Curriculum Vitae - University of Toronto

Name and Information
Brendan Donald Kenneth McLellan
Email: [email protected]
Phone: 617-373-4456
Address: Northeastern University
360 Huntington Ave
Boston, MA
Citizenship
Canadian
Academic Training and Degrees
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Ph.D. Mathematics, September 2005 - August 2010. University of Toronto, Toronto, Ontario, Canada.
o Thesis Title: Non-Abelian Localization and U(1) Chern-Simons Theory
o Advisor: Professor Lisa Jeffrey
M.Sc. Mathematics, September 2003 - June, 2005. University of Toronto, Toronto, Ontario, Canada.
o Topic: Symplectic Geometry
o Advisor: Professor Lisa Jeffrey
B.Sc. Honours, Mathematics (summa cum laude), September 1999 - August, 2003. Queen’s
University, Kingston, Ontario, Canada.
Professional Employment
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Research Instructor, Northeastern University, Boston, Massachusetts, USA. August 28, 2013 – April
30, 2016.
Postdoctoral Fellow, Centre for Quantum Geometry of Moduli Spaces, Aarhus, Denmark. August 1,
2011 – July 31, 2013.
Postdoctoral Fellow, University of Alberta, Edmonton, Alberta, Canada. September 1, 2010 – July 30,
2011.
Research Areas
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Mathematics: Analytic Torsions, Knot Theory, Geometric Analysis on 3-Manifolds, Quantum Topology.
Physics: (Constructive) Quantum Field Theory, (Classical) Quantum Gravity.
Awards and Honours (Selected)
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Blyth Fellowship in Mathematics: September 2008 - April 2009, (Institutional) University of Toronto.
($3000 CAD)
National Engineering and Research Council of Canada Graduate Scholarship D Award:
September 2005 - September 2008, (National) University of Toronto. ($105,000 CAD)
Ontario Graduate Scholarship: September 2003 - September 2005, (Provincial) University of Toronto.
($35,000 CAD)
National Engineering and Research Council of Canada Undergraduate Summer Research Award:
April 2003 - September 2003, (National) Queen's University. ($7200 CAD)
Millennium Award: September 2002 - April 2003, (National) Queen's University. ($3000 CAD)
National Engineering and Research Council of Canada Undergraduate Summer Research Award:
April 2002 - September 2002, (National) Queen's University. ($7200 CAD)
Ralph and Nellie Jeffrey Award in Mathematics: September 2001 - April 2002, (Institutional) Queen's
University. ($1200 CAD)
Millennium Award: September 2000 - April 2001, (National) Queen's University. ($3000 CAD)
Queen's Engineering Entry Scholarship: September 1999 - April 2000, (Institutional) Queen's
University. ($3000 CAD)
Publications
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Jørgen Andersen, Bejamin Himpel, Søren Jørgensen, Johan Martens, Brendan McLellan. “The
Witten-Reshetikhin-Turaev invariant for links in finite order mapping tori, I.” Published on arXiv (2014)
http://arxiv.org/1408.2499 [math.GT], .
Brendan McLellan. “Analytic Torsion and Symplectic Volume.” Submitted. Published on the arXiv
(2014) http://arxiv.org/1208.2436 [math.GT].
Brendan McLellan. “Localization in Abelian Chern-Simons Theory.” J. Math. Phys., (2013) Vol. 54, No.
2.
Lisa Jeffrey and Brendan McLellan. “Eta-invariants and anomalies in U(1) Chern-Simons theory.” CS
Theory: 20 Years After, AMS/IP Studies in Advanced Mathematics 50 (2011) 173-199.
Brendan McLellan. “Gravitational Chern-Simons and the Adiabatic Limit.” J. Math. Phys., (2010) Vol.
51.
Brendan McLellan. “Non-Abelian Localization and U(1) Chern-Simons Theory.” University of Toronto
Thesis (2010).
Lisa Jeffrey and Brendan McLellan. “Nonabelian localization for U(1) Chern-Simons theory.”
