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Mathematics

Posts about mathematics. Upcoming conferences, conference descriptions, papers I am reading, papers I am writing, pre-prints, all sorts of goodies. Also some of my thoughts about mathematical education and such.

2009.09.30 10:12:57 BST Ahhh! Cruft discovered in pre-print. Ack, I should've known better. I stayed up a bit later on Monday night than I intended to. I was asked, by Claude, last week, about whether certain cases (in particular the Born-Infeld model) not cove

2009.09.28 15:12:09 BST Causality of generalized wave-maps--paper on arXiv Oh, almost forgot. New paper on arXiv. Gary Gibbons showed via explicit computations using eigenvalues that the Skyrmion equation obeys the dominant energy condition. In my paper, I proved the dominan

2009.07.03 22:41:26 EDT Valentine for the relativity geek This just came randomly into my head (well, while I am trying to think up a T-shirt design). A (really geeky) valentine's day card for your favourite relativity geek: Rμν - ½ R gμν

2009.06.12 11:42:48 EDT Introducing my new blog: Asking Questions After thinking about it for a while, I've decided that I will get a WordPress account. Most of the reasons are given in this post from a few months ago. In any case, this will not mean the death of bl

2009.05.06 16:45:31 EDT Journal: Call me doctor Whoa! I am a PhD* now. I didn't sleep too well last night. I was way too nervous. There was really no reason for me to be though: I do not know (which is different from there doesn't exist) of a case

2009.04.29 19:46:57 EDT Unconventional Derivation of Kerr Metric I've posted one set of lecture notes on an unconventional derivation of the Kerr metric. This is a condensation of the lecture I gave on Apr 23 for MAT 451 in Princeton University.

2009.04.17 18:22:07 EDT Dissertation status: finished! The dissertation is done! Actually I finished it yesterday around 2:30 pm. But I haven't had the chance to blog about it until now. Something about having a late afternoon seminar yesterday, more semi

2009.03.28 17:16:04 EDT A problem in modular arithmetic In an New York Times Magazine article on Freeman Dyson, the following problem is posed: Does there exist a natural number in base 10 where if you move the last digit to the front, e.g. transfrom 12345

2009.03.19 12:02:42 EDT Gowers's experiment and future of blogOhm A remarkable on-line collaboration in mathematics happened recently. Tim Gowers initiated a fairly modest program some 6 weeks ago, trying to get a heuristic justification (or refutation) on how one s

2008.12.16 22:43:46 EST Illustrious company My advisor invited me over for dinner tonight. He wrote the book on nonlinear PDE techniques in the global theory for general relativity. Around the table were also I. M. Sigal, who wrote the book on

2008.11.04 15:54:43 EST Bubbling in harmonic heat flow, a la Struwe; Part I (This is an edited version of Pin's presentation on Michael Struwe's "On the evolution of harmonic mappings of Riemannian surfaces", 1985.) Outline Define the harmonic map flow Gagliardo-Nirenberg in

2008.09.25 15:38:39 EDT Some thoughts on Christodoulou's Formation of Black Holes This has gotta be the quickest I've ever read a paper. After about 2 weeks (8 working days to be exact), I finished "reading" (to be more precise, I skimmed the paper without checking all of the calcu

2008.09.18 14:46:02 EDT The "inverse" of a decreasing, right-continuous function is also decreasing and right-continuous A small math theorem that it took me an embarrassing long while to prove. Quite trivial actually. Theorem Let m be a function from R+ to R+ that is decreasing and continuous on the right. Define f fro

2008.09.10 15:58:02 EDT Some news Good news: With the weather pretty nice outside, it doesn't take long to bike over to the Institute of Advanced Studies. I took it easy on the way over, and the ride was 15 minutes from Fine Hall to S

2008.07.13 22:59:15 EDT Kerr-Newman paper posted on arXiv Finally! I have changed from a consumer of scientific progress to a producer thereof: my first respectable paper has been posted to arXiv. It is on "A space-time characterization of the Kerr-Newman me

2008.05.22 21:17:49 EDT 5-sided Sierpinski Gasket While in the stall attending to some personal business today, I read the graffiti as usual. One particular one is a pretty poor attempt at an Apollonian gasket. Somehow from there I started wondering

2008.04.24 15:37:35 EDT On Doron Zeilberger Scanning through the offered seminars today, I came across an entry that I've already mostly missed (in part because my office hourse): Between 2:15pm and 3:15pm today, Professor Doron Zeilberger of

2008.03.27 10:22:22 EDT New Upper Bound for Rubik's Cube Solutions Posted on the arXiv: Twenty-Five Moves Suffice for the Rubik's Cube. Tomas Rokicki (Stanford trained computer scientist [I didn't know CS can be listed on the Math Genealogy Project...]; logic puzzle

2008.03.25 17:09:51 EDT Some exact integrals Doing integrals are often hard things. Beyond the traditional bag of tricks that include standard change of variables, trigonometric substitutions, and such, there are often integrals here and there t

