2012 Summer Research

Definition: Summer 2012 means April-August 2012.
This page includes: Progress log | Tasks at a glance | Current problems | Violin checklist

Black -- Writing; Purple -- Reading; Green -- Thinking; Light Purple -- Face Bumping; Blue -- Dreaming/Questions/Locations

• April 16-18
  • 16: TwistsWalls: rewrote abstract based on Marco's suggestion, restructured and rescoped.
  • 16: Talk by Marten van den Nest: generalized stabilizer codes.
  • 16: Dijkgraaf-Witten: set out to read "Topologial Gauge Theories and Group Cohomology".
  • 18: Janet Hung, Yidun Wan and Yanwen Shang: physical finance? from string-net to lattice models, with goal to understand edge modes; appearance of 2-cohomology in Chen_groupcoh.
• April 23-29
  • 23: Daniel Gottesman: Set out to focus on writing up the geometry of fault tolerance paper.
  • 24: Daniel Gottesman: Decided on outline.
  • 24: GeoCodes: Started writing and finished Sections 2.1 (Local unitaries and transversal gates) and 2.2.1.
  • 25: GeoCodes: Finished Sections 2.2.2 and 2.2.3 (==> finished Section 2.2 Fibre bundles).
  • 26: GeoCodes: Cleaned up Section 2.2.
  • 26: Wikipedia: Read about holonomy versus monodromy.
  • 26: Nakahara: Read Sections 5.6.1 (Lie groups) and 5.2.1 (Differentiable maps).
  • 27: Wikipedia: Started read about Ehresmann connection. [Moved into my new office @PI!]
  • 27: Daniel Gottesman: Discussed a bit about ancillas and measurements, magic state distillation, swap gates, as well as challenges and natural examples for the discrete formulation.
  • 28: Nakahara: Read Section 5.2.2 (Tangent vectors).
  • 28: GeoCodes: Started writing Section 2.3.1 (Ehresmann connection and horizontal subspaces).
  • 29: GeoCodes: Finished Section 2.3.1 and started writing Section 2.3.2 (Horizontal lift and parallel transport).
• May 1, 4-12, 17:
  • 1: GeoCodes: Worked a tiny bit on Section 2.3.2.
  • 4: GeoCodes: Partially finished Sections 2.3.2 and started writing 2.3.3 (Holonomy).
  • 5: Wikipedia: Read about covariant derivative.
  • 5: GeoCodes: Wrote some of Section 2.3.4 (Flatness of connection and Monodromy).
  • 6: Nakahara: Started to read Section 5.2.3 (One-forms).
  • 7: Daniel Gottesman: Amused about the advertisement effect of the paper outline on his blackboard.
  • 7: Nakahara: Finished reading Section 5.2.3, the part of Section 5.2.6 (Induced maps) I am interested in, and Section 5.3.0 (Flows and Lie derivatives); started reading Section 5.3.1 (One-parameter group of transformations).
  • 8: Nakahara: Finished reading Sections 5.3.1 and 5.3.2 (Lie derivatives).
  • 9: GeoCodes: Cleaned up Section 2.3.1.
  • 9: GeoCodes: Finished Sections 2.3.2, 2.3.3 and 2.3.4 (==> finished Section 2.3 Connections ==> finished Section 2 Preliminaries).
  • 10: Daniel Gottesman: some discussion about the QI aspects of the paper.
  • 11: GeoCodes: Worked on Section 3 (A unified geometric picture for quantum fault tolerance).
  • 11: GeoCodes: Finished Section 1.5 (Conventions and notations).
  • 11: Daniel Gottesman: argued about sameness/difference between the right topology on the submanifolds and the induced topology from the big manifold.
  • 12: GeoCodes: Worked on Section 3.
  • 17: GeoCodes: Worked on Section 3, divided it into subsections.
  • 17: GeoCodes: Finished Section 3.1 (Quantum fault tolerance), started Section 3.2 (Unitary FT operations as loops in Gr(K,N)).
  • 17: GeoCodes: Updated Section 1.5.
• May 21-May 27:
  20: Arrived @Caltech. :-)
  • 21: TwistsWalls: Simplified organization of Sections 1 (Introduction), 2 (Mathematical preliminaries) and 3 (From categorical data to Hamiltonian models}.
