I. Every article in this field is remarkably long.

I’ve currently got articles whose lengths are 60, 58, 50, 39, 59, 56, 58, 76, and 50 pages long in my “reading queue”. Of the others, there are none that are shorter than 25 pages with the exception of Gabai’s second article (18 pages, though sandwiched between a 60 page original and a 58 page triquel).

One would think that longer automatically implies “more detailed” (i.e., less terse, less difficult to read, etc.), but this isn’t necessarily the case; in particular, Gabai’s articles are ridiculously complex and brilliant and amazing, and even legitimate 3-manifold topologists specializing in foliation theory confess that it takes forever (literally not literally) to make it through even one of them.

My prediction is that when my son’s in college, the average math Ph.D. will take 10 years. Give or take.

Reading, and reading, and teaching, and reading, and reading, and…

So, to summarize the direction of my most recent mathematical endeavors: I woke up and decided that part of my aspiration was to become a geometric topologist, and I did that despite the fact that topology is (far and away) my worst subject.

That sounds precisely as terrible as it probably is.

Been reading a lot.

Reading a lot a lot.

Spending a lot of time on the precalc class I’m teaching this semester, too.

A routine is finally starting to shape up, which means things are getting back to normal; I’m hoping blogging becomes a part of that again. Hoping.

Right now, I’m learning about surface automorphisms in hyperbolic space and working on collecting a library of data about the current status of classifications of manifolds with hypercomplex structures. I’m downloading articles constantly, reading seemingly nonstop, and always feeling behind.

I couldn’t be happier.

Here’s hoping that the new year is being as kind to all you folks!

Updates and the like

Welp, I haven’t been around these parts in a bit. That’s not to say I haven’t been working, though; I’ve just been working through things that don’t necessarily make good reading…

…like math….

Okay, so maybe that’s not entirely true. I have, however, been spending a lot of time on just a couple projects for my advisors and so there hasn’t been an abundance of topics to post about here. I think I’m getting to a point, though, where I can start posting some things here and maybe use that to reconcile the fact that I can’t understand most things I read, etc. We’ll see.

So yea…the semester’s over. It turned out not to be a terrible one for me in the end despite being pretty terrible throughout. The upshot: I managed a 4.0 that semester and ended up with advisors. That’s a victory for sure.

I’ll do my best to come back around these parts in the next day or two and post something of substance. I’d like to try to do some sort of expositing on geometric topology things (foliations, laminations, universal circles) and maybe some Clifford things too; I’d also like to attempt to reconcile my previous goal of learning how to do things from Hatcher. 

Maybe I can do all of the above. 🙂

Until next time….

Stopping in:

1. I exist.
2. The semester is winding down.
3. Business is picking up.

So far this semester, I’ve had a bunch of exams (A’s on all of them), given two seminar talks (one “eh,” one worse than that), and I’ve made progress towards my advisor / candidacy situation. I still have more exams (blah), two more presentations (double blah), and some fellowship things to get done.

I’d like to say that in the midst of all this, I’ll stop by more, say more things, post more solutions, etc., but at the rate it’s going, I’ll likely not be back here until December something-er-other. 

I hope this finds everyone well and that the holidays treat you and yours particularly special.