2009 Summer Learning and Research

To monitor and motivate my own learning and research, I decided to create a blog to document my progress, along with a wishlist and a summary. Despite my usual objections and occasional discomfort in sharing personal comments with a potentially unknown readership (unlike before, when my website wouldn't show up on google searches), I'll include personal comments here to make things a little more interesting (also for myself) to read.

Definition: MY 2009 SUMMER begins on Wednesday, April 22, 2009 (the day after my last comprehensive exam -- Real Analysis) and ends on Saturday, August 22, 2009 (the day when I return from Germany).

Blog

Green Other than math
Red Bad or Evaluation
Purple Unfinished
Magenta In retrospect

• April 24 (Friday)
  • I finally created this blog after finishing my real analysis final this Tuesday, and completing my audition and some extensive TA work on Wednesday.
  • I read part of Konopka, Fotini and Simone's paper "Quantum Graphity: a model of emergent locality" (hep-th/0801.0861)
• April 26 (Sunday)
  • We played in the Brampton Bridge Sectional on Sunday in the 199er Swiss Team event. We sucked in the morning, but did much better and came first in the afternoon, winning us many bridge books to improve our skills with.
• April 27 (Monday)
  • I heard a talk (PI Special Colloquium) on "Integrability in gauge/string dualities" by Pedro Vieira. I took home the broad meaning of the word 'integrability', and the fact that there are some dualities between gauge theories and string theories, perhaps along with some vague advantages such dualities offer. But I am not sure how nice/well-understood such dualities are; if they are nice, why is it so difficult to transform between the two pictures?
• April 28 (Tuesday)
  • The first organizational meeting for the Quantum Groups and Representations (QGR) Learning Seminar happened today. We decided that 2pm on Tuesdays is a good time, and Stephen will be leading a discussion on Ginzburg and Kumar's paper "Cohomology of quantum groups at roots of unity" next time.
  • I wasted 3 hours staring at my summer schedule without coming to any conclusion.
• April 29 (Wednesday)
  • I discuss with Silvia something about classical Lie representation theory.
  • I went to a talk given by Blake Winter based on his recent paper "On codimension two ribbon embeddings" (math.GT/0904.0684). Not being a knot theorist and having arrived late, I totally did not understand why this was interesting though Dror seemed quite interested. Oh well.
  • I went to see Opera Atelier's production of "The Coronation of Poppea" AGAIN since the opening night this past Saturday! I suppose I am searching for inspirations.
• April 30 (Thursday)
  • Today I've ONLY wasted 1 hour staring at my schedule (so far).
  • I got started on Dror's paper "On Khovanov's categorification of the Jones polynomial".
  • I made a webpage for our summer QGR seminar (http://www.math.utoronto.ca/lzhang/Seminars/qgr_seminar.html).
  • All sore and tired from yesterday's ballet class; however, I will still need to say bye to Zsuzsi and Balazs tonight as they are leaving for Hungary tomorrow.
• May 1-3 (Friday-Sunday)
  • Moving and too much moving. 8 hours at IKEA on Saturday, wearing. Sunday, we enjoyed the relaxation of a rubber bridge game with Robin and Meg coming -- much delayed -- straight out of the battle field at my place.
• May 4 (Monday)
  • I gave another shot at Dror's paper "On Khovanov's categorification of the Jones polynomial", but I got stuck on page 2 because I didn't know what the grading of a graded vector space was useful for or the definitions of a few related notions, but now Omar and Sergey have explained them to me at the Northwestern conference.
  • I did a little bit of (but not enough) reading for Tuesday's seminar, namely the first page or so of Lusztig's paper "Quantum groups at roots of unity", the first three paragraphs of Ginzburg's paper "Cohomology of quantum groups at roots of unity", and the first half page of Lusztig's paper "Finite dimensional Hopf algebras arising from quantized universal enveloping algebras". I wondered what 'simply laced' meant, which I subsequently learnt from tomorrow's seminar. Reading these papers makes me wish that I knew more about Lie representation theory and homological algebra.
• May 5 (Tuesday)
  • We had a good discussion at the seminar though we didn't get very far in the paper.
• May 7 (Thursday)
  • I read section 1.5 of Bredon, and discussed 1.1-1.3 with Iva.
  • Moving is so stressful (guess what I did yesterday), and I am trying to switch out of emergency mode and to get enough sleep.
• May 8 (Friday)