  • 21: TwistsWalls: Cleaned up parts of Section 3.1.1 (The semisimple monoidal category VecG=Rep(O(G))), worked on Section 3.1.3 (Kitaev model I: Kit(Gamma,O(G))).
  • 21: GeoCodes: Wrote some more of Section 3.2.
  • 22: GeoCodes: Worked on Section 3.2, more about the metric on the Grassmannian and the bijection with quotient space.
  • 22: Alexei: told me about his current project on the classification of topological phases of (or edge modes between) gapped systems which are free of long-range interactions (2 hours ... still to be continued).
  • 23: ENO Homotopy: read intro and beginning of appendix. √
  • 23: GeoCodes: Thought more about metric on the Grassmannian for Section 3.2.
  • 23: IQI Group Meeting: marathon 3-hour meeting and Indian dinner, where Alexei reported on the use of homotopy theory to describe the braided G-crossed extended category containing the enlarged set of bulk excitations when a symmetry group G acts on an anyonic system.
  • 23: GeoCodes: Started writing Section 3.3 (The tautological bundle \xi(K,N) and P(K,N) over Gr(K,N)).
  • 24: Daniel (Skype): chatted about Sections 3 and 5 of GeoCodes.
  • 24: GeoCodes: Finished Section 3.2. √
  • 25: Jenia (& Isaac): Discussed about Chern-Simons term, partition of (gapped Hamiltonian) topological phases by symmetry group and TQFTs.
  • 25: TwistsWalls: Wrote some of Sections 3.1.3 and 3.2.3 (Kitaev model II: Kit(Gamma,k[G])).
  • 25: Alexei: Discussed about walls to produce certain condensation algebras.
  • 26: GeoCodes: Worked some on Section 3.3, did some searching for Section 3.4 (Further geometrical structures).
  • 26: EastinKnill: Finished reading. √
  • 27: GeoCodes: Wrote more of Section 3.3.
• May 28-June 1:
  • 28: Davydov: Read Section 4.2.
  • 28: Alexei's notes: Read the first 4 pages.
  • 29: Alexei's notes: Read pages 5-9.
  • 29: Talk by Peter Maurer: Experimental progresses on quantum control of spins at NV centres, including applications to bio-imaging, QI etc.
  • 30: Alexei's notes: Read pages 9-10, 12-13, 15-16.
  • 30: Alexei's notes: Started a summary.
  • 30: Jenia: taught me about symmetry group on ground state space, representations of the symmetry group and the appearance of 2-cohomology.
  • 30: IQI Group Meeting: I helped order Thai food for the meeting! John talked about black hole evaporation.
  • 31: TwistsWalls: Section 3.1.2 (The module categories M(K,\psi) over VecG) -- wrote about the construction of M(K,\psi). √
  • June 1: IQIM Seminar Day: lots of talks, posters and conversations with NSF people and IQIM members.
  • June 1: TwistsWalls: Finished most of Section 3.1.2, except for checking the triangle axiom. √
• June 2-4:
  • 2: GeoCodes: Removed some old and useless stuff in later sections, finished 1st draft of Section 3.3. √
  • 2: GeoCodes: Worked on Section 3.4.
  • 3: GeoCodes: Worked on Section 3.4.
  • 4: GeoCodes: Wrote more of Section 3.4.
• June 5-10:
  • 5: Davydov: Browsed a bit of Sections 2 and 3.
  • 5: Chen_groupcoh: Read Abstract, Introduction I.A (Background) and I.B (Motivation), and started reading Appendix C (1D representations and projective representations of U(1) x Z_2 and U(2) semidirect-product Z_2. √
  • 5: GeoCodes: Worked on Sections 3.4 and 5, moved Section 2.1 to 5.1.
  • 6: GeoCodes: Most finished writing Section 3.4. √
  • 6: GeoCodes talk prep: for IQI group meeting, done in 2 hours. √
  • 6: My talk: on GeoCodes @ IQI Group Meeting.
  • 6: GeoCodes: Rewrote and expanded on part of Section 3.4.
  • 7: Chen_groupcoh: Read Sections I.C (Summary of results) and II.A (SO(3) SPT states).
  • 7: Wikipedia: Read half of the article about T-symmetry.
  • 7: Alexei: general SPT phases, pullback bundles, discrete gate sets and gravitational anomalies (2.5 hours). √
  • 7: Jenia: Introduced non-linear sigma models to me, mildly discussed about currents.
