2016 August and Fall Research
Definition: August 2016 means August 8-31, 2016. Fall refers to September to December.
This page includes:
Progress log |
Tasks at a glance |
Current problems
Progress log
Black -- Writing;
Purple -- Reading;
Green -- Thinking;
Light Purple -- Face Bumping;
Blue -- Dreaming/Questions/Locations/Admin
- August 8-12
- 8: Reorganized "Past scientific projects" on main webpage, and set up this webpage for August 2016. √
- 8: Searched for and organized recent references on boundaries and domain walls: Wan, Jurgen, Kong/Kitaev.
- 9: Searched for and organized recent references on boundaries and domain walls: Kirillov.
- 9: Attended PSI's Classical Mechanics lecture #1, and met Alvaro (PSIon) and discussed lecture material over lunch. √
- 9: Started reading Hung and Wan's paper "Generalized ADE Classification of Gapped Domain Walls".
- 9: Continued to add and organize references on boundaries and domain walls.
- 10: Weekly day off (Wednesday).
- 11: Attended PSI's Classical Mechanics lecture #3.
- 11: Digested Classical Mechanics lecture #3 notes, came up with questions to ask. √
- 11: Continued to read Hung and Wan's paper "Generalized ADE Classification of Gapped Domain Walls".
- 11: Attended PSI's Classical Mechanics tutorial #2.
- 12: Attended PSI's Classical Mechanics lecture #4.
- 12: Attended PSI's Classical Mechanics tutorial #3.
- August 13-27: Two-week vacation ...
- 13, 15, 16 & 17: Followed PSI's Classical Mechanics lecture #2. √
- 16, 17, 18 & 20: Worked on problems from tutorial #2.
- 20: Digested Classical Mechanics lecture #4 notes. √
- 20 & 21: Followed PSI's Classical Mechanics lecture #5.
- 22 & 23: Followed PSI's Classical Mechanics lecture #6.
- 24 & 25: Followed PSI's Classical Mechanics lecture #7.
- 26, 27, 29 & 30: Followed PSI's Classical Mechanics lecture #8.
- August 29-September 2:
- 29: Attended PSI's Condensed Matter lecture #1, and had lunch with PSIons.
- 30: Attended PSI's Condensed Matter lecture #2 (late).
- 31: Attended PSI's Condensed Matter lecture #3.
- September 1: Attended the last 15 minutes of PSI's Condensed Matter lecture #4.
- 1: Digested Condensed Matter lecture #1. √
- 2: Attended PSI's Condensed Matter lecture #5.
- 2: Digested Condensed Matter lecture #2. √
- September 6-9:
- 6: Reviewed Part 1 (Introduction) of my partially-completed thesis. √
- 6-8: Reviewed Section 2 (The Algebras and Categories) of my thesis, alongside, making a to-read and to-do list for thesis.
- 7: Started making a table cateloguing mathematical structures versus physical roles, added to Section 1.2 (The main ideas).
- 8: Digested Condensed Matter lecture #3. √
- 8: Reviewed Section 3 (Construction of Bulk QD Models) of my thesis.
- 9: Started using Toggl to track math/physics work time.
- 9: Reviewed Section 3 (Construction of Bulk QD Models) of my thesis.
- 9: Browsed arXiv:1609.02037 (Cong et al.).
- September 12-16:
- 12: Browsed arXiv:1609.02037 (Cong et al.).
- 13: Browsed arXiv:1609.02037 (Cong et al.).
- 14: Browsed arXiv:1609.02037 (Cong et al.).
- 15: Browsed arXiv:1609.02037 (Cong et al.).
- 16: Browsed arXiv:1609.02037 (Cong et al.).
- September 20-23:
- 20: Browsed arXiv:1609.02037 (Cong et al.).
- 21: Browsed arXiv:1609.02037 (Cong et al.).
- 22: Browsed arXiv:1609.02037 (Cong et al.).
- 23: Browsed relevant parts of arXiv:1609.02037 (Cong et al.). √
- 23: Briefly reviewed my thesis.
- 23: Studied Fourier transform over finite groups.
- September 26-October 1:
- 26: Reviewed arXiv:0712.0190 (Bombin et al.).
- 26: Compared thesis Hamiltonian with that in arXiv:1609.02037 (Cong et al.). √
- 26: Emailed Joel. √
- 27: Sick day.
- 28: Reviewed my thesis.
- 29: Worked out kinks in thesis: site independence of Hamiltonian B operators. √
- 29: Talked to Beni about boundaries (in higher dimensions) and SPT phases.
