2009 Fall Learning and Research

Here, I blog about math along with my other happenings. I also keep a wishlist for things I'd like to learn about and a summary outlining things I've accomplished.

Definition: MY 2009 FALL begins on Sunday, August 23, 2009 (after I get back to Canada) and ends on Saturday, December 26, 2009 (the day when I return from my 2-week vacation).

Blog

Green Other than math/physics
Red Evalution
Purple In progress
Blue Finished (at least for now)
Magenta In retrospect

• August 24 (Monday)
  • Barkalov-Kirillov: read Chapter 'Introduction' (p1-8)
  • Fulton-Harris: read Chapter 'Preface' and 'Using This Book' (pv-x)
  • I rehearsed voice+piano with Taotao in the evening.
• August 25 (Tuesday)
  • Dror's paper, "On Khovanov's categorification of the Jones polynomial": read part of Section 3.1
  • Levin and Wen's paper, "String-net condensation: A physical mechanism for topological phases": read Section 1 and 3
  • 1st Meeting with Joel and Bruce after summer (1 hr)
  • Found and printed out Brundan and Stroppel's paper, "Highest weight categories arising from Khovanov's diagram algebra IV: The super case"
  • We got invited to the 'Good-bye Fionntan' party at Dror's place in the early evening. It was very enjoyable, preceeding a good production of Dido and Aeneas attended.
• August 26 (Wednesday)
  • Brundan and Stroppel's paper, "Highest weight categories arising from Khovanov's diagram algebra IV: The super case": skimmed through parts
  • Knot at lunch (2 hr)
  • Perrin: read Chapter 'Preface'
  • I was hindered by a huge unfortunate stomachache during and after the conference dinner, limiting my eating ability and making me worried. I didn't have to end up in the emergency room, which was a relieve.
• August 27 (Thursday)
  • Meeting with Joel and Bruce: I started off the discussion by talking about quiver representations, and Joel finished off by describing and motivating the Gabriel Theorem. (2 hr)
  • Barkalov-Kirillov: skimmed through introduction paragraphs to Chapter 1-5
  • I had a good voice+piano rehearsal with Taotao; it's our second rehearsal ever, and hopefully not the last one.
• August 28 (Friday)
  • Perrin: read Chapter 'Notation'
  • Extensive updates of my 2009 summer and fall (this) learning webpages
  • Flying tonight to a wedding in the U.S. ... made it! The wedding and dinner on Saturday was fun, with a great variety of food and some dancing, but until very late ... zzz.
  
  
• August 30 (Sunday)
  • Dror's paper, "On Khovanov's categorification of the Jones polynomial": finished Section 3.1
  • Discussion with Daniel: about constant promise gap problem
• August 31 (Monday)
  • Dror's paper, "On Khovanov's categorification of the Jones polynomial": read part of Section 3.2
  • Brundan and Kleshchev's paper/book, "Representations of shifted Yangians and finite W-algebras": read a tiny bit, but spitted it back out immediately
  • Hector's paper, "Topological subsystem codes": read Section 1 (Introduction)
  • Discussion with Daniel: about QMA_EXP completeness result in 1-dimensional systems
• September 1 (Tuesday)
  • Dealing MGSA-related emails, and of course my daily musical practices.
• September 2 (Wednesday)
  • Meeting with Joel: I talked about space constructions in Dror's paper
  • Knot at lunch (2 hr)
  • We began making the MGSA presentation for the grad orientation event today, among many MGSA things I've been busy with at my 'spare time' this week.
• September 3 (Thursday)
  • Perrin: read Sections 0.0, 0.1 and part of 0.2 (in Chapter 'Introduction') (p1-5)
  • Lauda's paper, "A categorification of quantum sl(2)": read Section 1 (Introduction) (p1-3) and observed the rough structure of the paper
  • Dror's paper, "The fundamental theorem of Vassiliev invariants" : sporadic looking-through and rereading of certain parts
  • Bredon: some Section 1.12 (p35-37), some Section 1.17 (p57)
  • Aharonov, Gottesman, Irani and Kempe's paper, "The power of quantum systems on a line" : read Abstract and part of Section 1 (Introduction) (p1-2)
  • Discussion with Daniel: about decoherence-free subspace vs. noiseless subsystems vs. (usually active) subsystem codes (all fall in the category of operator QEC apparently)
• September 4 (Friday)
  • Voice and violin lessons in the suburbs of Toronto. A day in transit.
  • I was able to make my way back to Waterloo by 6pm in order to have dinnner here and play bridge at the local bridge club (the K-W Bridge Studio), and we came third (out of 7 or 8) in the beginners' game!
• September 5 (Saturday)
  • I spent some time thinking about how I am going to afford paying for both voice and violin lessons every week. That's about $150/week, well actually it's $160/week.
  • Levin and Wen's paper, "String-net condensation: A physical mechanism for topological phases": read Section 2
  • Konopka, Fotini and Simone's paper, "Quantum Graphity: a model of emergent locality": read Section II.C.1 and part of II.C.2 (p7-9)
  • Poulin's paper, "Stabilizer Formalism for Operator Quantum Error Correction": read introduction section (p1 out of 4 pages)
  
