2011 Winter Learning and Research

Here, I blog about math along with my other happenings (not very consistently). I also keep a summary outlining things I worked on or have accomplished. I try to practice the violin everyday, so it's intentionally left of the record because it's quite regular. Winter 2011 refers to January-April 2011.

Blog

Green Other than math/physics
Magenta Goals
Red Attention!

• Feb 11 (Friday)*
  • Attended a Gmail tutorial.
  • Organized website and added (beginning of) notes.
  • Read Section III.1 of Perrin [Algebraic Geometry].
• Feb 13 (Sunday)
  • Read p.4-9 of Kirillov's paper.
  • Read p.3-4 of Joel's notes.
• Feb 14 (Monday)*
  • Looked over and dealt with my finances -- prep for 5th year.
  • Read p.5-7 of Joel's notes.
  • Extensively explored iGoogle -- mainly for academic use.
• Feb 15 (Tuesday)*
  • Read p.9-14 of Kirillov's paper.
• Feb 16 (Wednesday)
  • Teaching prep for MAT157 -- 2 hours.
  • Read p.14-15 of Kirillov's paper.
  • Emailed my mentorship students.
  • Teaching prep for MAT135 -- 0.5 hour.
  • Read p.7-8 (Finished Section 1) of Joel's notes.
• Feb 17 (Thursday)*
  • Organized the table of contents for my thesis.
  • HHO concert.
  • Read p.8-10 of Joel's notes.
• Feb 18 (Friday)
  • Covered Karene's MAT347 tutorial.
  • Read p.10-12 (Finished Section 2) and p.13-14 of Joel's notes.

READING WEEK
• Feb 20 (Sunday)*
  • Share comment on Zsuzsi's talk.
  • Read p.15-18 of Kirillov's paper.
  • Worked on MathCamp application.
• Feb 21 (Monday)*
  • Read p.14-16 of Joel's notes.
  • Reorganized academic homepage and blog.
  • Read p.63-64 of Bredon, and some miscellaneous paragraphs from Chapter 2.
  • Worked on MathCamp application.
  • Worked on letter to Murty regarding job fair.
• Feb 22 (Tuesday)*
  • Planned trip to Caltech in April.
  • (Over-)Planned the week.
  • Read p.64 of Bredon.
  • Register for RCM Theory Exam -- History 1: An Overview.
  • Worked on MathCamp application (recommender).
• Feb 23 (Wednesday)*
  • Read p.64 and p.66 of Bredon.
  • Started writing notes for "Short Course on Differential Geometry".
  • Worked on planning of trips to Berkeley and Quebec in June.
• Feb 24 (Thursday)*
  • Worked on Section II.1 of Bredon and wrote some notes.
  • Met with mentorship students for the first time: introduced topological spaces and continuous maps.
• Feb 25 (Friday)
  • CONFERENCE @ FIELDS.
  • Reread p.13-14 of Joel's notes.
  • Read some Chapter II of Bredon.
  • Finished Harry Potter Book 2.
• Feb 26 (Saturday)
  • CONFERENCE @ FIELDS.
  • Reread p.14-16 of Joel's notes.
  • Received juggling lesson from Allen.