Geometric analysis and mechanics, Birkhäuser (Progr. Math. Vol. 292, 199-212 (2011))
Other Publications
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Brendan McLellan. “Symplectic Geometry, Non-Abelian Localization and Path Integrals.” Research
Course Notes. (2011) Draft on Website: http://www.math.utoronto.ca/mclellan/researchfiles.html.
In Preparation
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Chris Beasley, Brendan McLellan, Ruoran Zhang. “Self-linking for Legendrian Knots,” Research
Article. Draft on Website: http://www.math.utoronto.ca/mclellan/researchfiles.html.
Brendan McLellan. “Perturbative Chern-Simons Theory Revisited.” Research article. Draft on Website:
http://www.math.utoronto.ca/mclellan/researchfiles.html.
Brendan McLellan. “Abelian Chern-Simons Theory and Contact Torsion.” Research article. Draft on
Website: http://www.math.utoronto.ca/mclellan/researchfiles.html.
Brendan McLellan. “On Conformally Flat Sasakian Three-Manifolds.” Research article. Draft on
Website: http://www.math.utoronto.ca/mclellan/researchfiles.html.
Selected Presentations
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January 2014: Boston University, Geometry and Physics Seminar. Invited Speaker.
Titled, “Abelian Analytic Torsion and Symplectic Volume.”
November 2013: Northeastern University, Analysis and Geometry Seminar. Invited Speaker.
Titled, “Abelian Analytic Torsion and Sympletic Volume.”
November 2013: Northeastern University, Baby Analysis and Geometry Seminar. Invited
Speaker. Title, “An Introduction to Path Integrals and Chern-Simons Theory.”
October 2013: Northeastern University, Research Seminar in Mathematics. Invited Speaker.
Titled, “Contact Chern-Simons Theory.”
October 2012: Centre for Quantum Geometry of Moduli Spaces Nielson Retreat. Titled,
``Perturbative Chern-Simons Theory Revisited.''
September 2012: Invited speaker. Instituto para a Investigaçao Interdisciplinar da Universidade
de Lisboa. Titled, ``Perturbative Chern-Simons Theory Revisited.''
March 2012: Invited speaker. CRM Barcelona. Titled, ``On a Conjecture for the Analytic Torsion
Arising from Localization in Abelian Chern-Simons Theory.''
October 2011: Invited speaker. Centre for Quantum Geometry of Moduli Spaces Nielson Retreat.
Titled, ``Gravitational Chern-Simons and the Adiabatic Limit.''
August 2011: Invited speaker. Aarhus Gauge Theory Workshop at the Centre for Quantum
Geometry of Moduli Spaces. Titled, ``Non-Abelian Localization and U(1) Chern-Simons Theory.''
June 2011: Invited speaker. GEOMAPS workshop at the Centre for Quantum Geometry of Moduli
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Spaces. Titled, ``Reidemeister Torsion and Symplectic Volume for Seifert Manifolds.''
June 2011: Invited speaker. CMS Summer Meeting at the University of Alberta. Titled, ``NonAbelian Localization and U(1) Chern-Simons Theory.''
September 2010: Invited speaker. Geometry and Physics seminar at the University of Alberta.
Titled, ``Shift Symmetry Reduction and U(1) Chern-Simons Theory on Sasakian three-manifolds.''
July 2010: Invited Speaker. Pure Mathematics Geometry and Topology Seminar at the University
of Waterloo. Titled, ``U(1) Chern-Simons Theory on Sasakian three-manifolds.''
March 2010: Symplectic Seminar at the University of Toronto. Titled, ``Eta Invariants and Anomalies
in U(1) Chern-Simons theory.''
January 2008: Graduate lectures at the University of Toronto (3 lectures). On localization,
equivariant cohomology and non-abelian localization for Yang-Mills theory.
April 2007: Graduate seminar lecture at the University of Toronto. On the equivariant localization
theorem and the Duistermaat-Heckman theorem.
June-July 2005: Short lecture series at the University of Toronto (5 lectures). On quantum field
theory and T-duality leading to mirror symmetry for elliptic curves.