  
• September 6 (Sunday)
  • 2 hours of (uninterrupted) violin practice tires me out. I am glad that I can afford such luxury.
  • Perrin: finished Section 0.2 and started Section I.1 (p5-9)
• September 7-10 (Monday-Thursday)
  • It's a week of mine donated for the benefit of others (various others: including my housemates, the MGSA, and some friends). No math, and little peace of mind for music either. A lot of stress, and too many 'important' things to deal with, and too little sleep! I should blame myself less for not having done much and for having messed up my own life, considering how much I might have done for others. But I really need some balance, and it's probably my fault that I had given that up this week.
• September 11 (Friday)
  • I watched half an hour of a talk by Fotini on PIRSA, when my sleep was interrupted twice in the morning due to high level of stress.
  • Lunch with Yura, both as friends and in hope to recruit him for next year's MGSA, but unsuccessfully. Besides the work aspect, the lunch was enjoyable.
  • I had my violin lesson on the way out of Toronto, and I found out that my violin teacher has increased his hourly rate since I last studied with him (more than three years ago).
  • We were needed in the open section to even out the numbers at the bridge club today. We kind of survived in the open game, coming 6th (out of 8) among all N-S pairs, and 3rd (out of 5) among the flight B N-S pairs.
• September 12 (Saturday)
  • Party day for quantum information postdocs! It's a bit like another orientation I am co/vice-organizing.
  • More bridge with Robin and Meg, and a couple more hours of diagnosis play. How much I needed a break from the past week's obligations and stress! Feeling better already.
  
