2020 Winter Research

Definition: Winter 2020 means January-April 2020.
This page includes: Progress log | Tasks at a glance

Progress log

Black -- Writing; Purple -- Reading; Green -- Thinking; Light Purple -- Face/Mind Bumping; Blue -- Dreaming/Locations/Non-science

January 6-10 (Monday-Friday) [9.5 hours]:
- 6: Logging: Recovered (public) online research logging practice. [1 hour]
- 6: Book Riehl: Read page 31 in Section 1.5 (Equivalence of Categories). [0.75 hour]
- 7: Logging: Set up this research blog for 2020 winter. [0.5 hour]
- 7: Book Riehl: Read pages 31-32 in Section 1.5. [1 hour]
- 8: Book Riehl: Read pages 32-33 in Section 1.5. [1.5 hours]
- 9: Talk by Owen Gwilliam: "A bulk-boundary correspondence with factorization algebras". [1 hour]
- 9: Book Riehl: Read pages 33-34 in Section 1.5. [1.25 hours]
- 9: Meeting with Tobias: Went over all questions I had on pages 32-34 of book Riehl. [1 hour]
- 10: Book Riehl: Read pages 34-35 in Section 1.5, finishing Section 1.5. [1 hour]
- 10: Book Riehl: Read pages 36-38 in Section 1.6 (The Art of the Diagram Chase). [0.5 hour]
January 12-17 (Sunday-Friday) [7.25 hours]:
- 12: Goal setting: Reviewed some research notes, and set research goals for the week while working in a cafe with Tobias. [0.25 hour]
- 13: Book Riehl: Read pages 38-40 in Section 1.6. [0.75 hour]
- 14: Book Riehl: Read pages 40-42 in Section 1.6. [1.25 hours]
- 15: Book Riehl: Read pages 42-43 in Section 1.6, finishing Section 1.6. [0.25 hour]
- 15: Book Riehl: Read pages 44-45 in Section 1.7 (The 2-category of categories). [1 hour]
- 16: Considered summer conferences and schools at PI. [0.25 hour]
- 16: Book Riehl: Read pages 45-47 in Section 1.7, finishing Section 1.7. Also did some exercises from Section 1.7. [1 hour]
- 16: Goal setting: Set research goals for the remainder of the week, and reading goals for next week. [0.25 hour]
- 16: Fractons directions: Contemplated my approach to the research area. [0.25 hour]
- 17: Meeting with Tobias: Went over all questions I had on pages 35-47 of book Riehl. [2 hours]
January 20-22, 24 (Monday-Wednesday, Friday) [6 hours]:
- 20: Book Riehl: Read pages 49-50 in Section 2.0 (intro to Chapter 2: Universal Properties, Representability, and the Yoneda Lemma). [1 hour]
- 21: Book Riehl: Read page 50 in Section 2.0, finishing Section 2.0. [5 minutes]
- 21: Book Riehl: Read pages 50-52 in Section 2.1 (Representable functors). [1 hour]
- 21: Fractons literature: Did some literature search, and decided to learn some BF theory first. [0.5 hour]
- 21: Fractons directions: Emailed Beni to ask for a meeting/some perspectives. [0.25 hour]
- 22: Discussion with Beni: about my fracton project and a bit about the fracton research landscape. [0.5 hour]
- 22: Talk by Jacob Bridgeman: "(2+1)D topological phases, defects & quantum computing". [1.75 hours]
- 24: Book Riehl: Read page 52 in Section 2.1. [1 hour]
January 27, 29-31, February 1 (Monday, Wednesday-Saturday) [11.25 hours]:
- 27: Book Riehl: Read pages 52-53 in Section 2.1. [2 hours]
- 29: Book Riehl: Read pages 53-54 in Section 2.1. [1.5 hours]
- 29: Book Riehl: Reviewed questions from Section 1.1 (Abstract and Concrete Categories). [10 minutes]
- 30: Paper Koppen: Reacted to this paper, and had initial discussions with Daniel, Tobias and Joel. [1 hour]
- 30: Paper Koppen: Read pages 1-2, including the abstract and part of Section 1 (Introduction). [1 hour]
- 30: Meeting with Tobias: Discussed paper Koppen. [1.25 hours]
- 30: Meeting with Tobias: Went over all questions I had from Section 1.1 and some questions from pages 48-54 of book Riehl. [0.75 hour]
- 31: Email exchange with Joel: I summarized some differences between paper Koppen and our work, and suggested some next steps. Joel responded encouragingly and with concrete suggestions. [1 hour]
- Feb 1: Paper Koppen: Read pages 2-4, finishing Section 1 and Section 2.0 (intro to Hopf-algebraic and representation-theoretic labels for surfaces with cell decomposition), and starting Section 2.1 (Bicomodule algebras over Hopf algebras for line defects). [1.25 hours]
- 1: Email exchange with Vincent: I let him know of my independent work on the topic while pointing out some differences, and sent him my slides from Oxford 2018. [0.75 hour]
- 1: Email exchange with Joel: I asked Joel for suggestions about how to proceed (especially whether to read paper Koppen further), and tried further to speculate on the main technical difference between paper Koppen and our work (i.e. the total Hilbert space size). [0.5 hour]
February 3-7 (Monday-Friday) [11.75 hours]:
- 3: Read Tobias' email. [10 minutes]
- 3: Read Vincent's email. [5 minutes]
- 4: Tobias' draft: Started and finished reading it. [2.5 hours]
- 4: Email exchange with Tobias. [0.75 hour]
- 4: Email exchange with Joel. [0.25 hour]
- 5: Tobias' draft: Started to edit the draft. [10 minutes]
- 5: Research notes: Worked on proving a conjectured lemma involving tensor product of H-comodule algebras, which turned out to be false. [1 hour]
- 5: Meeting with Tobias: Went over all questions from Tobias' draft. [2.75 hours]
- 6: Email exchange with Joel and Tobias: Discussed how to respond to Vincent. [1 hour]
- 6: Tobias' draft: Edited the draft, to correct for mistakes and to incorporate (some of the) elaborations from yesterday's discussion with Tobias. [1.25 hours]
- 7: Tobias' draft: Edited the bit about the topological 3-category in question, and emailed to ask Tobias a bunch of questions about it. [1.75 hours]
February 9-12, 14 (Sunday-Wednesday, Friday) [8.25 hours]:
