Begin again to begin

I haven’t been around these parts in a long time, and unlike previous revisits, I’m not going to come here and swear to change things. I’m also not going to begin with the big life update like I used to do: I’m just going to say that things are very different for me now, and that life has a curious way of humbling even those who humble themselves.

So what’s this about, then?

Well, I’m going to aim to use this as an outlet for things, and I’m going to try to keep “things” as math things. I’m going to pursue things that interest me at the time; if I had to guess, I would say that these will almost never be Algebraic Topology.

For now, I’m going to be interested in Thurston’s Princeton Lecture Notes.

Though I have no goals, my immediate plan is to focus on becoming better by working through the details of these notes, online, publicly, for everyone to see. Feel free to come and learn, or to laugh at my failures, or (best for me) to share knowledge that you have. Everyone is welcome.

Stay safe, everyone, and stay tuned for Thurston.

It’s a little late but: Happy holidays, everyone!

I’ve been doing a lot of paid work lately: Lots of web design stuff and lots of Wolfram thangs. Paychecks and rent and what not. Good news.

Math things to come. Soon.

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!

I’ve been quiet again, but not because I’m (immediately) falling into stagnancy: I’ve merely been focusing my energies on other things that have needed to be addressed for a while!

In this case, it’s the building of a new professional webpage. I haven’t done anything to one since 2012 (!!!) and it’s definitely way past time for that to happen. Heh.

Don’t worry, though: I’ve already bookmarked some interesting proofs and I’ve also been working on some new math (that may get a post or two at some point) when not running the usual new resident errands. Busy busy!

Yours in math…

Visiting Philadelphia

So there was a bit of a “math holiday” for me over the last few days as I took my lady and our son to Philadelphia for her birthday. We didn’t do anything too exciting but it was our first time visiting the city (and our first road trip since settling down in Morrisville a couple weeks ago) so it was good times.

And wouldn’t you know – today when I got home, I had a math book waiting in my mailbox! Always good to get an unexpected math haul!

I’ll probably get back into serious math tomorrow…hopefully, anyway…and at least part of my time will be spent studying so-called “locally metric spaces” with my bud L. I’m excited.

Yours in math…

2014 in review

The WordPress.com stats helper monkeys prepared a 2014 annual report for this blog.

Here’s an excerpt:

The concert hall at the Sydney Opera House holds 2,700 people. This blog was viewed about 23,000 times in 2014. If it were a concert at Sydney Opera House, it would take about 9 sold-out performances for that many people to see it.

Click here to see the complete report.

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

Giving “crowdfunding” a shot

Giving “crowdfunding” a shot

I decided to write up a little spiel about myself and my journey through mathematics, hoping to convince some amazingly generous benefactor to share their good fortune. While I’m hoping to procure funding from other sources (always applying, always hoping), it’s good to have another option, just in case.

I’ll try to keep everyone posted on how this plays out. 🙂

You can solve the cube – with commutators!

This is a super interesting read.

Geometry and the imagination

After a couple years of living out of suitcases, we recently sold our house in Pasadena, and bought a new one in Hyde Park. All our junk was shipped to us, and the boxes we didn’t feel like unpacking are all sitting around in the attic, where the kids have been spending a lot of time this summer. Every so often they root through some box and uncover some archaeological treasure; so it was that I found Lisa and Anna the other day, mucking around with a Rubik’s cube. They had persisted with it, and even managed to get the first layer done.

I remember seeing my first cube some time in early 1980; my Dad brought one home from work. He said I could have a play with it if I was careful not to scramble it (of course, I scrambled it). After a couple of hours of frustration…

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The Riemann hypothesis in various settings

So Terence Tao has posted a blog regarding the Riemann Hypothesis. He notes that his blog is one that makes “no new progress” on the hypothesis, but later refers to the entry as one in which he is “simply arranging existing facts together”.
And THAT, ladies and gentlemen, would be the perfect way for someone as amazing as Tao to provide a subtle, suave introduction to a long series of posts, the culmination of which could be an actual proof to Riemann’s actual hypothesis.
Has the already-brilliant Terry Tao solved the Riemann Hypothesis? Stay tuned to his quadrant of internet space to find out….

What's new

[Note: the content of this post is standard number theoretic material that can be found in many textbooks (I am relying principally here on Iwaniec and Kowalski); I am not claiming any new progress on any version of the Riemann hypothesis here, but am simply arranging existing facts together.]

The Riemann hypothesis is arguably the most important and famous unsolved problem in number theory. It is usually phrased in terms of the Riemann zeta function $latex {\zeta}&fg=000000$, defined by

$latex \displaystyle \zeta(s) = \sum_{n=1}^\infty \frac{1}{n^s}&fg=000000$

for $latex {\hbox{Re}(s)>1}&fg=000000$ and extended meromorphically to other values of $latex {s}&fg=000000$, and asserts that the only zeroes of $latex {\zeta}&fg=000000$ in the critical strip $latex {\{ s: 0 \leq \hbox{Re}(s) \leq 1 \}}&fg=000000$ lie on the critical line $latex {\{ s: \hbox{Re}(s)=\frac{1}{2} \}}&fg=000000$.

One of the main reasons that the Riemann hypothesis is so important to number theory is that the zeroes of…

View original post 12,730 more words