  
• September 13 (Sunday)
  • Updated/added earlier content to this webpage.
  • Konopka, Fotini and Simone's paper, "Quantum Graphity: a model of emergent locality": read Sections II.C.2 (partial), II.C.3, III.A (partial), III.B (partial), III.C, IV (partial), V (partial) and Section VI (p9-12, 13-14, 15-18, 19-20, 22-24)
  • Dinner party at Lucian and Vanessa's place. I look forward to being a guest, and not an organizer.
• September 14 (Monday)
  • I tried to renew my passport this morning, but found out that I would have to re-apply because my current passport was issued in another country.
  • Konopka, Fotini and Simone's paper, "Quantum Graphity: a model of emergent locality": reread and finished Sections I and II (p1-10)
  • Try my frustration with Fido! I also need to work on subletting my place downtown, and/or find ways to pay for my music lessons.
  • The bright side is that I successfully got a wiki account from Dror for the Algebraic Knot Theory class. I think the course number is MAT1350HF.
  • We are getting our first homework already in the Introduction to algebraic geometry and commutative algebra (MAT1155HF) class with Joel.
  • Perrin: finished reading Section I.1 and began I.2 (p9-11)
• September 15 (Tuesday)
  • My voice teacher was happy that Anna Ronai offered to accompany me free of charge at the NATS competition! I guess I was rewarded for my good deeds! I was surprised for being rewarded, and it's funny how I was surprised.
  • Once I got back to Toronto, I was upset, infuriated and troubled by the shared parking situation in my backyard. Things were fortunately resolved relatively peacefully.
  • Decision-making is hard! I spent a lot of time today wondering (for the n-th time) whether I should keep my place in Toronto or not, and how I would like to spend my semester/school year. I talked to friends and asked for opinions, but none of them wanted to decide for me. :-( Maybe I should get new friends ... just kidding
  • Dinner with Zsuzsi and Stephen. Zsuzsi told me about her summer teaching experience.
  • I went to Hart House Orchestra (HHO) 1st (out of 2) open rehearsal, to play and to see people. People acted like they were happy that I had returned. I don't take such things serously, though it's probably better than if they don't want to see me again. This year, I am planning to audition and play with the HHO to keep my cellist friend, Tom, company.
  • So far so good (except for the parking incidence). Trying to relax. And trying to think that I do not have to fill the entire MGSA cabinet for the next generation.
• September 16 (Wednesday)
  • A hectic day. Visa for my dad, Starbucks, people caught me to talk about the MGSA cabinet nominations and got me started (there goes my hope to minimize my effort in this regard after having conducted a few rounds of recruitment), Joel's talk, Math aid centre hours far away, followed by the MGSA first social of the year and election results. Not to mention events skipped. I briefly felt the relief in the absence of the President title, but quickly realized that I would have to do some things to ensure a smooth transition. Confusions.
  • Perrin (wonderful 'peace' at Starbucks): continued with Section I.2, started Section I.3 (p11-13)
  • From 10pm-midnight, after my violin practice, me and my guarantor combatted with various computers and printers in school to produce a presentable passport application for me. The solution was still not perfect, mind you.
  • I needed sleep, and was getting more and more worked up. However, I managed to post an ad to sublet my room during my last waking hours.
• September 17 (Thursday)
  • Meeting with Joel: I described the quantum graphity model. Joel thought it was interesting! :-)
  • Some scheduling complication arose after my violin lesson, and I got anxious for hours and made lots of phone calls and emails. I hope things will work out.
  • Instructorship is not for me until maybe the summer. I need time for research right now, plus it's so difficult to tame my schedule!
  • I am trying hard to cram the chorus parts in Mozart's opera "Cosi fan tutte". I will be in the chorus when Opera Kitchener puts on the show on October 3 (evening) and 4 (afternoon). Alas, the parts need be memorized (ideally by this Saturday).
  • Tomorrow will be good hopefully. :-)
• September 18 (Friday)
  • Success with my passport application this time!
  • Browsed around on the Algebraic Knot Theory (AKT) class wiki and learned how to edit
  • Watched the AKT September 10 Lecture online: until 0:32:33
  • We did well in bridge today, coming 1st amongst all N-S pairs in the open section (Club Champianoship today).
• September 19 (Saturday)
  • I had a whole day (actually only 11am-1pm, then 2-3:30pm) of chorus rehearsal with Opera Kithener. Our show of "Cosi fan tutte" is on October 3 & 4!
  • It took me 3 hours just to go through all the emails related to the room sublet.
  • We had a nice dinner with Iva at Ematei. We have vague plans to meet once more before she flies away. But that's it. :-(
  
  
• September 20 (Sunday)
  • Showing my room all day to potential sublettees.
  • Managed to still practice singing in the morning and the violin in the evening. It's funny that one of my housemates, Tom, chooses to practice the cello at the same time to minimize the duration of disturbance to other housemates.
• September 21 (Monday)
  • I did spend the morning going to my voice lesson today.
  • Math-wise, I am suffering from the lack of it in the past 2 weeks. I have forgotten why I was curious about certain things and what I was thinking about.
  • Dror's paper, "Khovanov's homology for tangles and cobordisms": read and reread up to the end of Section 1.1 (p1443-1447)
  • Perrin: looked at p12-13 again
  • We watched half of a detective movie tonight because I was so tired/sleepy that I couldn't practice music. As usual, I got pretty bogged down by details, so we had to rewind a lot to catch everything people were saying. We covered about 1 hour worth of the movie in 2 hours. I did enjoy the movie though (fortunately).
• September 22 (Tuesday)
  • We had a lengthy discussion about how the PI quantum information group meetings should be run over lunch. A number of people participated in the debate. I don't think an agreement was reached, but there's a decider.
  • I experimented with annotations on Dror's online video recording archive. In particular, I annotated the AKT September 10 Lecture, Hour 1 until about 0:36:30.
• September 23 (Wednesday)
  • Perrin: finished reading proofs and cleared up some things on p12-13
  • Perrin: Read part of Appendix A.1 on algebra review, until near the end of A.1.1 (p199-200)
• September 24 (Thursday)
  • Meeting with Joel: asked my questions about Perrin.
  • Success with school year sublet!
• September 25 (Friday)
  • Poulin's paper, "Stabilizer Formalism for Operator Quantum Error Correction": read the "OQEC theory" section and the "stabilizer formalism" section, as well as part of the section on "stabilizer formalism for OQEC" (p1-2)
  