  • 8: Talk by Gorjan Alagic: obfuscating circuits, quantum to quantum, classical to quantum.
  • 9: Quantiki: Read about quantum error correction and detection conditions in the article "Quantum error correction and fault tolerance".
  • 9: Daniel: Discussed audience feedbacks for my talk and 3 new major directions for the GeoCodes project (1 hour). √
  • 9: EastinKnill: Reviewed answers to past questions.
  • 9: GeoCodes: Added new subsections and started to make modifications based on audience feedbacks about my talk.
  • 9: Chen_groupcoh: Read Sections II.B (SU(2) SPT states), III (Local unitary transformations) and IV.intro (Canonical form of many-body states with short range entanglements).
  • 10: Chen_groupcoh: Read Sections II.C (U(1) SPT states), II.D (Bosonic topological insulators/superconductors) and II.E (Other SPT states).
  • 10: Visited the JPL Open House.
• June 11-16:
  • 11: TwistsWalls: Section 3.1.2 -- mostly finished.
  • 11: TwistsWalls: Made hexagon for Section 2.1.3 (Monoidal functors and monoidal equivalence).
  • 12: Talk by Olivier Landon-Cardinal: on variational tomography.
  • 12: TwistsWalls: Worked some on Sections 2.1.3 and 2.1.5 (Module functors and equivalence of module categories).
  • 12: Roger, Jenia and Olivier: Exciting discussion about group cohomology, projective representations, Ext and Tor functors, gapless edge modes and conformal field theory (physical formulation).
  • 13: Alexei: Discussed details about the procedure to go from condensation algebra to categorical data for walls, project idea with Roland, project idea about categorification-quantization, funding next year and PhD committee (agreed). √
  • 13: TwistsWalls: Restructured the article in a major way. √
  • 14: TwistsWalls: Incorporated Alexei's suggestions into thesis plan, reviewing and digesting the ideas. √
  • 14: John: Asked for money, the misery of my day. :-(
  • 15: Alexei: was shown the table of contents for my thesis, made few corrections but he asked if I was setting out to write a book on the subject (we laughed), and taught me about Karoubi envelope.
  • 15: TwistsWalls: Mentally split thesis into 2 papers -- LatticeModels and AlgWalls, and a 3rd, Ribbons.
  • 15: Jenia: more discussions about group cohomology and classification of interacting bosonic SPT phases.
  • 16: Chen_1Dsymmetric: Started reading Section 1 (Introduction), with the goal to understand how group cohomology enters into the description of quantum states.
• June 18-22, 25-26:
  • 17: Arrived @Berkeley.
  • 18: MSRI: Attended MSRI lectures on "Noncommutative crepant resolutions" and "Noncommutative projective geometry".
  • 18: Organized research projects in my mind.
  • 18: Wikipedia: Read some about (projective) resolution and projective module.
  • 18: Roland: answered questions about Kitaev's old paper on toric code etc.
  • 19: MSRI: Attended MSRI lectures on "Noncommutative crepant resolutions".
  • 19: Wikipedia: Read about Karoubi envelope.
  • 19: GeoCodes: Made changes and performed some restructuring on print-out of a draft. √
  • 20: MSRI: Attended MSRI lectures on "Noncommutative crepant resolutions".
  • 20: MSRI: Read Day 1 of Michael's lecture notes. √
  • 20: MSRI people: taught me about locally ringed spaces, blowup and with little success ideal/module sheaves.
  • 21: MSRI: Attended MSRI lectures on "Noncommutative crepant resolutions".
  • 21: MSRI people: taught me about coherent sheaves and tautological line bundles over CP^1.
  • 21: Wikipidia: Read a tiny bit (and not very well) about K-theory and some about moduli spaces.
  • 21: MSRI: Read some of Day 2 of Michael's lecture notes.
  • 22: MSRI: Attended MSRI lectures on "Noncommutative crepant resolutions".
  • 25: MSRI: Attended MSRI lectures on "Symplectic reflection algebras".
  • 25: GeoCodes: Implemented some of the changes from June 19 in Tex file.
  • 26: MSRI: Attended MSRI lectures on "Deformations of algebras in noncommutative algebraic geometry".
• June 28, July 2-4, 6-7:
  • 28: GeoCodes: Finished implementing changes from June 19, mostly for Section 3; as well as compactified the structure of Section 3.