Selected Conferences and Workshops
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Northeastern University, “Current Developments in Moduli Theory.” October 24-26, 2014.
Centre for Quantum Geometry of Moduli Spaces, “(u,v,w knots)x(topology, combinatorics, low and high
algebra)” by Dror Bar-Natan (University of Toronto), May-June 2013.
Centre for Quantum Geometry of Moduli Spaces, Conference on Topological Recursion and Quantum
Algebraic Geometry. January 2013. Aarhus, Denmark.
Centre for Quantum Geometry of Moduli Spaces Nielson Retreat
October, 2012, Sandbjerg Estate. Sandbjerg, Denmark
Recent Advances in Topological Quantum Field Theory
September, 2012, Instituto para a Investigaçao Interdisciplinar da Universidade de Lisboa.
Conformal and CR Geometry Workshop
July-August, 2012, Banff International Research Station, Banff, Alberta, Canada
School on Geometry and Quantization of Moduli Spaces
April, 2012, CRM Barcelona, Spain
Centre for Quantum Geometry of Moduli Spaces Nielson Retreat
October, 2011, Sandbjerg Estate. Sandbjerg, Denmark
Aarhus Gauge Theory Workshop
August, 2011, Centre for Quantum Geometry of Moduli Spaces. Aarhus, Denmark
GEOMAPS workshop
June, 2011, Centre for Quantum Geometry of Moduli Spaces. Aarhus, Denmark
CMS Summer Meeting
June, 2011, University of Alberta. Edmonton, Alberta, Canada
Geometric Flows in Mathematics and Physics
April, 2011, Banff International Research Station. Banff, Alberta, Canada
Workshop on Connections in Geometry and Physics
May, 2010, Perimeter Institute. Waterloo, Ontario, Canada
Workshop on Connections in Geometry and Physics
May, 2009, Perimeter Institute. Waterloo, Ontario, Canada
Conference in Honour of Peter Orlik
August, 2008, Location: Fields Institute. Toronto, Ontario, Canada
Conference on Mathematical Physics and Geometric Analysis
January, 2008, Location: Fields Institute. Toronto, Ontario, Canada
Ontario Topology Seminar
July, 2007, Fields Institute. Toronto, Ontario, Canada
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July, 2005, Fields Institute. Toronto, Ontario, Canada
Great Lakes Geometry Conference
April-May, 2005, Location: Perimeter Institute. Waterloo, Ontario, Canada
Distinguished Lecture Series: Edward Witten
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April, 2005, Location: University of Toronto. Toronto, Ontario, Canada
Coxeter Lecture Series: Robert Dijkgraaf
January, 2005, Fields Institute. Toronto, Ontario, Canada
Workshop on Mirror Symmetry
November, 2004, Perimeter Institute. Waterloo, Ontario, Canada
Selected Teaching
• Course Instructor
Course: MAT 2341 – Differential Equations and Linear Algbra (2nd year undergraduate course x 2
sections)
Date: Fall term, 2014
Location: Northeastern University. Boston, MA, USA
Responsibilities: Lecturing, holding weekly office hours, individual tutoring and invigilating exams.
• Course Instructor
Course: MAT 3150 – Real Analysis (3rd year undergraduate course)
Date: Winter term, 2014
Location: Northeastern University. Boston, MA, USA
Responsibilities: Lecturing, holding weekly office hours, individual tutoring and invigilating exams.
• Lecturer
Course: MAT 1341 – Engineering Calculus (x 2 sections)
Date: Fall Term, 2013
Location: Northeastern University. Boston, MA, USA
Responsibilities: Lecturing, holding weekly office hours, individual tutoring and invigilating exams.
• Course Instructor (Masters Course)
Course: Knot Theory (with Professor Andrew Swann)
Date: Winter Term, 2013
Location: Centre for Quantum Geometry of Moduli Spaces. Aarhus, Denmark
Responsibilities: Lecturing, holding weekly office hours, individual tutoring and writing/invigilating
assignments/exams.