  
• September 27 (Sunday)
  • Perrin: continued with Section 1.3 on irreducibility (p14)
• September 29 (Tuesday)
  • Meeting with Joel: I presented short proof about knots, and we discussed about research directions. Joel partially described/motivated to me Chandrika's summer project. Then we had lunch with Tom where we acheived neither mathematical nor German goals. But they seemed to enjoy chatting about University of Waterloo, which is cool.
• September 30 (Wednesday)
  • Poulin's paper, "Stabilizer Formalism for Operator Quantum Error Correction": reread sections on "OQEC theory" and "stabilizer formalism" (p2)
• October 1 (Thursday)
  • Poulin's paper, "Stabilizer Formalism for Operator Quantum Error Correction": reread and finished the section on "stabilizer formalism for OQEC" (p2-p3)
• October 2 (Friday)
  • Usual Friday activities (voice lesson, Math Aid Centre hours at Vic, then violin lesson) followed by a Opera Kitchener dress rehearsal, mixed with horrible traffic (due to weather presumably). It amounts to a total of 6 hours of driving, and a missed violin lesson.
  
  
• October 3-4 (Saturday-Sunday)
  • Attended one day (Saturday) of the Southern Ontario Group and Geometry workshop organized by Joel and others.
  • Two performances with Opera Kitchener in "Cosi fan tutte" on Saturday night and Sunday afternoon.
  
  
• October 5-9 (Monday-Friday)
  • Grading, and lots of grading! Also planned out the long weekend.
  
  
• October 15 (Tuesday)
  • Refreshed and slightly stressed (by the amount of rehearsals coming up) after the long weekend away. It was as usual a full day of meetings, teaching and rehearsals. Mimi and I had our first rehearsal of the Beethoven violin sonata for our upcoming December recital.
  • Meeting with Joel: Joel told me more about the connection between quivers and the Lusztig's canonical basis for a Kac-Moody algebra.
  • Geometric Representation Theory Seminar: I went to the first part of Brian Smithling's presentation on "Local models for ramified unitary groups". I didn't understand everything, but I enjoyed the talk.
• October 14 (Wednesday)
  • Dowling and Nielsen's paper, "The geometry of quantum computation": read Section 1 (Introduction)
  • I rehearsed with Anna Ronai for the first time today.
  • We got back to playing bridge at the local bridge club after 3 weeks of hiatus, and we did okay, coming 2nd (out of 6) amongst the flight B pairs, and 5th (out of 10) amongst all pairs in the STaC (open) game.
• October 15 (Thursday)
  • I had my first pointe shoes fitting appointment this morning, which was fun.
  • Discussion with Aasa et al.: about QC as geometry.
  • Nielsen, Dowling, Gu and Doherty's paper, "Quantum Computation as Geometry": Read up to and including the definition of d(I,U)
  • Quantum Gravity Group Meeting: I briefly heard Ignacio Cirac talking about black hole analogue in Bose-Einstein condensates.
  • Freedman, Nayak, Walker and Wang's paper, "On picture (2+1)-TQFTs": began to read the very beginning
  • PSI courses: explored the PSI wiki
  • Updated and reformatted this web page and its sub-pages quite a bit.
  