- 29: Attended Mathematical Physics Seminar by Alex Weekes: Shifted Yangians, loop groups, and (co)products. (Slept a lot.)
- 30: Reviewed my thesis.
- 30: Drafted email to Joel (unfinished).
- October 1: Drafted email to Joel (unfinished).
- 1: Reviewed my thesis.
- October 3-9:
- 3: Worked out kinks in thesis: suitable projections of A and B operators ...
- 3: Managed research to-do list.
- 3: Researched literature for Beni's project.
- 3: Browsed arXiv:1503.07208 (Yoshida).
- 3: Browsed arXiv:1509.03626 (Yoshida).
- 4: Browsed arXiv:1509.03626 (Yoshida).
- 5: Reviewed my thesis.
- 6: Emailed Tobias.
- 6: Followed PSI's Condensed Matter lecture #4 ...
- 6: Reviewed my thesis.
- 7: Reviewed my thesis.
- 7: Meeting with Tobias: Worked through thesis till end of Section 3.
- 7: Edited thesis.
- 7: Worked out kinks in thesis: actions on, and decomposition of, the Kitaev Hilbert space ...
- 8: Edited thesis: sent out question, set up meeting.
- 8: Tried to Google search simple algebra decomposition (bimodule isomorphism).
- 8: Emailed Jordan: ask about search techniques on Google.
- 9: Followed PSI's Condensed Matter lecture #4 ...
- October 10-14:
- 10: Thanksgiving holiday.
- 10: Conducted Google search on left regular representation.
- 10: Conducted library book search on semisimple algebra decomposition.
- 10: Browsed textbook "Groups and Representations".
- 11: Attended PSI's QFT I Lecture #1.
- 11: Reviewed my thesis.
- 12: Reviewed my thesis.
- 12: Reviewed research notebook.
- 13: Prepared for talk on arXiv:1609.02037 (Cong et al.)
- 14: Prepared for talk on arXiv:1609.02037 (Cong et al.)
- 14: Discussion with Tobias.
- October 18-22:
- 18: Organized literature for thesis project and PI desk.
- 18: Managed thesis project to-do list.
- 18: Reviewed my thesis.
- 19: Read notes on "The Peter-Weyl Theorem for Classical and Quantum sl_N".
- 19: Read notes on "Topics on Representation Theory: Finite Groups and Character Theory".
- 20: Read notes on "Topics on Representation Theory: Finite Groups and Character Theory".
- 21: Read notes on "Topics on Representation Theory: Finite Groups and Character Theory".
- 22: Read notes on "Topics on Representation Theory: Finite Groups and Character Theory".
- October 26-28:
- 26: Read notes on "Topics on Representation Theory: Finite Groups and Character Theory".
- 26: Performed Google search on Peter-Weyl Theorem, found a good version for compact groups.
- 27: Read paper on "Characters of Hopf Algebras" (Larson).
- 27: Read notes on "The Representation Ring and the Centre of a Hopf Algebra" (Witherspoon).
- 28: Read notes on "The Representation Ring and the Centre of a Hopf Algebra" (Witherspoon).
- 28: Discussion with Tobias.
- November 2-4:
- 2: Read notes on "The Representation Ring and the Centre of a Hopf Algebra" (Witherspoon).
- 2: Attended Colloquium by Vaughan Jones: Scale invariant transfer matrices and Hamiltonians.
- 3: Read Sujeet's research statement, Part III.
- 3: Brief discussion with Jon Yard: class field theory, Dijkgraaf-Witten theory, and Langlands.
- 3: Attended Mathematical Physics Seminar by Davide Gaiotto: Geometric Langlands applications of boundary field theories.
- 3: Brief discussion with Tobias.
- 4: Set research goals for today.
- 4: Drafted email to Tobias (unfinished).
- 4: Read Tobias' email.
- 4: Managed thesis project to-do list.
- November 8:
- 8: Responded to Tobias' email.
- 8: Edited thesis.
- 8: Browsed arXiv:1501.04995 (Gogioso and Zeng).
- November 11:
- 11: Browsed arXiv:1501.04995 (Gogioso and Zeng).
- November 16-19:
- 16: Browsed arXiv:1501.04995 (Gogioso and Zeng).
- 17: Browsed arXiv:1501.04995 (Gogioso and Zeng).
- 18: Browsed arXiv:1501.04995 (Gogioso and Zeng).
- 19: Browsed arXiv:1501.04995 (Gogioso and Zeng).