  • I attended the first talk of the conference "Connection in Geometry and Physics" by someone from MIT (must be Denis Auroux). I couldn't really get my mind off of the housing matter, but I was relaxed by the distraction, however little, offered by the talk.
  • The rest of my day didn't go well as I had to turn down my summer TA offer because of my planned trip to the Northwestern conference. I was strongly grieved by the unfairness of the summer TA policy-reality combination though it's not any single person's fault. I also felt horrible about my summer financial situation and for having spent a lot at IKEA last Saturday. It was extremely traumatizing, and decided that I must sublet my place starting June to survive the summer.
  • I decided to skip my voice lesson tomorrow because I was feeling sick.
• May 9 (Saturday)
  • I went to a bunch of talks this afternoon as part of the conference "Connection in Geometry and Physics". And I was reasonable sociable at lunch and at the conference banquet. To be honest, I wasn't particularly engaged by this particular conference, just as I suspected.
• May 10 (Sunday)
  • I was sick today (and on-and-off for the last two days) and I had to visit a walk-in clinic in the morning. In the afternoon, I opted to celebrate Mother's Day at my parents' (and we played darts together) instead going to the conference after all the hardship and sickness.
• May 11 (Monday)
  • I was hanging out at a local (Waterloo) conference on quantum information (TQC) for companionship, but as planned I didn't really pay attention to any talks. However, I got more reading done today than most recent days (probably due to the absence of anxiety).
  • I read Section 1.6 and 1.7 of Bredon.
  • I read the first 4 paragraphs of the Appendix in Ginzburg's paper "Cohomology .." for tomorrow's seminar, and spent most of that time learning a few definitions which include that of the Ext functor.
• May 12 (Tuesday)
  • During the last week's QGR seminar, we decided that Silvia would lead a discussion on the Appendix of the Ginzburg's paper (on certain cohomology of associative algebras) this week. But she had a fever, so Stephen went up instead. We were in the process of computing the cohomology of Sym(n) when I had to leave. Stephen put much more thought into it afterwards and should be posting a complete solution at some point.
• May 13-16 (Wednesday-Saturday)
  • I made significant progress in organizing my place on Wednesday, which made my room livable.
  • I was unable to work on Thursday even though I went into my office with the intention to get some work done (both due to a constant lack of sleep and worries about finding a subletter for June-August). And great, the toilet insisted on not working, though I was much less bothered by it than most of my floor-mates.
  • After taking a nap on Friday afternoon, I felt more energetic and we had a dinner party at Stephen's place that evening. It was nice and relaxing (totally worth it).
  • On Saturday, I did more work on my place (with my parents' help) and some preparation for moving out. I showed one person my room.
• May 17 (Sunday)
  • A smooth travel to Evanston for the Northwestern Workshop (and Conference) on Topological Field Theories. The place made a good first impression on me. However, dinner at Joy Yee's Noodles was disappointing.
  • I managed my daily vocal practice upon arrival after shamefully skipping the last two days.
  • In the evening, I reminded myself what I was stuck with in Dror's paper "On Khovanov's categorification ..", and asked my questions the next day.
• May 18 (Monday)
  • First day at the workshop. A lot (too much) of standing in the lecture hall that my back still hurts hours after. Jacob Lurie seemed like a wonderful speaker, and David Ben-Zvi was somewhat useful too. I opted to sit on the floor (hence giving up on seeing the blackboard, and eventually felt asleep) during Bertrand Toen's lecture.
  • The Toronto students hanged out for lunch and dinner, and Sergey joined us for dinner. We intended to go over David's lecture at some point, but we forgot to do it today. It sounds like we will be exploring downtown Chicago tomorrow after the talks, something that's less scary to be done with a familiar group. Despite what it might seem, we are actually very open to hanging out with people from other universities, but there just hasn't been any convenient opportunities. (I know, I skipped the reception today to practice singing, but I just had to ...)
• May 21 (Thursday)
  • Notes for the Northwestern workshop have been posted by Alex Hoffnung (texed) and Evan Jenkins (handwritten); see also conference notes on nLab.
  