  
• October 19 (Monday)
  • Freedman, Nayak, Walker and Wang's paper, "On picture (2+1)-TQFTs": read part of introduction section (p1-2)
  • Fulton-Harris: read summary of Part I and part of Section 1.1 (p1-4)
  • Gelfand-Manin: read Section 1-3 of 'Reference Guide' (pXIIV-XV)
  • PI QI Group meeting: Steve on topological entanglement entropy.
• October 20 (Tuesday)
  • Meeting with Joel: Joel helped me get started on Geiss et al.'s paper "Semicanonical bases and preprojective algebras"; and I told him very briefly about Nielsen's work on geometry of QC.
  • Geometric Representation Theory Seminar: A very education talk! "Koszul Duality of Perversed Sheaves" by Zhiwei Yun. I learned the differences between perverse, tilting and IC (intersection cohomology) sheaves.
• October 21 (Wednesday)
  • Did some thinking about research interests, and made some effort to focus.
  • Aharonov, Gottesman, Irani and Kempe's paper, "The power of quantum systems on a line" : read Section 1.1 and part of 1.2 (p2-4)
• October 22 (Thursday)
  • Discussion with Aasa et al.: more about QC as geometry. At the end of the meeting, we decided that we are done with the topic for now.
  • Geiss, Leclerc and Schroer's paper, "Semicanonical bases and preprojective algebras": read Sections 1.1-1.4 and 1.8, also read part of Section 1.5 (p1-4)
  • Aharonov, Gottesman, Irani and Kempe's paper, "The power of quantum systems on a line" : finished Section 1.2, and read part of Section 1.3 (p4-6 with hole)
• October 23 (Friday)
  • Aharonov, Gottesman, Irani and Kempe's paper, "The power of quantum systems on a line" : read Section 1.4 (p6-7)
• October 24 (Saturday)
  • Aharonov, Gottesman, Irani and Kempe's paper, "The power of quantum systems on a line" : asked questions up to near the end of Section 1.2 (This took a long time!), and began reading Section 1.5 (p7)
  
  
• October 25 (Sunday)
  • Humphreys: read Section 9.1 and part of 9.2 (p42-43)
• October 26 (Monday)
  • Discussion with Francesco: about quantum graphity model.
  • Chat with Iva: about life and a bit about representation theory.
  • Humphreys: finished reading Section 9.2, and read Section 9.3-9.4 (p43-45)
  • Perrin: continued with Section 1.3 on irreducibility (p14)
• October 27 (Tuesday)
  • Meeting with Joel: a long one. I asked most of my questions about the introduction section of Geiss et al.'s paper.
  • I practiced a tiny bit of German with Tom, and we made plans to study German together in the months to come.
• October 28 (Wednesday)
  • Perrin: finished Section 1.3 on irriducibility, and started Section 1.4 on Nullstellensatz (p15)
  • Posted some questions under 'Things I want to understand' in my current Wishlist, and added items under 'Things I'd like to write up'.
  • Discussion with Hector: He proposed such an interesting project!
  • Buerschaper and Aguado's paper, "Mapping Kitaev's quantum double lattice models to Levin and Wen's string-net models": Read Sections 1-3 and 5 (p1-3, p6)
• October 29 (Thursday)
  • Discussion with Tsuyoshi: about quantum PCP and complexity of 1-d Hamiltonian problem.
  • Lahtinen's expository paper, "Anyons, Quantum Double Symmetry and Topological Quantum Computation": read Section 1 (p1-10)
• October 30 (Friday)
  • Humphreys: read half of Section 10.1 (p47-48)
  • Perrin: looked at the beginning of Sec 1.4 again (p15)
  
  
• November 2 (Monday) Learning about the Kitaev Model of Anyons
  • Kitaev's paper, "Fault-tolerant quantum computation by anyons": roughly read through Sections 5 and 6 (p13-25)
  • Hector's paper, "A Family of Non-Abelian Kitaev Models on a Lattice: Topological Condensation and Confinement": read Section 1 (Introduction) (p1-2)
• November 4 (Wednesday) Learning about the Levin-Wen Model of String-nets
  • In transit to Santa Barbara. On route, I read:
  • Levin and Wen's paper, "String-net condensation: A physical mechanism for topological phases": read Section 4.A and part of Section 4.B (p4-7)
  • Humphreys: read Sections 10.1 and 10.2 (p47-50)
• November 5 (Thursday)
  • Levin and Wen's paper, "String-net condensation: A physical mechanism for topological phases": finished reading Section 4.B (p7)
  • Skype meeting with Hector: intensely discussed questions and issues about models of Kitaev and Levin-Wen, talked about short-term future direction.
• November 6 (Friday)
  • Proofread Daniel's paper for Physics Canada (p1-3).
  • Kitaev's paper, "Fault-tolerant quantum computation by anyons": read Section 0 (p1-2)
  
  
• November 7-8 (Saturday-Sunday)
  • Saw friends in LA.
  