  • 29-July 1: Weekend in Mountain View with friends. :-)
  • July 2: GeoCodes: Started writing Section 2.1.4 (Pullback of a fibre bundle).
  • 3: GeoCodes: Finished writing Section 2.1.4. √
  • 3: Daniel: Discussed academic plan for the fall; need to keep GeoCodes under 30 pages!
  • 3: GeoCodes: Thought about including the universal properties of tautological bundle and of pullback bundle.
  • 4: Organized research projects in Google Docs.
  • 6: ENO Homotopy: random selections. √
  • 7: ENO Homotopy: random selections, including Section 2.4 and part of Section 2.5.
• July 13-20:
  • 11: Moved into my new PI office!
  • 13: Chen PIRSA: Watched Xie's talk on PIRSA, first 17 minutes.
  • 13: Wikipedia: Read about triplet state.
  • 14: Xiao-Gang: told me about building an analogy of TQFTs based on entanglement spectrum for short-ranged entangled states in (3+1)D, as well as a possibly new group cohomology theory arising from the study of short-ranged entangled fermionic topological phases, as well as posting the question (with existing answer) of how to compute the group cohomology of a Lie group, e.g. U(1), using spectral sequences or by truncating to finite dimensions on a PI canoe trip. √
  • 14: Chen PIRSA: Finished watching Xie's video, from minute 17 to 73. √
  • 15: GeoCodes: Started adding to Section 2.2.4 ((Projective) flatness of a connection and monodromy).
  • 15: GuWen_intFerm: skimmed proof on Page 17.
  • 16: GuWangWen_2Dclassification: Read Section I (Introduction).
  • 17: GeoCodes: Finished adding to Section 2.2.4. √
  • 17: GeoCodes: Rewrote introduction of Section 3. √
  • 17: Xiao-Gang: Discussed about money, "teaching" and projects: algorithm for computing data for Drinfeld center of a spherical fusion category, or more interestingly understanding symmetry enriched (LRE) topological phases.
  • 17: GeoCodes: Started adding to Section 3.1 (Key ingredients of quantum fault tolerance).
  • 17: Joel: Summarized and explained about SET phases.
  • 18: Reorganized projects by areas on Google Docs.
  • 18: GeoCodes: Started working on Sections 3.2 and 3.3.
  • 19: Xiao-Gang: I was offered money.
  • 19: GeoCodes: Finished writing Sections 3.2.1 (Quantum error-correcting codes) and 3.2.2 (Space of codes as Gr(K,N)). √
  • 19: GeoCodes: More or less finished writing 3.2.4 (Continuous unitary transformation of codes as paths in Gr(K,N)). √
  • 19: GeoCodes: Finished writing Sections 3.3.1 (Unitary transformation of codewords) and 3.3.2 (Space of encodings as \xi(K,N)). √
  • 20: GeoCodes: Started writing Section 3.3.4 (Continuous unitary transformation of codewords as paths in \xi(K,N)).
  • 20: PSI 2010/11 -- Theoretical Physics by Nima -- Lecture 1A: Watched the first 52 minutes on PIRSA.
  • 20: PSI 2009/10 -- Condensed Matter (Review) by Xiao-Gang -- Lecture 1: Watched the first 3 minutes on PIRSA.
  • 20: PSI 2011/12 -- Condensed Matter by Nandini -- Lecture 1: Watched the first 9 minutes on PIRSA.
• July 21-28:
  • 21: Schauenburg: Read part of Section 1 (Introduction) and reviewed the purpose of studying this paper (Alexei's notes).
  • 22: Schauenburg: Finished reading Sections 1 and 2.1 (Monoidal categories). √
  • 22: Schauenburg: Started reading Section 2.2 (Algebras and modules) and Section 4 (The center construction on commutative bimodules).
  • 23: nLab: Read a bit about "left adjoint" and "diagram".
  • 24: PSI 2009/10 -- Condensed Matter (Review) by Xiao-Gang -- Lecture 1: Finished watching.
  • 25: Wikipedia: Read enough about coequalizer.
  • 25: Mac Lane: Read enough about coequalizer in Section VI.6 (Split Coequalizers).
  • 25: Mac Lane: Read some of Section IV.1 (Adjunctions). √
  • 25: Schauenburg: Finished reading Section 2.2, started reading Section 2.3 (Faithfully flat descent).
