**
Department of Mathematics
University of Toronto
40 St. George Street
Toronto, Ontario
Canada M5S 2E4
Email: lzhang *at^ math *dot^ utoronto *dot^ ca
Office: Perimeter Institute, Room 224
Office phone: (519) 569-7600 ext. 6242
**

- Ph.D. candidate in Mathematics (2007-2013)
- Advisor: Joel Kamnitzer
- CV (PDF format, updated January 2012/May 2011)
ToDo: Post new version! - Research Statement (PDF format, updated October 2010)
ToDo: Post new!

*
I am a Ph.D. student working on the border of mathematics (geometry, Hopf algebras, categories and TQFTs) and physics (quantum information and condensed matter physics), with an open heart towards computer science (algorithms, complexity theory and programming).
*

**Research in progress:**arXiv Front | Google Scholar- 2015 Summer: [Learning & Research] Topological Order Series.
- Secret Math-Physics-CS Society [closed circle].

**Publications:**Publications and Term papersToDo: list publications here directly for now. **Recent talks:**ToDo: needs a separate page. - All transversal gates are topological (PI QI Group Meeting, October 31, 2012).
- All transversal gates are topological (USC QI & CMT Seminar, October 12, 2012).
- All transversal gates are topological (IQI Group Meeting, June 6, 2012).
- Kitaev's quantum double models as extended topological quantum field theories (JCHS, August 1, 2011).
- Mathematics & Topological Quantum Computation (Women in Physics Canada, July 20, 2011).
- Kitaev's quantum double models & (2+1)-dimensional extended TQFTs (8th Canadian Student Conference on Quantum Information, June 17, 2011).
- Introductory talk on (2+1)D extended TQFTs and doubled topological phases (IQI Special Seminar, April 22, 2011).
- Notes (PDF)

- Kitaev's quantum double model for topological quantum computation: representations, higher categories and extended TQFTs (Graduate Student Seminar, U of T, April 6, 2011).
- Quantum groups and the Grothendieck ring of R (Khovanov-Lauda Categorification Learning Seminar, U of T, March 31, 2011).
- Notes (PDF, not detailed)

**[Poster]**Twists arising from group automorphisms in the Kitaev model (QIP poster session a, January 10, 2011).- Modular Tensor Categories and Quantum Double of a Finite Group (Bakalov-Kirillov Learning Seminar, U of T, October 6, 2010).
- Ribbon operators in 2D lattice anyon models (QI Group Meeting, Perimeter Institute, June 7, 2010).
- Mini-course on Quantum Groups (a series of 9 lectures -- Grad Talks, Perimeter Institute, 2009 Winter, M11-12).

**Unpublished:**ToDo: clean up and upload term papers etc. **Code repository:**ToDo: translate to C++ and post my codes. **Ongoing learning:**Wishlist (books) -- Some good gifting ideas in there in case you want to get me something. ;-) [Any title with the (no hard copy) indicator; (no hard copy) titles in__Books I must read__section is preferred to those in__Supplementary books__section.]

**Seminars I have (co-)organized/(co-)led to date:**- 2011 May-2013 January: Women-in-Math Seminar (
*monthly*, variable times and locations, U of T). - 2012 Fall: TQFT meetings (F11-12:30, Alice, PI).
- 2009 Early Summer: Quantum Groups and Representations Learning Seminar (T2-4, HU1028, U of T).

- 2011 May-2013 January: Women-in-Math Seminar (
**Memorable seminars I attended:**- 2015 Summer: Xiao-Gang Wen's Topological Order Series, organized by Yidun Wan (Tuesdays and Thursdays, PI)
- 2011 Winter: Joel and Oded's Learning Seminar on Higher Representation Theory and Categorification (R2:30-4, BA6183, U of T).
- Related reference: Lauda's Four Lectures.

- 2010 Fall: Joel's Learning Seminar on Bakalov-Kirillov (W9, BA6180, U of T) on MTCs-TQFTs-MFs (Q & A).

**Courses I audited (typically incomplete):**- 2011 Winter: MAT 1196HS -- Representation Theory: Representation Theory of Lie Groups (Joel, (M)WF9, BA6183, U of T).
- 2010 Fall: MAT 1120HF -- Lie groups and Lie algebras (Meinrenken, (M)WF1, BA6183, U of T).
- 2010 Fall: MAT 1124HF -- Topics in Matrix Theory (Choi, W6-8:30, BA6183, U of T).