  
• November 9 (Monday)
  • Chatted with Kevin Walker: $RT(D(A))\; =\; TV(A)$
  • Slacked off on my birthday.
• November 10 (Tuesday) Understanding the Kitaev Model of Anyons
  • Attended talk by Sarah: "Streaming universal entanglement concentration"
  • Kitaev's paper, "Fault-tolerant quantum computation by anyons": read part of Section 1 (p2-5)
• November 11 (Wednesday)
  • I finished annotating the AKT September 10 Lecture, Hour 1 and annnotated AKT September 10 Lecture, Hour 2 until about 0:14:30.
  • Geiss, Leclerc and Schroer's paper, "Semicanonical bases and preprojective algebras": read Sections 2.1-2.3 (p6-7)
  • Attended talk by Matt Hastings: "Pairs of almost commuting matrices"
• November 12 (Thursday)
  • Applied to MSRI's January workshops.
  • Chatted with Iva: about free categories, and about quivers and Lusztig's bases.
  • Geiss, Leclerc and Schroer's paper, "Semicanonical bases and preprojective algebras": read Sections 2.4-3.3 (p7-8)
  • Amazing sushi dinner at Arigato Sushi.
• November 13 (Friday)
  • Finally I had a walk along the beach.
  • Geiss, Leclerc and Schroer's paper, "Semicanonical bases and preprojective algebras": read Sections 4.1-5.6 (p9-10)
  • Attended talk by Daniel: "Computationally hard problems in translationally invariant spin systems"
• November 14 (Saturday)
  • Geiss, Leclerc and Schroer's paper, "Semicanonical bases and preprojective algebras": read Sections 5.7-6.3 (p11-14)
  • Kitaev's paper, "Fault-tolerant quantum computation by anyons": finished reading Section 1 (p5)
  • I also spent lots of hours planning, including some research projects planning.
  
  
• November 16 (Monday)
  • Trying to recover from the stressful travel experience and obsessive planning, as well as the resulted sleep deprivation.
  • I did some work for one of my potential near-future academic travel plans (Germany).
• November 18 (Wednesday)
  • Attended talk by Bill Wooters: "Why does nature like square root of negative one?", i.e. real versus complex quantum mechanics
  • Savage's paper, "Geometric and Combinatorial Realization of Crystal Graphs": rough reading of abstract and introduction (p1-3)
  • Updated the summary table below (hoping to get myself back together for some enjoyable=good work after so much stress).
  • Kitaev's paper, "Fault-tolerant quantum computation by anyons": started reading Section 2 (p6)
• November 19 (Thursday)
  • Applied for QIP funding.
  • Got a fancy haircut today after a long wait.
  • Discussion with Hector: about Kitaev's ribbon operators, and local operators as a special case. What about general quantum doubles (for T & L)?
• November 20 (Friday)
  • Kitaev's paper, "Fault-tolerant quantum computation by anyons": read more of Section 2 (p6-7)
  • Dinner with Zsuzsi, and violin lesson with Mimi.
  • Today I accidentally drove to Woodstock, missing my highway exit by 28 km. I should start paying attention when I drive.
• November 21 (Saturday)
  • I competed in the NATS auditions today. It went relatively well even though I did not win. The event was like a huge party. I enjoyed seeing again many singers and accompanists that I knew there.
  • I learned my lesson about parking on a slope. Very embarassing and potentially scary.
  
  
• November 22 (Sunday)
  • We competed in the open section of the STaC Swiss Teams bridge event with Aninda and Urbasi today. We did okay (with many mistakes and some good plays), coming 1st (out of 3) among all flight C teams, and 7th (out of 12) among all teams
  • Kitaev's paper, "Fault-tolerant quantum computation by anyons": read a little of Section 2 (p7-8)
  • I spent 3 hours finishing sewing the ribbons onto my pointe shoes (started 3 weeks ago). It was hard, but I think I was getting better at it.
• November 24 (Tuesday)
  • Meeting with Joel and Chandrika: about Chandrika's summer project on quiver varieties.
  
  
• December 3 (Thursday)
  • Meeting with Joel: Joel gave an overview of our short-term goals of the quiver project.
  • I picked up some of the MAT 237 assignments, and started grading away.
  