  • 25: PSI 2009/10 -- Condensed Matter (Review) by Xiao-Gang -- Lecture 2: Finished watching.
  • 25: Xiao-Gang's book: Finished reading Preface.
  • 26: Wikipedia: Read plenty of the article on equalizer -- excactly what I thought it was.
  • 26: Zsuzsi: Attended her WIM talk on "Odd Khovanov homology via hyperplane arrangements". √
  • 26: Joel: Verbally reported on my Californian trip.
  • 27: PSI 2009/10 -- Condensed Matter (Review) by Xiao-Gang -- Lecture 3: Watched the first 28 minutes.
  • 27: Xiao-Gang's book: Finished reading Sections 1.1 (More is different) and 1.2 (`Elementary' particles and physics laws), started reading Section 1.3 (Corner-stones of condensed matter physics). √
  • 27: Alexei's notes: Partially reviewed and clarified the idea for thesis, especially in relation to the Schauenburg paper. √
  • 27: Schauenburg: Read tentatively most of Section 2.3.
  • 27: Mac Lane: Read a little bit more of Sections VI.6, and started reading Section VI.7 (Beck's Theorem).
  • 28: PSI 2009/10 -- Condensed Matter (Review) by Xiao-Gang -- Lecture 3 (Semiclassical approach and Phase transition): Roughly finished watching from minute 28.
• July 29-August 3:
  • 29: Mueger: Read intro to Section 1, Sections 1.1 (Classical Frobenius Algebras), half of 1.2 (Adjoint Functors and Adjoint Morphisms), half of 1.3 (Subfactors) and all of 1.4 (Organization of the paper) (2 hours). √
  • 29: AlgWalls and GeoCodes: Refamiliarized a little (1 hour).
  • 30: GeoCodes: Reorganized again the big bundle part of Section 3 (Sections 3.1-3.4).
  • 30: GeoCodes: Understood how to better describe the big principal bundle physically (1 hour). √
  • 30: Mac Lane: Read half of Section II.7 (Graphs and Free Categories) (1.5 hours). √
  • 31: Mueger: Finished reading Section 1.2, read some of Sections 3.1 (From two sided duals to Frobenius algebras), 3.2 (A universal construction, super long), 5.4 (More on weak monoidal Morita equivalence), and beginning of 6.1 (Frobenius and Hopf algebras over Fields) (2 hours). √
  • August 1: Oliver: Shared opinions about Xiao-Gang's series of works on SPT phases; also learned about Oliver's current work on telling (or narrowing down) which topological phase a given Hamiltonian belongs to by numercially generating an (almost) spanning set of ground states and finding via topological entanglement entropy (or something similar, but computationally more efficient) a `canonical' basis for computing the S and T matrices.
  • 1: Xiao-Gang's book: Finished reading Sections 1.3, 1.4 (Topological order and quantum order), 1.5 (Origin of light and fermions), 1.6 (Novelty is more important than correctness) and 1.7 (Remarks: evolution of the concept of elementary particles) (1.5 hours). √
  • 1: Fermions and K-theory: Searched arXiv and printed out two relevant papers by Alexei (and coauthor) (0.5 hour).
  • 1: GeoCodes: Edited Section 3.3.1 (The tautological vector bundle \xi(K,N)), wrote the bulk part of Sections 3.3.2 (Space of codewords as \xi(K,N)) and 3.3.3 (Continuous unitary transformation of codewords as paths in \xi(K,N)) (==> finished Section 3.3, minus topology) (1.5 hours). √
  • 2: GeoCodes: Worked and elaborated on Section 3.4.1 (The tautological principal bundle P(K,N)) (1.5 hours).
  • 2: Alexei's honeycomb paper: Read some of Appendix F, provoking (0.5 hour).
  • 2: Mueger: Finished rough reading of Section 1.3, read two thirds of Section 2.1 (50 minutes).
  • 2: PSI 2009/10 -- Condensed Matter (Review) by Xiao-Gang -- Lecture 4 (Variational approach): Very roughly watched the first 33 minutes (1 hour).
    • 2: Xiao-Gang's book: Read intro to Section 2.1 (Semiclassical picture and path integral), skimmed through Section 2.1.1 (Propagator of a particle), started reading Section 2.1.2 (Path integral representation of the propagator), and picked up a tiny bit from Section 2.4 (Applications of the path integral formulation) (simultaneous 1 hour).