• Teaching Assistant
Course: General Undergraduate Calculus and Linear Algebra
Date: Winter and Fall Terms, 2012
Location: Centre for Quantum Geometry of Moduli Spaces. Aarhus, Denmark
Responsibilities: Individual tutoring
• Course Instructor (Ph.D. course)
Course: Symplectic geometry, Non-Abelian Localization and Path Integrals
Date: Fall Term, 2011
Location: Centre for Quantum Geometry of Moduli Spaces. Aarhus, Denmark
Responsibilities: Lecturing, writing course material, holding weekly office hours, individual tutoring and I
invigilating exams.
• Lecturer
Course: MAT100Y - Engineering Calculus
Date: 2010-2011 year. September-December
Location: University of Alberta. Edmonton, Alberta, Canada
Responsibilities: Lecturing, holding weekly office hours, individual tutoring and invigilating exams.
• Lecturer
Course: MAT102Y - Engineering Linear Algebra
Date: 2010-2011 year. January-April
Location: University of Alberta. Edmonton, Alberta, Canada
Responsibilities: Lecturing, holding weekly office hours, individual tutoring and invigilating exams.
• Course Instructor
Course: MATA23H3 - Linear Algebra
Date: Summer Term, 2010
Location: University of Toronto. Toronto, Ontario, Canada
Responsibilities: Planning and teaching weekly lectures, supervising and collaborating with two
teaching assistants, developing assignments and weekly quizzes, holding office hours every week,
developing a midterm test and final exam, invigilating the test and exam, grading the final exam and
generally keeping up to date with departmental deadlines and requirements.
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Course Instructor
Course: MATA23H3 - Linear Algebra
Date: Summer Term, 2009
Location: University of Toronto. Toronto, Ontario, Canada
Responsibilities: Planning and teaching weekly lectures, supervising and collaborating with two
teaching assistants, developing assignments and weekly quizzes, holding office hours every week,
developing a midterm test and final exam, invigilating the test and exam, grading the final exam and
generally keeping up to date with departmental deadlines and requirements.
Lecturer
Course: MAT135Y - Calculus
Date: 2008-2009
Location: University of Toronto. Toronto, Ontario, Canada
Responsibilities: Lecturing, holding weekly office hours, individual tutoring and invigilating exams.
Teaching Assistant Positions
Courses:
MAT124YH - Calculus,
MAT133Y - Calculus and Financial Mathematics,
MAT137Y - Calculus for Math Specialists,
MAT135Y - Calculus and MAT187S - Calculus for Engineers,
Trinity Math Tutor.
Date: 2003-2008
Location: University of Toronto. Toronto, Ontario, Canada
Responsibilities: Tutorial instruction, invigilator of term tests and grading.
Teaching Assistant
Course: MATH 212 - Abstract Algebra
Date: 2001-2002
Location: Queen's University, Kingston, Ontario, Canada
Responsibilities: Tutorial instruction, invigilator of term tests and grading.
Selected Activities
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Canadian Mathematical Society Member
Master Class, “(u,v,w knots)x(topology, combinatorics, low and high algebra)” by Dror Bar-Natan
(University of Toronto), May-June 2013.
Conference Co-organizer, Topological Recursion and Quantum Algebraic Geometry, Centre for
Quantum Geometry of Moduli Spaces, Aarhus, Denmark, Winter 2013.
Master Class, ``The Ehrenpreis conjecture,'' by Vladimir Markovic and Jeremy Kahn, Aarhus, Denmark,
Summer 2012.
School on Geometry and Quantization of Moduli Spaces, CRM, Barcelona, Spain, Spring 2012.
Conformal Field Theory Course, Aarhus, Denmark, Winter 2012.
Master Class, ``Vortex Equations and Hamiltonian Gromov-Witten Invariants,'' by I. Mundet i Riera,
Aarhus, Denmark, Winter 2012.
Pedagogical Training Course for Assistant Professors, Aarhus, Denmark, Fall 2011.
High School mathematics mentor, University of Toronto, Tornoto, Ontario, Canada, 2009.

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