  
• June 6 (Saturday)
  • I found a cool website, the AMS Graduate Student Blog (http://mathgradblog.williams.edu/)
  • It was silly of me to have spent today and yesterday working out my music-related schedule for the coming year. But as a result, I did find myself a couple more auditions this month among other things.
  • I need to be working on my QGR talk for Tuesday! And I wish I knew something about Yangians. I've also been feeling inclined to write up some expository notes.
• June 15-19 (Monday-Friday)
  • I spent the week in Ottawa attending the Summer School in Geometric Representation Theory and Extended Affine Lie Algebras. I learnt some interesting things, and learnt that certain things are interesting.
• June 22 (Monday)
  • Today I organized some of my earlier research notes and a big pile of papers which I intended to read.
• August 3 (Monday)
  • Alas, it's been a long time since I last wrote. The biggest learning I've done in the last little while was the German language.
  • Last week, roughly Tuesday to Friday, I read about some basics of quivers and their representations from Brion's paper "Representations of quivers" (finished up to Section 1.2, around the middle of p10). I was going to write up a short little summary with some proofs filled in, but then at the moment I think that it might not be worth it.
  • Of course, I was also at the Cologne Summer School on Geometry of Representations last week, attending some (but not all) lectures.
  • This past weekend, I read a bit of Gelfand-Manin (until the bottom of p3) and some of Bredon (finished up to p29, though by some silly mistake I thought it was p39, totally unintentionally).
  • Today, I arrived at the nice Max-Plank Institute at Bonn for their Chern-Simons Gauge Theory: 20 years after workshop.
• August 9 (Sunday) -- date posted on facebook
  • I gave a couple of of mini-performances in Germany (twice singing and once on the violin), and had a lot of fun. I enjoyed a night of fun salsa dancing with an inspiring partner (Roland van der Veen), and my first experience of jazz-music-making (with the violin) was amazing (encouraged and sided by Louis Kauffman, and of course educated by quite a few talented and more experienced non-classical musicians).
• August 15 (Saturday): THOUGHTS ABOUT RESEARCH
  • This time, I am actually blogging because I think I have something to say. For one thing, maybe I'll finally admit that I don't care about most of the questions people are asking in representation theory (though this can potentially change on a later day), not just that I don't know why people care. Even when I know why people care, it doesn't mean that I can bring myself to do the same. But for some reason, I had always expected myself to be able to do that (not limited to representation theory), and had given myself a lot of troubles/excuses for not having succeeded. Today, somebody asked me why I decided to study quantum groups, following me asking another Lucy why she chose Yangian for her PhD thesis (because I wanted her to convince me that it was actually interesting or special). And my answer was remarkable easy -- I wanted to solve problems in quantum computing (don't ask me why, I don't think I really believe in it, but let 'I think it's a [more] fun model' suffice). It made me think that maybe I should use my original intent, which I still feel compelling, to help me focus on the relevant math. I had totally forgotten about why I ended up here in the first place. It was somewhat intentional because I wanted to get a complete mathematics immersion, to keep my mind open, and to try to see it from what I thought was a pure mathematics student's point of view (forgetting all of my backgrounds, and not cheating using previous experiences or be biased). But I think I am coming to the conclusion that I am not going to get enough motivation that way, I mean not being myself. I tried to be a fresh sheet for people to write on, a easy boat for people to sail (of course I am not very successful at that as always), and I still remember Joel's objection to having me as a student if I were to continue my pursue in TQC-ish mathematics. I also wanted to get away from that myself as it's a bit (though not very) close to my boyfriend's research area. It's not the first time I've switched fields for such some-what silly reasons, but this time I actually already decided to do my PhD on that (the mathematical side of TQC) following some serious thinking, troubling and undecisiveness in January 2008. And I was really happy that I was able to set my mind to something, which had been extremely hard research-wise since about the 3rd year of my undergrad (now thinking back), especially at that depressive time. I thought I would be more open to suggestions (as I always liked to claim) when I got better, but I guess I didn't. Anyway, I think I have to do what I feel is my own.
• August 16 (Sunday):
  • Of course, what I wrote yesterday was mostly to untie the knots for myself, who has a tendency to feel subtly oblidged (hence resisting what I 'should' do and discouraging myself from looking for something else), and at the same time, feel guilty for not complying.
  • I am looking forward to the new series of lectures starting tomorrow. Hopefully they will be better than those last week.