  
• December 8 (Tuesday)
  • Savage's paper, "Finite-dimensional algebras and quivers": read Sections 1 and 2 (p1)
  • We saw "Sound of Music" in theatre in Toronto. It was great!
• December 9 (Wednesday)
  • Savage's paper, "Finite-dimensional algebras and quivers": read Sections 3 and 4 (p2-4)

Wishlist (Go to Longer Wishlist)

• Things I want to understand:
  • Why hasn't the semicanonical basis been quantized? (posted Oct. 28)
  • How to make the theory of topological phases more rigourous? (posted Oct. 28)
• Things I'd like to write up:
  • notes about quiver representations. (posted Nov. 12)
  • an expository article about the Kitaev model and the Levin-Wen model. (posted Nov. 12)
  • Understand and compare all existing frameworks of topological phases.
  • Understand and compare all existing concrete lattice gauge models and string-net models.
• Math textbooks to read:
  Algebraic Geometry
  • Eisenbud, "Commutative Algebra: with a View Toward Algebraic Geometry"
  • Perrin, "Algebraic Geometry: An Introduction" [Course website]
  Algebraic Knot Theory
  • Dror, "AKT-09" (online video course on Algebraic Knot Theory, 2009 Fall)
  Representation Theory
  • Fulton & Harris, "Representation Theory -- A First Course" (Fulton-Harris)
  • Humphreys, "Introduction to Lie Algebras and Representation Theory"
  Geometry
  • Bredon, "Topology and Geometry"
  Homological Algebra & Category Theory
  • Gelfand and Manin, "Methods of Homological Algebra" (Gelfand-Manin)
  • Mac Lane, "Categories for the Working Mathematician"
  Quantum Groups
  • Kassel, "Quantum Groups" (should finish)
  TQFTs
  • Turaev, "Quantum Invariants of knots and 3-Manifolds"
  • Barkalov and Kirillov, "Tensor Categories and Modular Functors" (Barkalov-Kirillov)
• Physics textbooks to read:
  • Sakurai, "Modern Quantum Mechanics"
  • Peskin & Schroeder, "An Introduction to Quantum Field Theory"
  • Wen, "Quantum Field Theory of Many-body Systems"
  • Perimeter Institute, PSI courses 2009-2010
• Math papers to read:
  • Brion's paper, "Representations of quivers"
    Lusztig's paper, "Canonical Bases Arising from Quantized Enveloping Algebras"
    Crawley-Boevey and Schroeer's paper, "Irreducible components of varieties of modules"
    Geiss, Leclerc and Schroer's paper, "Semicanonical bases and preprojective algebras"
    Savage's paper, "Geometric and Combinatorial Realization of Crystal Graphs"
    Savage's paper, "Finite-dimensional algebras and quivers"
  • Dror's paper, "On Khovanov's categorification of the Jones polynomial"
    Dror's paper, "Khovanov's homology for tangles and cobordisms" (Dror_2)
    Lauda's paper, "A categorification of quantum sl(2)"
    Khovanov's paper, "A categorification of the Jones polynomial"
  • Freedman, Nayak, Walker and Wang's paper, "On picture (2+1)-TQFTs"
  • Dror's paper, "The fundamental theorem of Vassiliev invariants" (Dror_3)
• Physics papers to read:
  • Levin and Wen's paper, "String-net condensation: A physical mechanism for topological phases"
    Kitaev's paper, "Fault-tolerant quantum computation by anyons"
    Buerschaper and Aguado's paper, "Mapping Kitaev's quantum double lattice models to Levin and Wen's string-net models"
    Lahtinen's expository paper, "Anyons, Quantum Double Symmetry and Topological Quantum Computation"
    Hector's paper, "A Family of Non-Abelian Kitaev Models on a Lattice: Topological Condensation and Confinement" (Hector_2)
  • Hector's paper, "Topological subsystem codes"
    Poulin's paper, "Stabilizer Formalism for Operator Quantum Error Correction"
  • Nielsen's paper, "A geometric approach to quantum circuit lower bounds"
    Nielsen, Dowling, Gu and Doherty's paper, "Quantum Computation as Geometry"
    Nielsen, Dowling, Gu and Doherty's paper, "Optimal control, geometry, and quantum computing" (Nielsen et al._2)
    Dowling and Nielsen's paper, "The geometry of quantum computation"
  • Aharonov, Gottesman, Irani and Kempe's paper, "The power of quantum systems on a line"
    Gottesman and Irani's paper, "The Quantum and Classical Complexity of Translationally Invariant Tiling and Hamiltonian Problems"
  • Konopka, Fotini and Simone's paper, "Quantum Graphity: a model of emergent locality"

Summary