- November 21-22:
- 21: Browsed arXiv:1501.04995 (Gogioso and Zeng).
- 22: Discussion with Tobias.
- December: (to be summarized here)
- To-Do:
- ----- for myself -----
- Analyze properties of finite-dimensional Hopf C*-algebra in depth.
- Summarize/process Tobias' notes into my own notebook, or into TeX file.
- Reorganize/clean up my thesis, based on corrections, suggestions and new proofs.
- (Input all edits on current copy of thesis into TeX file.)
- Put in thesis my answer/proof to ToDo 10.
- ----- for next meeting with Tobias -----
- Work on Section 3, Lemma 7, Proposition 8 -- work out action correpondences of L and T operators ... in graphical calculus.
- Further formulate notes for A and B operators, especially the B projection.
- Further my understanding of character theory for finite-dimensional Hopf C*-algebras.
- Write up notes for condensation, based on Cong et al.
- Write up notes for categorical stuff, based on Cong et al.
- Discuss mathematics of higher D boundaries.
- ----- for communications with Joel -----
- Finish reviewing thesis.
- Which element T is used for boundary A operator? Check properties. Email Joel.
- ----- for meeting with Jon -----
- 5: Re-read the Dijkgraaf-Witten paper.
- ----- for talk at group meeting -----
- Articulate what's in Cong and not in Beigi-Shor.
- Follow threads for Cong et al., extract structures.
- ----- for communications with Iris -----
- Ask Iris Questions, fix mistakes(?).
- ----- for meeting with Kevin -----
-
- ----- for chat with Pavel -----
-
- ----- for meeting with Beni -----
- Read up Beni's 3 papers on higher-D boundaries.
- Read up (3+1)D gauge theory background papers, referenced by Sujeet.
- -----
- when?: Followed PSI's Condensed Matter lecture #4.
- when?: Digested Condensed Matter lecture #5.
- -----
- Review, reorganize and complete Appendices A & B.
- Reorganize and complete Section 2.
- when?: Organize references for thesis.
- when?: Study references for thesis.
- when?: Read arXiv:1307.8244 (Kong).
- when?: Read about quantum groupoid.
- when?: Input all edits on all old copies of thesis into TeX file.
Tasks at a glance
Black -- Individual work in math/physics/CS;
Purple -- Scientific interactions;
Light Purple -- Talk given;
Green -- Papers posted.
◊ 1 hour/day;
♣ 2 hours/day;
♦ 3 hours/day;
♥ 4 hours/day;
♠ 5 hours/day;
∇ 6+ hours/day.
OR
◊ 2 sessions/week;
♣ 4 sessions/week;
♦ 6 sessions/week;
♥ 8 sessions/week;
♠ 10 sessions/week.
(1 session = 2-3 hours)
| Date |
|
Thesis |
HighDBoundaries |
DiagrammaticKitaev |
|
Classical mechanics |
Condensed matter |
|
Other topics |
| August 8-12 |
|
◊
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♣
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| August 13-27 |
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◊
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| August 29-September 2 |
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♣
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| September 6-9 |
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♣
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◊
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| September 12-16 |
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♣
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| September 20-23 |
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♣
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| September 26-October 1 |
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♣
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| October 3-9 |
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◊
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0.5
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0.5
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| October 10-14 |
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1.5
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| October 18-22 |
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1.25
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| October 26-28 |
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2
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| November 2-4 |
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1
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0.5
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| November 8 |
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1
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| November 11 |
|
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0.75
|
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| November 16-19 |
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0.5
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| November 21-22 |
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2.25
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Current problems
ToDo:
1. Read Dijkgraaf-Witten paper, and write intro.
2. Translate to Hamiltonian.
3. Read Nakahara Sections 5.6.2, 5.6.3 and 5.7.3; reread 10.1 and 10.2.
Small puzzles (currently solving Dijkgraaf-Witten):
1. BG ... H4(BG,Z) classifies 3D Chern-Simons gauge theories.
2. Wess-Zumino interactions ... classified by H3(G,Z).
3. 2D sigma models ... map from H4(BG,Z) to H3(G,Z).
4. topological spin theories & chiral superalgebras.
5. 2D (holomorphic) orbifold models.
6. Chern-Simons functional
*7. 2-cocycles in definition of fibre bundles versus 3- and 4-cocycles in Dijkgraaf-Witten theory.
Large puzzles:
1. Appearance of Drinfeld centre.
2. Relation to CFTs.