• Feb 27 (Sunday)
  • CONFERENCE @ FIELDS.
  • Read p.17-19 (Finished Section 3) of Joel's notes.
  • Finished 1st draft of MathCamp application.
• Feb 28 (Monday)
  • Read p.1-2 of Kapustin's paper (done with it for now).
  • Learned about the life of Bach. Apparently, he's contemporary with Handel, but their music has so little resemblance.
• Mar 1 (Tuesday)*
  • Read p.1-3 (Finished Section 1) of Kitaev & Kong's paper.
  • Got 'promoted' at the MSO by John (the conductor). Well, just a much better seat, but the nice thing is that the people sitting around me also seemed to approve of my intrusion. :-)
  • Finished MathCamp application.
  • Provided encouragement to Vika, my loving friend.
• Mar 2 (Wednesday)
  • MAT157 prep: Read p.363-368 of Spivak's "Calculus".
  • Read p.24-26 of [Lauda].
• Mar 3 (Thursday)
  • Booked flight for my Berkeley trip in June; looked into Santa Marta conference in August.
  • Super efficient compared to my normal state: curiously looked through much of [Lauda]!
  • Mentorship meeting #2: We introduced category theory this time, motivated by the example of 'the category of' topological spaces (along with continuous maps between them), i.e. we developed the axioms based on what holds for topological spaces. Then I sketched another example of a category -- the category of vector spaces (along with linear maps between them). The point was to convince Tuan that the notation of a category is in fact more general (or to convey what 'generality' means), and much of mathematics can be looked at via this point of view. Though linear algebra is a very important subject in mathematics on its own.
  • Read p.19-20 of Joel's notes.
  • Learned about the lives of Haydn and Mozart. Mozart was 20 years younger than Haydn but died almost 10 years earlier. I think Mozart was not my type -- overspending and flirtatious.
• Mar 4 (Friday)*
  • Began learning XY-pic from Aaron's Tutorial. It's a really good tutorial as it's exactly the way I like to learn about such things, emphasizing on understanding and hands-on experimentation. Given the way it's taught there (and everything being pretty useful), I think I'll master it pretty quickly.
  • Learned about the lives of Schubert, Chopin, Berlioz and Puccini. Like Mozart, Schubert and Chopin also died young(er).
• Mar 5 & 6 (Weekend) -- Trip to Maryland!
  • Read p.3-4 of Kitaev & Kong's paper.
  • Tried/Practiced juggling with three penguins -- record: 11 counts when the first penguin landed.
  • Discussed with Daniel a geometrical description of transversal gates (for fault tolerance), where topology dictates 'logical' properties; also talked about a similar description for QEC.
  • Visited favourite stores in Bethesda: Apple Store and Barnes & Noble; as well as the Smithsonian National Museum of Natural History in D.C.
  • Learned about the lives of Debussy, Stravinsky, Leonard Berstein and Alexina Louie.

• Mar 7 (Monday)
  • Read p.4-7 of Kitaev & Kong's paper.
  • Read p.20-22 of Joel's notes.
• Mar 8 (Tuesday)
  • (Re)read p.21-23 of Joel's notes. (1.5 hrs)
  • 4 hours of MAT135 MAC.
  • Penguins are my company.
• Mar 9 (Wednesday)
  • Read p.7-11 of Kitaev & Kong's paper. (2 hrs)
  • 2 hours of MAT157 office hours.
  • Provided moral support to a few MGSA event organizers.
  • Read p.23-25 of Joel's notes. (1 hr)
• Mar 10 (Thursday)
  • (Re)read p.24-26 (Finished Section 4) of Joel's notes. (1.25 hrs)
  • 2 hours of MAT135 tutorials.
  • Almost 3 hours of Mentorship meeting #3: introduced the category of vector spaces, similar to #2 but to a different set of students; also described our (unrealistic) "goals".
  • Read p.11-13 of Kitaev & Kong's paper. (2.25 hr)
  • Composed letter to Dror, Jordan and Travis regarding PhD Program Lengths stats and TA workload. (3.5 hr)
• Mar 11 (Friday)
  • Understood p.13-14 of Kitaev & Kong's paper (1 hr), and discussed the paper with Joel (2 hrs).
  • Emailed mentorship students. (1.25 hrs)
  • Game Night!