  • ON MY REVIVED INTEREST IN VIOLIN (Context: Just before I left for Germany, I started missing my violin, which I haven't really touched much since my first year at university, with the exception of a few months near the end of my undergrad. But I decided to travel without it to protect it from perils.) There are so many nice and fun violin concertos out there! And so many wonderful violinists! I am trying to decide which violin concerto to work on when I come back to my violin. Continue with Paganini, switch to Brahms, Tchaikovsky, Elgar, Prokofiev, Sibelius, Stravinsky or Shostakovich? Hard work is fun sometimes! Yo, I've learned only Bruch, Saint-Saens, one of the Mozarts and a bit of Vivaldi. It's good to know that there's so much out there to be learned and explored (perhaps a useful attitute to have towards math as well). Music makes me love life and energizes me (when I am not depressed; and it tends to make me cry when I am)! It reminds me of my high school years.
• August 17 (Monday):
  • The lectures this week seem much better!
  • Doing music also makes people hate me (for practicing loudly). Think about this: Each concert takes about 100 hours of practice, and say each of these hours 'rewards' me with 1 unit of hatred; then at the performance, I would need at least 100 loving audience members to offset the growing enmity (implicit assumption clear).
• August 18 (Tuesday):
  • My snail-paced and intercepted reading brings me to p34 of Bredon. I wonder when, if ever, I will be able to successfully convince myself to start reading a book not from the first page. Bredon is the only physical book I brought with me, and one that I am reading with Iva Halacheva. (We skype weekly, and sometimes we discuss questions from the reading. We had a fruitful discussion a couple of weeks ago, clarifying a confusing or confusingly-written proof.) The reading hasn't been very exciting so far. Maybe that's the problem with starting form the beginning. Anyway, it's okay.
  • I discovered the wonderful and ample resources on Geometric Langlands and TQFTs on Ben-Zvi's homepage
• August 20 (Thursday):
  • I AM NOT A GOOD FOLLOWER/LISTENER/READER. I don't enjoy following people's conversations/thoughts most of the time, and that explains why I am much more of a one-to-one conversationer than a group one. And if you look at my close friends, you will find that most of them are good listeners and often easy-going, so that I can steer the conversation without much effort. Maybe blogging would be perfect for me for that reason. :-) I enjoy people who give me meaning responses and feedbacks, but I get frustrated and would quit if I feel that I don't have sufficient control of where the conversation is going. Similar problems occur in mathematics. In a talk, whether we like it or not, the speaker would go down a path that he chooses. Often I can't be convinced to follow; sometimes I just drag along and suffer from the inner struggles since I think I ought to try harder since it's math (looking around, many people seem to be trying), plus that I am stuck sitting there anyway; and more often I figure maybe it's better just not to go. Don't get me wrong. I enjoy good talks (regardless of how much I understand concretely), but only when I am in the mood to listen and follow people's thoughts. When reading a book, we have to follow the author's thoughts or narrations all the time. For subjects I study, I often make myself do it (and sometimes I succeed) because I guess it's the way you learn to think like others about certain things. But for random stories, I usually just don't bother; it's too tiring and not really enjoyable. However, I sometimes enjoy hearing bits of other people's conversations, when I think they are not intended for me, usually about math or science (I am in my own world so I can interpret the discussion in whatever way I like, as long as it makes sense and it doesn't even have to be correct). Sometimes people give talks on subjects that I am quite interested in, but I would ignore/skip them because I am not in the mood (and I am too often not in the mood). It's a bit of a pity. It would be nice if more lectures/talks are recorded, so that I (and others like me) could watch them when I do feel like it. Sending me to a conference/summer school is perhaps a waste of money in terms of the number of talks I go to (with a few exceptions), but I have been paying attention to how people take their research.
  • I am not a good reader, hence I am not a good writer ... haha ... I am excited about the new semester and as usual I am worried that I will be doing too much. Anyway, the plan is to start reading for the Algebraic Geometry course two weeks before classes start; and when classes start, I'll be doing some reading with Roland van der Veen (from Amsterdam) over Skype.
  • I'd like to create some webpages with more mathematical content, as well as an online resource pool for things I am interested in (starting with math, and probably ending in math).
• August 21 (Friday):
  • I went to a bunch of talks on this lat day of the Bremen Summer School on Structures in Lie Representation Theory. In particular, like Catharina Stroppel's topic of presentation.
• August 22 (Saturday):
  • I made some good progress on Dror's paper "On Khovanov's categorification of the Jones polynomial" while in transit from Germany to Canada.
  • I read the introduction section of Dror's paper "Khovanov's homology for tangles and cobordisms".

Wishlist (Go to Longer Wishlist)

• Reading for the summer:
  • Bredon, "Topology and Geometry"
  • Gelfand and Manin, "Methods of Homological Algebra" -- scarcely touched
  • Kassel, "Quantum Groups" -- scarcely touched
  • Barkalov and Kirillov, "Tensor Categories and Modular Functors" -- not touched at all
  • Knapp, "Lie Groups Beyond an Introduction" -- not touched at all

Summary

I guess I have only accomplished a tiny fraction of what I had hoped to accomplish this summer. But I think the fall term will be much better. :-)