  • 3: Mac Lane: Reread and finished Section II.4 (Functor Categories), read half of Section II.5 (The Category of All Categories) (1.5 hours).
  • 3: GeoCodes: Worked on Section 3.4.1 (45 minutes).
  • 3: Mueger: Finished first reading of Section 2.1, finished reading Section 2.2. (1 hour 20 minutes).
  • 3: GeoCodes: Touched a little upon Sections 3.4.2 (Space of encodings as P(K,N)) and 3.4.3 (Continous unitary transformation of encodings as paths in P(K,N)) (10 minutes).
  • 4: Went to Pinery Provincial Park and Stratford.
• August 7-10:
  • 7: Mac Lane: Read a bit more of Section II.5.
  • 8: Mueger: Finished a rough reading of Section 3.1, skipped proof for now.
  • 8: Mueger: Read part of Section 3.2, including about the "1-morphisms" and "2-morphisms as sets". √
  • 9: Mueger: Read more of Section 3.2, about "Vertical composition of 2-morphisms", then skimmed through the rest of Section 3.2.
  • 9: Daniel: gave feedback on draft of GeoCodes.
  • 9: Fuchs et al: Read some of Section 1 (Introduction).
  • 10: Schauenburg: Read a little bit of Section 3 (The center construction on general bimodules).
• August 12-17, 19-20:
  • 12: GeoCodes: Basically finished proof of Theorem 3.11 in Section 3.4.1.
  • 13: Fuchs et al: Finished reading Section 1, started reading Section 2 (Mathematical preliminaries).
  • 14: Fuchs et al: Finished reading Section 2.1 (Module categories), started reading Section 2.2 (Bicategories and Deligne products).
  • 15: Fuchs et al: Finished reading Section 2.2, read Sections 2.6 (The Witt group), started reading Section 2.3 (Drinfeld center and enveloping category).
  • 16: Fuchs et al: Finished reading Section 2.3.
  • 17: Fuchs et al: Finished reading Section 2.4 (Central functors), started reading Section 2.5 (Lagrangian algebras).
  • 19: Fuchs et al: Finished reading Section 2.5, started reading Section 3 (Bicategories for boundary conditions).
  • 20: Fuchs et al: Read more of Section 3.
• August 22-27, 29, 31:
  • 22: Chen_1Dsymmetric: Reread part of Section 1.
  • 22: Emailed Mike and Alexei.
  • 22: Fuchs et al: Finished reading Section 3, started reading Section 4 (Bicategories for surface defects).
  • 23: Cousin: told me about the physics behind cathode ray tube (eletrical lensing effect) and solar cells.
  • 23: Grover et al: Read part of Section I (Introduction).
  • 23: GeoCodes: Reorganized paper, broke the original Section 3 into new Sections 2, 4 and 5, original Section 2 became new Section 3. √
  • 24: GeoCodes: Worked on Section 6.1. [I was so lazy today!]
  • 24: Set up blogs, including one for Math-Physics-CS.
  • 25: Grover et al: Finished reading Section I, and mostly finished Section II (Structure of entanglement entropy for gapped phases).
  • 26: Fuchs et al: Finished reading Section 4, started reading Section 5 (Lagrangian algebras and abelian Chern-Simons theories).
  • 26: Jenia: Answered two of his blogposts.
  • 27: Bei, Robert K. and Mike M.: Had a fun day with friends and colleagues, also some interesting discussions.
  • 27: Fuchs et al: Finished Section 5.
  • 29: Fuchs et al: Finished reading Section 6 (Relation with special symmetric Frobenius algebras), omitting some proofs.
  • 29: Joel: I posted some questions about Fuchs et al. for Joel.
  • 29: IQC meeting: about RAship project.
  • 31: GeoCodes: Worked on Section 6.1 (The toric code and the fault-tolerant operations).

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)

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.

July 15: 2--2.5--3--2.5--0.5--2--0
July 22: 0--0--0--1.5--1--0--2
July 29: 3--0--2--2.5--2--2--2
August 5: 2.5--0--0--3--2--0--0
August 12: 2--3.5--2"--0--1"--2.5--2
August 19: 2.5--(1+2j)--0--1--0--0--0
August 26: 0--0--0--0--0--0--N/A