Lucy Liuxuan Zhang
SAAI String Quartet (high school years)
Department of Mathematics
University of Toronto
40 St. George Street
Canada M5S 2E4
Email: lzhang *at^ math *dot^ utoronto *dot^ ca
Office: Perimeter Institute, Room 224
Office phone: (519) 569-7600 ext. 6242
Who am I
- 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).
Current Academic Activities
Research & Output
- Publications: Publications and Term papers ToDo: 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).
- 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- Unpublished: ToDo: clean up and upload term papers etc.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.]
Past Academic Activities
- Seminars I have (co-)organized/(co-)led to date:
- Memorable seminars I attended:
- Courses I audited (typically incomplete):
- 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.
- 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
- Magnetohydrodynamical turbulence at various scales
- 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.
- Full-year: TA for PHY138Y (Physics for the Life Sciences I)
- Winter: TA for MAT185S (Linear Algebra for Engineering Science I)
- Summer 2010
- Full-summer: Marker and Math Aid for MAT237Y (Advanced Calculus)
- 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).
- 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.
People I've worked with
Researchers I like for various reasons
- Senior people:
- New generation:
Online Math Resources
- Sources of inspirations/agreement
- Math Blogs (in order of interest)
- Mathematical Repository
- Workshops and Summer Schools Listing
- Math Jobs
- Math books
- Math movies
- Math/Physics musicians
- Dance: Ballet & Swing & Tap & Salsa & Tango & Ballroom
- Excercises: Gymming & Swimming & Running & Yoga & Team sports & Horseback riding & Juggling