- 9: Meeting with Tobias: Discussed various issues related to the definition and properties of the topological 3-category, answering the questions in my Feb 7 email. [1.5 hours]
- 10: Email exchange and discussion with Tobias: about various matters. [1.25 hours]
- 10: Email exchange with Joel and Tyler: ultimately about quasi-ness. [0.25 hour]
- 10: Tobias' draft: Continued to edit the part about the topological 3-category. [1.25 hours]
- 11: Email exchange with MSRI: regarding reimbursement requirements for their workshop. [1 hour]
- 11: Tobias' draft: Re-examined the part about the topological 3-category, while consulting Schommer-Pries' thesis. [0.25 hour]
- 12: Discussion with Jon Yard and Tobias: about whether to include quasi-ness. [0.75 hour]
- 12: Email exchange with Joel: about whether to include quasi-ness. [0.25 hour]
- 14: Tobias' draft: Continued to edit the part about the topological 3-category. [1.75 hours]
February 18 (Tuesday) [1.5 hours]:
- 18: Email exchange with Kevin: status/challenge report, and request to put Fractons project on my back burner. [0.75 hour]
- 18: Tobias' draft: Continued to edit the part about the topological 3-category, and emailed Tobias with a couple of questions. [0.75 hour]
February 19-March 16 [0 hour]:
- Feb 19-Mar 3: 2-week intensive violin studies in Mississauga, culminating in a concert in Waterloo on March 3.
- Mar 4-18: Took time to switch attention back to science, after making progress in scheduling next year's concerts and amidst concerning pandemic.
March 17-20 (Tuesday-Friday): [6 hours]
- 17: Talk by Theo, virtually at MSRI: "Gapped condensation in higher categories".
- 18: Talk by Xie, virtually at MSRI: "Fracton order: relation to and features beyond TQFT".
- 18: Talk by Nicholas Jewell, virtually at MSRI: "COVID-19".
- 19: Talk by Christoph Schweigert, virtually at MSRI: "Bulk fields in conformal field theory".
- 19: Talk by Emily Cliff, virtually at MSRI: "Modules over factorization spaces, and moduli spaces of parabolic G-bundles".
- 20: Talk by Kevin Walker, virtually at MSRI: "Low-dimensional G-bordism and G-modular TQFTs".
March 22, 25 (Sunday, Wednesday): [1.25 hours]
- 22: Tobias' draft: Tried to sit down and start writing about Hamiltonian realizations. But failed to produce anything meaningful, due to avoidance, self-distractions and some psychological/technological barriers. [0.5 hour]
- 25: Talk by Julia Plavnik, virtually at MSRI: "How to zest your modular categories". [0.75 hour]
March 31, April 3 (Tuesday, Friday): [4.25 hours]
- 31: Research skills: Learned to use Genius Scan. [1.25 hours]
- 31: Research skills: Learned more about LaTeX. [0.25 hour]
- Apr 3: Research skills: Learned to use Genius Scan. [1.25 hours]
- 3: Research skills: Learned to use Adobe Acrobat. [0.5 hour]
- 3: Tobias' draft: Successfully started writing about Hamiltonian realizations, overcoming a psychological hurdle. [1 hour]
April 14-17 (Tuesday-Friday) [11 hours]
- 14: Research notes: Reviewed old research notes and started writing new research notes. [1.75 hours]
- 15: Research notes: Combed through old notes, and tried to add/rewrite a couple of things. Major progress: Wrote down domain wall A operators, without help, based on bulk and boundary A operators. Also, reminded myself of edge orienation issues of all sorts for A operators. [3.75 hours]
- 15: Tobias' draft: Edited to include new pictures of domain wall and collage of boundary A operators, including allowed edge reversals. [0.25 hour]
- 15: Email exchange with Tobias. [0.25 hour]
- 16: Tobias' draft: Added paragraphs to explain the pictures I added yesterday. [2.25 hours]
- 16: Email exchange with Joel. [0.25 hour]
- 16: Email exchange with Tobias. [0.5 hour]
- 17: Research notes: (Re)wrote down domain wall B operators, on both sides of the domain wall, along with some edge orientation flips and for different cyclic numberings of the edges. [1 hour]
- 17: Tobias' draft: Edited to include the new picture of domain wall B operators mentioned above. [0.75 hour]
- 17: Email exchange with Tobias. [0.25 hour]
April 19-21 (Sunday-Tuesday) [8.5 hours]
- 19: Email exchange with Tobias. [0.25 hour]
- 19: Tobias' draft: Read new sections and responding comments added by Tobias. [1 hour]
- 19: Meeting prep: Prepared for meeting with Tobias tomorrow by coming up with, listing and organizing questions and comments in newsly created meeting notes document. [0.5 hour]
- 20: Tobias' draft: Continued to read new sections and responding comments added by Tobias. [1 hour]
- 20: Online meeting with Tobias: Discussed many of the responding comments, as well as addressed any questions and comments I had about the new sections. In addition, we discussed about manifold-TQFT and Hamiltonian-TQFT issues. [2 hours]
- 21: Meeting notes / Tobias' draft: Followed up on and cleaned up yesterday's meeting notes, including looking up technical definitions online, thinking through ideas and questions, and performing minor edits to Tobias' draft. [3 hours]
- 21: Research notes / To-do list: Reviewed old research notes, compared with the content of Tobias' draft, and updated research to-do list. [0.5 hour]
- 21: Email exchange with Tobias: in attempt to clear up a stubborn point of confusion, following up on yesterday's meeting disucssion. But we did not yet reach a conclusive answer. [0.25 hour]
April 30 (Thursday) [2.75 hours]
- 30: Tobias' draft: Edited out the questions which had been addressed, and worked on creating revised operator pictures to be inserted. [2.75 hours]