• Mar 13 (Sunday)
  • Read p.26-28 (Finished Section 5.1.1-5.1.2) of Joel's notes. (2 hrs)
  • Read p.14-16 and p.17-18 of Kitaev & Kong's paper. (2 hrs)
  • MAT157/135 prep: Read p.368-373 of Spivak's "Calculus". (0.75 hr)
• Mar 14 (Monday)
  • Read selection (~5 pages) from Chapters 1 & 2 of Bredon. (1.5 hrs)
  • Voted on 2011-2012 Grad course offers. (2 hrs)
  • Read p.1-4 of Webster's paper (1.5 hrs) -- Introductions are tough reads.
  • organized/overviewed [LK1] and [LK2] (0.5 hr).
• Mar 15 (Tuesday)
  • Read p.2-5 of [LK1]. (2.5 hrs) -- Introductions are tough reads.
  • Had an inspiring discussion over lunch with Laurent Freidel and Lee Smolin about the role and status of TQFTs and categorification in quantum gravity; I am getting interested in the geometric aspect (i.e. connections and Lagrangian) and what 'quantum geometry' should look like. (1 hr)
  • Stressed about parking. (~2 hrs)
• Mar 16 (Wednesday)
  • Read p.5-9 (Finished Section 2.1) of [LK1]. (1 hr)
  • 2 hours of MAT157 office hours; 2 hours of Mentorship meeting #4/1-2a.
  • Received chess lesson from Artem! Systematic and nice! (3 hrs)
  • Dealt with parking issue. (~3 hrs)
• Mar 17 (Thursday)
  • Read p.10-11 of [LK1]. (1.25 hrs)
  • MAT157/135 prep: Read p373-377 of Spivak's "Calculus". (0.75 hr)
• Mar 18 (Friday)
  • Read p.11-15 and p.17-18 of [LK1]. (3.25 hrs)
  • Read p.16 of Kitaev & Kong's paper. (0.75 hr)
• Mar 19 (Saturday)
  • Discussed with Daniel about geometry of Fault Tolerance and QEC. (3 hrs)
  • Read p.106-109 (Fiber Bundles) and p. 267 (Stokes' Theorem) of Bredon. (2.5 hrs)
  • Discussed with Daniel/myself about math, e.g. Grassmanians and categorification. (1 hr)

• Mar 20 (Sunday)
  • Read p.28-29 of Joel's notes. (1.25 hrs)
  • Read p.45-48 of [Lauda]. (1.5 hrs)
  • Reread p.108-109 (Fibre Bundles); read p.111-113 (Induced Bundles), p.286-287 (de Rham's Theorem) and p.72 (Induced Structures) of Bredon. (2.25 hrs)
• Mar 21 (Monday) -- wasn't feeling so well
  • Organized relevant TQC literature and summarized a few questions. (2 hrs)
  • Read p.1 of Buerschaper and Aguado's "Mapping Kitaev's quantum double lattice models to Levin and Wen's string-net models". (1 hr)
  • Attended Daniel's talk on the application of quantum repeaters to optical interferometry experiments, and offered some comments.
  • Made 'Table of Contents' for Buerschaper's hierarchy paper. (0.5 hr)
• Mar 22 (Tuesday)
  • Discussed with Daniel about geometry of FT and QEC, and its usefulness for understanding Kitaev's quantum double model. (1.5 hr)
  • Performed in the Math Talent Show.
• Mar 23 (Wednesday)
  • Read p.22-23, p.25-27, p.35 and p.48 of [LK1]. (4 hrs)
• Mar 24 (Thursday)
  • Read p.28-43 of [LK1]. (4 hrs)
  • Chess lesson #2 from Artem. (1.5 hrs)
• Mar 25 (Friday)
  • Read p.44-49 of [LK1]. (2.25 hrs)
  • Chess lesson #3 from Artem. (1.5 hrs)
• Mar 26 (Saturday)
  • Read p.19-20 of [LK1]. (2 hrs)
  • MSO dress rehearsal and concert. (6 hrs)