2008.03.23 13:29:05 EDT Square Root Came across on the web something my dad taught me when I was in 3rd grade that I promptly forgot and "rediscovered" by myself when I was in fifth grade. It is no longer useful in this day and age of c

2008.03.12 22:19:51 EDT Bootstrap argument Yesterday I mentioned the Ken Thompson ACM Lecture in my blog. Now that I am Vicodin-free and thinking clearly, I understood why the concept tickled me so. (Well, it would've tickled me regardless, si

2008.03.04 11:35:54 EST Lorenz v Lorentz I'm not quite sure from where I first heard this: that the proper spelling is Lorenz gauge and Lorentz transformation. The former is named after a Dane by the name of Ludwig Valentin Lorenz, the latte

2008.02.26 15:14:25 EST Walk or Wait redux Several weeks ago I wrote about a paper asking whether to walk or to wait at the bus stop, and proposed some possible generalizations. Apparently someone else also thought about possible generalizatio

2008.01.15 12:46:16 EST Mathematica stupiditiy Goshdarnit! I just did something very stupid. I asked Mathematica to compute a Riemann curvature tensor and print out the out put. But I forgot to tell it to simplify. The result was ... ginormous. I

2008.01.03 14:41:12 EST Walk or Wait? In the paper "Walk versus Wait: The Lazy Mathematician Wins", the authors Chen and Kominers examined the following problem A wants to get from the point 0 to the point d. A has two choices: either it

2007.11.16 14:35:31 EST Crystallographic space groups Today's "What's Happening in Fine Hall" lecture was given by John Conway on crystallographic space groups. An attempt at summary: The talk is motivated by the completion of a ten-year collaborative e

2007.10.15 21:58:03 EDT Black Holes; What Penrose tried and failed to disprove might just as well be true Just found this wonderful little snipplet from an article/lecture by S. W. Hawking. Citation: Hawking, S.W. "The Event Horizon", from Black Holes: Les Astres Occlus Ed. C DeWitt, B.S. DeWitt; 1972, Go

2007.08.20 12:43:32 EDT Philosophical musings on a Monday morning Starting from the Greeks Leucippus and Democritus, plenty of western philosophers and natural scientists alike have subscribed to a deterministic universe. Indeed, the precise laws of Newtonian mechan

2007.08.13 19:56:11 EDT Markus Keel's first lecture, or, how I learned to explain what I do for a living and defend myself against physicists Markus Keel, a senpai of mine (who left over 10 years ago), is back in Princeton for the week teaching Nonlinear Wave Equations and stuff for the program "Analysis and Geometry", an NSF Research Train

2007.04.18 21:15:40 CST Journal: Recap Lots to talk about here, so I'll actually include section headings. More Good Food Sometime around last weekend, I was in my office on the computer, and a westerner knocked on the door and asked in En

2007.04.13 08:38:03 CST Journal Whee! Two wonderful dinners in a row. Wednesday afternoon, Ionescu was invited to give a seminar on some recent stuff he has been studying with Sergiu. The problem is that of unique continuation: in p

2007.04.03 14:05:05 CST Counterexample to endpoint Sobolev embedding A question that has been bothering me a little while, which Ionescu kindly answered: We know that the Sobolev embedding doesn't hold in the end-point case Hs → L∞ when s = n/2. The question

2007.02.14 15:44:06 EST A mathematician muses on power outage I love Eli Stein. About 1 hour and 30 minutes into lecture today, the power went out in the room... Stein: Well, this might bring us to end slightly earlier. But don't panic... yet, at least the alarm

2007.01.10 12:01:14 EST A little pentagon theorem I came up with the following little question while randomly doodling on a piece of paper. TheoremGiven a pentagon ABCDE, for a given side, we call the diagonal of the pentagon which does not share a v

2006.10.10 17:49:22 EDT Knots I have been having a mild depression in the past few days. Mostly because I felt a bit lost: I was not sure what exactly that I should be doing or whether I have been working hard enough. And Math has

2006.08.19 14:13:45 EDT Prisoners and permutations A neat little puzzle (and its solution) at ScienceNewsOnline. The scenario is this: The names of 100 prisoners are placed in 100 wooden boxes, one name per box (assume the are all named differently).