**Recent conferences:**ToDo: needs updating. - Poster presentation at 14th Workshop on Quantum Information Processing, National University of Singapore, January 10-14, 2011.
- Simons Conference on New Trends in Quantum Computation, Stony Brook, November 15-19, 2010.
- Duntroon Workshop on Hitchin Fibration and the Fundamental lemma, Duntroon Ontario, August 23-27, 2010.
- Low-Dimensional Topology and Categorification, Stony Brook University, June 21-25, 2010.

**Past scientific projects (blog style, boring to read):**- Condensed matter & Mathematics
- Mathematics, Quantum information, Condensed matter & Computer Science
- 2014 Winter and Summer: [Research] Fault tolerance and Thesis (partial hiatus status).
- 2013 Fall: [Research] Faul tolerance, SET phases, Thesis (partial hiatus status).
- 2013 Summer: [Research] Fault tolerance, SET phases (partial hiatus status).
- 2013 Winter: [Research] Topological phases, Fault tolerance, Quantum compiler (partial hiatus status).
- 2012 Fall: [Research] Fault tolerance, Topological phases, Quantum compiler.
- 2012 Fall: Thesis research.
- 2012 Summer: [Research] GeoCodes, Defect theory, SPT phases, Noncommutative algebraic geometry.

- Mathematics & Quantum information
- 2012 Winter: [Research] GeoCodes.
- 2011 Fall: [Research] Kitaev's model and Defect theory.
- 2011 Summer: [Learning & Research] Extended TQFTs, Kitaev's model.
- 2011 Winter: [Learning & Research] Representation theory, Categorification, Extended TQFTs, Kitaev's model.
- 2010 Fall: [Learning & Research] MTCs-3dTQFTs-2dMFs, Topological twists in Kitaev's model using ribbon operators.
- 2010 Summer: [Learning] Representation theory, Topological twists in Kiteav's model using ribbon operators.
- 2010 Winter: [Literature study & Thinking] Quiver varieties, Topological phases, Categorification.
- 2009 Fall: [Literature study & Thinking] Algebraic geometry, Algebraic knot theory, Categorification, Quiver varieties, Topological phases etc.

- Mathematics
- 2009 Summer: [Learning] Topology, TQFTs, Quivers and Representation theory.
- 2008-2009: [Learning] Quantum Groups based on book by Kassel.

- Quantum information
- 2007-2008: [Learning] Topological quantum computation (I loved it because it was cool math and highly-interdisciplinary.)
- 2007 Summer: [Coding: turned out to be reproduction of existing results, but I haven't checked my code against theirs] Surface code simulation.
- 2006-2007: [Learning] Measurement-based quantum computation, topological quantum error correction, general quantum error correction, fault tolerance.

- Quantum cryptography
- 2005: [Research & Publication] Insecurity of differential-phase-shift QKD (I think I'll like it more if people can stop associating QKD with money).

- Magnetohydrodynamical turbulence at various scales
- 2005 Christmas [Research & Coding]: Testing theories of MHD turbulence. Turbulence in the solar corona, as dynamo mechanism?
- 2004-2005: [Research & Coding] Non-resistive dynamo.
- 2003-2005: [Research & Coding] Turbulence in molecular clouds.
**Related literature:**MHD references.

- Cosmology
- 2003: [Research & Publication] Developed a fast correlation function algorithm with weak lensing applications in mind.
- 2002 Summer [Coding: my code was incorporated into Hugh Merz's N-body simulation]: Had some fun with writing a fast transpose library for someone else's N-body simulation using Intel assembly language. I also tried writing an FFT library, but found it a bit hard because more sophisticated loop structures, which the low-level language didn't seem to like very much, were needed.
- 2001-2002: [Learning, programming and reproducing some old results] Learned FORTRAN 90, gravitational weak lensing, convolutions and other standard algorithms; and I found it fun to be able to tell computers to do things for me. See my U of T mentorship program poster.