• Mar 27 (Sunday)
  • Thinking. (2 hrs)
  • Meeting with Joel. (2 hrs)
  • HHO rehearsal (3 hrs).
• Mar 28 (Monday)
  • Read p.12, p.21, p.23-24 and p.39-41 of [LK1]. (4.25 hrs)
  • Read selection from [Kleshchev]. (2.25 hrs)
  • No violin.
• Mar 29 (Tuesday)
  • Read selection from [Kleshchev], focusing on Chapters 3 and 4. (4 hrs)
  • Participated in a nice lunch discussion with Rob Spekkens et al. about prospects and new directions for resource theory. (1.25 hrs)
  • Thinking: Greyhound bus and nice solo Konnichiwa dinner. (2 hrs)
  • No violin and skipped orchestra rehearsal. :-(
  • ... (0 hr?)
  • Big chunk of time emailing/browsing: including thinking about the talk next week ... (8 hrs)
• Mar 30 (Wednesday)
  • ... Read ... (0.5 hr?)
  • MAT157 office hours. (2 hrs)
  • Mentorship meeting #5: We talked more about categories. (2 hrs)
  • Met with Oded about my talk prep. We talked about socles in representation theory of Hecke algebras etc. (2 hrs)
  • ... Read & Organized? (1 hr)
  • Medium chunk of time emailing (mostly after winding down): including writing abstract for next week's talk ... (3 hrs)
  • No violin.
• Mar 31 (Thursday)
  • Talk prep in the morning. (3 hrs)
  • Gave a learning seminar talk. (1.5 hrs)
  • MAT135 tutorials. (2 hrs)
  • Tried to relax: scholarship reception; dinner, cake and late-night juggling with Allen and Iva. Inevitably, we learned some exciting math from Allen -- connections where you might not expect there to be one, or just magic of algebraic varieties. Well, I don't see enough applications of algebraic geometry, that's why I found it exciting.
  • No violin.
• Apr 1 (Friday)
  • Lots of math discussions in the morning. Among other things, I learned about Witten's recent work on analytic continuation of the Jones polynomial from one of Marco's students. (2 hrs)
  • CONFERENCE @ FIELDS: attended 3 talks, overly social day with conference participants. (all afternoon and early evening)
  • Nice evening tea with Artem (and Dana)!! I described to Artem the idea of what I wanted to write about.
  • No violin.

• Apr 2 (Saturday)
  • Started writeup (again) around a meaningful central idea: some productive and some obsessive organization, some paragraphs too and some new ideas for later. (7 hrs) ...
  • No violin.
• Apr 3 (Sunday)
  • Fun (i.e. light-hearted) shopping in St. Jacobs town. Got a bag! :-) Cupcake tasted much better than it looked.
  • Read a bit of [Buerschaper]. (2 hrs)
  • Discussed with Daniel about quantum resource theory and potential order/morphism definitions on (maybe special subsets of) QECCs; this is not the most obvious place to do resource theory, but I was hoping that some sense can be made in this context (no particularly good ideas at the moment). (0.5 hr)
  • Worked ineffectively on writeup: obsessive organization. (1.5 hrs)
  • Relaxed via watching 'Charm'.
• Apr 4 (Monday)
  • Worked a little on writeup. (1.5 hrs)
  • Looked up literature on weak Hopf C*-algebras, also known as quantum groupoids apparently. (2.5 hrs)
  • Attended QI group meeting talk by Debbie: on secure authentication, main idea of proof relied on universal composability. (1.5 hr)
  • Big chunk of time emailing ... (about music, math and friends) (10 hrs ... messed-up sleep pattern again)
  • No violin.
• Apr 5 (Tuesday)
  • Lunch discussion with Nick about continuous-variable cluster-state QC, with focus on the mathematical formulation of the physical transition between finite and (continuously) infinite in the physical world. (1 hr)
  • Received QIP reimbursement from Hector (yay!), and long-overdued brief checkups! (0.25 hr)
  • Blog update. :-) (0.75 hr)
• April 6 (Wednesday)
  • Talk prep in the morning. (2 hrs)
  • Gave a research talk in the Graduate Student Seminar (1 hr).
  • MAT157 office hours (2 hrs).
  • Mentorship meeting #6 and related: We went into some details about manifolds and did a few examples. (3 hrs)
  • Blog update. (1.45 hrs)

• Big pause in blogging!

Summary