2006.08.16 15:09:26 EDT Office Assignment Office Assignments are out. I will be in 408 Fine next year. The office phone number would be x4219. I'd be sharing it with Kevin, Aaron, Phillip, Zhong Tao, and Pin (with the exception of Zhong Tao,

2006.07.28 19:29:33 EDT More on Poincaré and Ricci flow Related to my post from yesterday about this, it seems that professor Gang Tian of Princeton and professor John Morgan of Columbia also posted a 473 page monograph titled Ricci Flow and the Poincar&ea

2006.07.27 21:13:03 EDT A short history of the geometrization conjecture (Update 07.28: a further development) It seems that I am a bit late on the bandwagon. My friends Aleks and Aaron, both geometric analysts (at least in some point of their careers), confirmed that they

2006.05.18 19:08:23 EDT General exam: barely cleared I made a complete fool of myself. If I were the examiner, I might not have passed me. It was disappointing and horrible. But I passed. Here's a transcript of what happened: Examiners: Sergiu Klainerma

2006.04.25 14:30:50 EDT German exam Okay, passed the second language exam. Now I only have the Generals left to look forward to for the remainder of this semester. Compared to the French exam, the German one was a lot less intensive. Bu

2006.04.05 05:12:33 EDT Notes on Strichartz Finished! Notes on Strichartz estimates here. The last section on application of the inequality to semilinear wave equations is a bit sketchy. The non-casual reader should be able to fill in the holes

2006.03.12 20:04:41 EST Journal: Orthogonality It got a tiny bit colder today, mostly because of the rain. I was originally planning on going out running (first time, like, ever; I decided that it would be a good way to work up my endurance). The

2006.02.28 11:01:46 EST Principle of Least Dog Action An article in ScienceNews reports that a mathematician at Hope College observed a curious phenomenon: his dog seems to know calculus. Tim Pennings (is/was) the chair of the math department at Hope Col

2005.12.04 22:12:34 EST Hurricane Epsilon Paul Erdös would be laughing uncontrollably. Record breaking 14 Hurricanes in this season. December hurricanes are rare, the last one was December 30, 1954. Tangentially related, An Erdös La

2005.11.16 23:11:47 EST Folding Paper: beyond Conventional Wisdom The conventional wisdom: It is impossible to fold any piece of paper, no matter how big, small, thin, or thick, more than 8 times. It has been cited by many sources and quoted often in kids' programs.

2005.11.03 13:38:50 EST Cover's Game In response to my recent post about Monty Hall problems, DJP send me a link to Cover's Game(*). (Courtesy of Harvard CS department CS220r: Cryptography taught by Professor Michael Rabin. For the 2005

2005.11.03 13:12:12 EST Some elementary thoughts on Littlewood-Paley theory Man, do I feel stupid for taking this long to figure it out. Since Qian asked me to look over her paper on the equivalence of Besov norms defined relative to Klainerman-Rodnianski's Geometric-Littlewo

2005.10.28 11:21:00 EDT On the stability of tables This is a problem I actually considered a couple years ago. It stemmed from a discussion I had with my suite-mates my second year at Argonne. Under what condition will a "table" be stable? The questio

2005.10.20 15:38:18 EDT Noether's theorem and Lorentzian Boost A good question about Noether's theorem that most textbooks do not address: what is the conservation law corresponding to Lorentzian boost? We first start with some background material. We are intere

2005.10.20 02:26:27 EDT Monty Hall Problems First, let's begin by looking at the classic Monty Hall Problem You died and went to the purgatory, where the devil himself shows you three doors. He tells you that behind two doors are express hand

2005.10.10 21:07:01 EDT Journal: Yellow Sale Wheee! Cheaper books! I am still waiting to see if Thierry Aubin's Some Nonlinear Problems in Riemannian Geometry will ever be on the yellow sale (151 dollars is way more than I want to pay for that b

2005.10.06 15:24:29 EDT Small combinatorics problem Suppose you start with N objects, you want to choose M of them, M (An application of this question: a pizza store carries 30 ingredients. You are allowed to put only one kind on a slice. A pizza has 8

2005.09.27 16:43:07 EDT Two analysis problems Problem 1: Consider a bounded domain U with C2 boundary. Let f denote a harmonic function in C2(U) that is continuous up to the boundary of U, which we denote by S. Let T be a subset of S, and suppose

2005.09.17 22:46:30 EDT RIP: Serge Lang Whoa! Just found out that Serge Lang passed away on September 12, this past Monday. He is an algebraist, and technically a 先輩(senpai)/學長(xue zhang) of mine: Ph.D. Princeton

2005.09.12 22:05:17 EDT Department Reception; Cooking Journal Today was the reception for first year grads. I woke up earlier than usual (8:30am), showered, dressed, doodled around, had breakfast, and left home at 10:30. Got to school by 11. Spent about half an

2005.09.05 02:34:15 EDT Why many published papers are not rubbish As usual, science reporters exaggerate the findings of a particular researchers in order to make a more shocking headline. New Scientist, the self-proclaimed "World's No. 1 Science and Technology News

2005.08.23 18:49:14 EDT The decline of science in America Harold Evans writes in the BBC about the decline of Science in the United States. If America were to continue on the present trend of catering to the lobbyists of large conglomerates, it will soon los

2005.05.09 00:51:00 EDT Self Referential Aptitude Test The Self Referential Aptitude Test is a self-contained logic puzzle: all the ingredients needed to solve the puzzle is right there. It took me about 15 minutes to find the answer.

© 2004-2008 Willie W. Wong, Sortir en Pantoufles: http://www.math.princeton.edu/~wwong/

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