- Condensed matter & Mathematics

- 2006-2007
- Full-year: TA for PHY138Y (Physics for the Life Sciences I)

- 2007-2008
- Winter: TA for MAT185S (Linear Algebra for Engineering Science I)

- 2008-2009
- Full-year: TA for MAT135Y (Calculus for Life Science I)
- Fall: Marker for MAT301F (Groups and Symmetries)
- Winter: Lecturer for Mini-course on Quantum Groups (9 lectures) at Perimeter Institute, Waterloo (M11-12)

- 2009-2010
- Full-year: TA for MAT135Y (Calculus for Life Science I)
- Full-year: Marker for MAT237Y (Advanced Calculus)

- Summer 2010
- Full-summer: Marker and Math Aid for MAT237Y (Advanced Calculus)

- 2010-2011
- Full-year: TA for MAT135Y (Calculus for Life Science I)
- Full-year: Marker for MAT235Y (Calculus for Life Science II)
- Fall: Marker for MAT237Y (Advanced Calculus)
- Winter: TA for MAT157Y (Analysis I)
- Winter: U of T Mentorship Program -- supervised 3 gifted high school students on an exploration of Topology, Algebra and Category theory (Towards TQFTs).
- Poster session: Thursday, May 26, 4-6pm @ UC West Hall (open to public).

- 2011-2012
- Full-year: TA for MAT135F and MAT 136S

- 2012: Successful private violin studio, with 4 students and a waiting list. Unfortunately, I am too busy to teach right now.

- PhD:
- Oliver Buerschaper (2013-)
- Alexei Kitaev (2012-) | Xiao-Gang Wen (2012-) | Michele Mosca (2012-)
- Joel Kamnitzer (Ph.D. advisor, 2008-) | Hector Bombin (2009-2011)
- Joe Repka (2007-2008) | Daniel Gottesman (2007, 2012-)

- Master:
- Daniel F. V. James (2006-2007) | Robert Raussendorf (2006-2007)

- Undergraduate:
- Joe Repka (2006) | Daniel F. V. James (2006)
- Hoi-Kwong Lo (2005)
- Chris Matzner (2003-2005)
- Ue-Li Pen (2001-2005)

- Senior people:
- Alexei Kitaev | Mike Freedman | Xiao-Gang Wen | John Preskill
- Mikhail Khovanov | Katrin Wehrheim | John Baez
- Terence Tao | Jacob Lurie | Edward Witten
- Allen Knutson | Pavel Etingof | Joel Kamnitzer (PhD advisor)

- New generation:
- Alex Fink | Jonathan Fisher | David Bland | Conan Wu | Travis Schedler
- Xie Chen
- Chris Hirata
- James Cook | Siu Man Chan | Siu On Chan | Igor Naverniouk

- Sources of inspirations/agreement
- Math Blogs (in order of interest)
- NeverEndingBooks -- I like!
- Secret Blogging Seminar | AMS Graduate Student Blog
- The n-Category Cafe and nLab
- Conan's Blog | Terry Tao's Blog
- MathOverflow
(with account)

- Mathematical Repository
- David Ben-Zvi's talks and notes
- John Baez's Seminar
- Chris Schommer-Pries's notes on TQFTs and homotopy theory.

- TeXing
- TikZ examples
- Aaron Lauda's XY-pic tutorial
- LaTeX symbols
- AMS symbols

- Workshops and Summer Schools Listing
- Math Jobs
- Math books
- Math movies
- Edward Frenkel's movies

- Math/Physics musicians
- So Takei (pianist)
- Benjamin Himpel (saxophonist-composer, his music page)
- Valentin Blomer (pianist)
- Catherine Sulem (violinist)
- Taotao Liu (collaborative pianist)
- Paul McFadden (cellist)
- Robert Gooding-Townsend (violist)

**Violin**& Voice & Piano -- check out my Music page for upcoming performances!- Improvisation & Composition -- Music blog [closed circle]
- Music history &
**Music theory**-- Some RCM theory exam results

- Dance: Ballet &
**Swing**& Tap & Salsa & Tango & Ballroom - Excercises:
**Gymming & Swimming**& Running & Yoga & Team sports & Horseback riding & Juggling

**Reading**-- Recently finished books, TV series and movies- Languages:
**French**& German & Italian & Spanish **Friendships**- Opinions: Psychology (including Less Wrong) & Philosphy & Religions & Politics
- Games: Bridge & Chess & Lumosity
- Programming: Google Code Jam
- Art: Collection & Drawing

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