Lucy Liuxuan Zhang

SAAI String Quartet (high school years)

Department of Mathematics
University of Toronto
40 St. George Street
Toronto, Ontario
Canada M5S 2E4
Email: lzhang *at^ math *dot^ utoronto *dot^ ca
Office: 215 Huron street, Room 1028

Who am I

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

I am a Ph.D. student working at the border of mathematics (topology, TQFTs and higher categories) and physics (quantum information and condensed matter physics).

Current Academic Activities

Research in progress: arXiv Front | Google Scholar | Current progress log (2012 Summer)
- A Mathematical Picture of TQC.
"Teaching" in progress:
- I am teaching the violin at my home studio.
Seminar I run:
- Women-in-Math Seminar (monthly, F2-3, BA6183, U of T).
Seminars I currently attend (sporadic/noncommittal):
- Dror's wClips Seminar (W12-2, BA4010, U of T).

Research & Output

Publications: Publications and Term papers ToDo: list publications here directly for now.
Recent talks: ToDo: needs a separate page.
- (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Unpublished: ToDo: clean up and upload term papers etc.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) (updated May 2011)
Research interests:
- Kitaev's quantum double model: mathematical formulation, defects and generalizations.
- Topological phases and topological quantum computation.
- Modular (tensor) categories, extended TQFTs and modular functors.
- Categorification of knot invariants and of quantum groups.
- Geometric quantum error correction and fault tolerance.
- Quantum algebra and representation theory.
Learning interests:
- Algebraic geometry, noncommutative geometry and stable homotopy theory.
- Quantum gravity.

Past Academic Activities

Memorable seminars I attended:
- 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).
Seminars I have co-organized to date:
- 2009 Early Summer: Quantum Groups and Representations Learning Seminar (T2-4).
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):
- Mathematics & Quantum information
  - 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.

Teaching

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

Collaborators

Daniel Gottesman

People I like for various reasons

Large-medium intersection:
- Alexei Kitaev
- Peter Shor | Mike Freedman
- Jacob Lurie | John Baez | Mikhail Khovanov
- Daniel Gottesman | Oliver Buerschaper | Hector Bombin | Xiao-Gang Wen | Robert Koenig (local related QI people)
- Joel Kamnitzer (advisor) | Dror Bar-Natan | Laurent Freidel | Marco Gualtieri (local related math people)
- Roland van der Veen | Wolfgang Soergel | Louis Kauffman | Catherine Sulem | Valentine Blomer | So Takei | Benjamin Himpel (his music page) | Ben Darwin (math/physics-music friends)
- Zsuzsanna Dancso | Jonathan Fisher (U of T grad students)
- Jens Eisert | Patrick Hayden | Hoi-Kwong Lo
- Allen Knutson | Christof Geiss | David Nadler | David Ben-Zvi | David Speyer | Robert Lipshitz
- Bei Zeng | Xie Chen | Sarah Croke | Debbie Leung (my lady friends)
Small intersection:
- Alex Fink | Chris Hirata
- Charlie Bennett

People I've worked with officially

PhD:
- Joel Kamnitzer (2008-2012) | Hector Bombin (2009-2011)
- Joe Repka (2007-2008) | Daniel Gottesman (2007)
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 (2001-2002)

Online Math Resources

Sources of inspirations/agreement
- Advices to mathematicians
- Women in Mathematics @ MIT
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
- Aaron Lauda's XY-pic tutorial
Workshops and Summer Schools Listing
Math Jobs
Math books
- BookFinder
Math movies
- Edward Frenkel's movies

Outside of Math (and Physics)

Artistic passions: see my Music page
- Violin, Voice, Improvisation/Composition.
Other hobbies:
- Mind cleansing/imaginative: Reading (in English/French/German).
- Exercise/stress-release: Swimming, Dancing.
- For fun: Programming, Bridge, Horseback riding.
- For profession: Music history, Harmony.