Tasks at a glance -- for record only

Black -- Individual work in math/physics/CS; Purple -- Scientific interactions; Light Purple -- Talks given; Green -- Papers posted.
◊ 1 hour/day; ♣ 2 hours/day; ♦ 3 hours/day; ♥ 4 hours/day; ♠ 5 hours/day; ∇ 6+ hours/day. OR
◊ 4-7 hours/week; ♣ 8-11 hours/week; ♦ 12-15 hours/week; ♥ 16-19 hours/week; ♠ 20-23 hours/week; ∇ 24+ hours/week.
(assuming 4-ish workdays a week)

Dates	Category theory	Thesis	Fractons	Other topics/tasks
January 6-10	◊ {Riehl}: Finished Sec 1.5, and started Sec 1.6 • Tobias Q&A			• Set up research log • Updated math homepage slightly
January 12-17	◊ {Riehl}: Finished Sec 1.6 and Sec 1.7 • Tobias Q&A • Set reading goals for next week	• Set research goals for a future week	• Contemplated my approach to fractons	• Considered PI conferences
January 20-22, 24	◊ {Riehl}: Finished Sec 2.0, and started Sec 2.1	• Jacob's talk	• Literature search • Beni discussion
January 27, 29-31, February 1	◊ {Riehl}: Reviewed Sec 1.1, and almost finished 2.1 • Tobias Q&A	0.6x◊ Reacted to paper Koppen, including: • a brief meeting with Joel • a long meeting with Tobias • email exchanges with Joel 0.4x◊ [Koppen]: Finished Sec 1 and 2.0 • Emailed Vincent
February 3-7		♣ Digested and edited Tobias' draft and had 2 meetings with Tobias • Worked on research notes • Email correspondences with Joel, Tobias and Vincent
February 9-12, 14		◊ Edited Tobias' draft, accompanied by a long meeting and various short discussions with Tobias • Discussed about quasi-ness with Joel, Tobias, Tyler and Jon Yard		• MSRI logistics
February 18		◊ Edited Tobias' draft	◊ Emailed Kevin
Feb 19-Mar 16	---	---	---	---
March 17-20		♣ MSRI workshop	• MSRI workshop
March 22, 25		• Attempted to edit Tobias' draft • MSRI workshop
March 31, April 3		◊ Edited Tobias' draft		• Set up mobile scanner • Caught up with research logging
April 14-17		♣ Worked on research notes ◊ Edited Tobias' draft • Email exchanges with Tobias • Email exchange with Joel
April 19-21		◊ Read Tobias' draft ♣ Meeting with Tobias, including meeting prep and organizing meeting notes • Email exchanges with Tobias
April 30		♦ Edited Tobias' draft