Update

Despite my hope to the contrary, it would appear that the math I’ve done while here so far as not parlayed into me blogging super-frequently. For what it’s worth: Life is busy. Just in case you were wondering. ^_^

Lately, I’ve been working from home more than I’ve been going to Princeton/IAS. My goal is to change that soon and I actually had a wonderful day at IAS today. I’d like to go tomorrow but I have a work meeting at the least convenient time one can imagine; there’s also no topology seminar at the University tomorrow, so I suppose I’ll be staying in and working again. No harm no foul, I suppose.

So what have I been working on? Well:

  • Universal Circles for Depth-One Foliations of 3-Manifolds. The gist here is: If you have a taut (e.g.) foliation on a 3-manifold, a theorem of Candel says we can find a metric on all the leaves so that they’re hyperbolic. Moreover, by tautness, you can lift to a foliation of the universal cover which is then a foliation whose leaves are hyperbolic discs. A ridiculously deep idea of Thurston was to look at the infinite circle boundaries of these disk leaves and maybe…glue them together? Canonically? And see if that gives insight about things?

    You probably already know how this ends: It’s doable (because he’s Thurston) and it does provide deep insight about the downstairs manifold (see, e.g., the articles by Calegari & Dunfield and/or Fenley, or Calegari’s book…)

    Now, let’s say we do this for certain classes of kind-of-understood-but-still-unknown-enough-to-be-interesting foliations like those of finite depth. Can we get cool manifold stuff by doing this process? I dunno, but maybe.

  • Homologies. My ATE was about Gabai’s work on foliating sutured manifolds, so studying sutured manifolds is something I’m still interested in. One way of doing that nowadays is with this colossal, ridiculously-powerful tool called Sutured Floer homology. So…you know…homology…but when talking with other grad students about the millions of homologies out there and about how nobody really understands what motivates discovers of them, I realized that there was a lot I needed to know before focusing on one homology foreverever. So I’m working on learning stuff about homologies.
  • Geometric Group Theory. Ian Agol is at IAS this year as the distinguished visitor and a lot of his work is on relationships between GGT and 3-manifolds. If you listen to any talk relating those two things, you realize there’s this whole dictionary of words and acronyms like QCERF and LERF and RAAG and Virtually SpecialResidually Finite, etc. etc. I think in order to someday bridge the gap towards doing work like those guys do, I need to know what all these words mean, and what better time to figure that out than right now?! So yea…I’m doing that some, too.
  • Dirac Operators, Spin manifolds,…. At some point soon, I’m going to start working on hypercomplex geometry again, and part of that will be the study of Dirac operators. So far, there are lots of perspectives on those, so we’re going to try to first establish the explicit connections between them and then maybe…do some stuff? I dunno. I also have stuff on Clifford analysis / geometry I want to look at, as well as some more things involving generalized geometries. Lots here.
  • Topological Quantum Computing. This is a pipe dream until I’m able to feed my family and progress on my dissertation. It’s on the radar, though.

Okay, so this was an update! I’ve also been bookmarking some interesting proofs I’ve run across so I’ll know where to look when I decide to expand things here, and…yea.

Oh! And my professional webpage finally exited alpha and went into beta! http://www.math.fsu.edu/~cstover.

And now, Morrrr…se homology. Morse homology. That’s what I’m looking at as a segue into Floer. Another late night ftw!

Later.

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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…

Settling in with a new life and a new schedule

Today is the fifth full day at our new place and things are finally starting to settle in. Until today, we’d been sleeping/sitting/otherwise living on the floor, for the most part. In particular:

  • A couple days ago, we got our Wifi connected so our internet access went from patchy and occasional to great and full-time.
  • After spending the first few days sleeping on the floor, we got a couple air mattresses on Monday. That came with some slight added comfort.
  • Today, our new couch came in. I can’t overstate how amazingly comfortable this fucking thing is, and believe me when I say: It’s completely changed my whole attitude to have a comfortable place to sit!

As a result of the added couch-induced comfort, I’m letting today be my first day transitioning to The Princeton Schedule of mathing all day and working (for a wage) at night. So far today, it’s been all 3-manifolds and foliations, particularly getting things I ought to already know typed into Mnemosyne so that I can make sure I know know them moving forward.

There’s so much math I should be better at; I’m really looking forward to using this year to bridge the gap from where I am to where I ought to be.

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.
  • 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:
  • 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

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.