Alexander Coward
Lecturer in Mathematics
Address: Department of Mathematics,
University of California, Berkeley, CA 94720,
United States of America.
• Phone: +1 530 746 8723, +1 (415) 323 9469
• e-mail: ude.yelekreb.htam|drawoc#ude.yelekreb.htam|drawoc
• Web page: http://www.alexandercoward.com
Research interests
• Topology and geometry in 3 dimensions. Particularly interested in: algorithms, complexity, knot invariants, normal surface theory, Heegaard splittings, triangulations, unknotting processes, physical knot theory.
Current positions
• July 2013–present. Lecturer, UC Berkeley.
• March 2013–present. Affiliate Associate Professor, Th´ai Nguyˆen University, Vietnam.
Previous positions
• July 2012–present. Research Associate, Department of Mathematics and Statistics, University of Sydney, Australia. Position supported by the Australian Research Council through Discovery Grant DP110101104.
• July 2010–June 2012. Krener Assistant Professor, Department of Mathematics, University of California, Davis.
• August 2011–September 2011. Visiting Professor, Th´ai Nguyˆen University, Vietnam.
• September 2009–August 2010. Lecturer, University of Oxford.
• July 2008–June 2009. Krener Assistant Professor, Department of Mathematics, University of California, Davis.
• October 2004–June 2008. Lecturer, St Catherine’s College, University of Oxford.
Education
• 2004 - 2008. D.Phil. (Ph.D. equivalent) in Mathematics, University of Oxford. Supervised by Prof. Marc Lackenby. Thesis title: Algorithmically detecting the bridge number of hyperbolic knots.
• 2003 - 2004. Postgraduate Certificate of Education (PGCE) with UK ‘Qualified Teacher Status’, Department of Education, University of Oxford.
• 1999 - 2003. M.Math. (First Class Honors) in Mathematics (combined bachelors and masters), University of Oxford.
Awards
• Pending Award Ceremony. Honorary Doctorate in Education, Th´ai Nguyˆen University, Vietnam.
• June 2012. Awarded the UC Davis G. Thomas Sallee Mathematics Teaching Award for the best teaching of lower-division mathematics over the previous year.
• June 2012. Nominated for the ASUCD (official student government of UC Davis) ‘Educator of the Year’ award. • 2006 - 2008. Senior Germaine Scholar, Brasenose College, University of Oxford.
• 2005 - 2008. Doctoral research funded by an Engineering and Physical Sciences Research Council (EPSRC) Studentship.
• 2000 - 2003. Senior Scholar at St Hugh’s College, University of Oxford (prize awarded to the top undergraduate each year across all subjects).
• Twice Represented Oxford University in the COMAP International Applied Mathematics Olympiad. 2001: Honourable Mention; 2002: Meritorious Winner.
• 2000. Winner of the Katherine Lawrence Memorial Prize in Mathematics, St Hugh’s College, University of Oxford.
Papers
• Ordering the Reidemeister moves of a classical knot, Alg. Geom. Top. 6 (2006) 659-671.
• (Joint with Marc Lackenby) Unknotting genus one knots, Comment. Math. Helv. 86 (2011) 383-399.
• (Joint with Benjamin A. Burton and Stephan Tillmann) Computing closed essential surfaces in knot complements, 29th ACM Symp. Comp. Geom., Rio de Janeiro, 2013 (to appear).
• (Joint with Marc Lackenby) An upper bound on Reidemeister moves, Amer. J. Math. (to appear).
• (Joint with Joel Hass) Topological and physical link theory are distinct, preprint, Pacific. J. Math. (to appear).
• Algorithmically detecting the bridge number of hyperbolic knots, preprint, arxiv.org/ abs/0710.1262.
• Crossing changes and circular Heegaard splittings, preprint, arxiv.org/abs/1210. 5812.
Papers arising from research projects supervised
• Julian Gold, A bound for orderings of Reidemeister moves, submitted
Selected talks
• Invited Address Topology/Geometry Seminar, UC Davis, 6th February 2013, Fast normal surface theory.
• Invited Address Algebra/Geometry/Topology Seminar, University of Melbourne, 26th October 2012, Crossing changes and circular Heegaard splittings.
• Invited Address Geometry, Topology and Algebra Seminar, University of Sydney, 18th September 2012, Unknotting genus one knots.
• Invited Address Geometry, Topology and Algebra Seminar, University of Sydney, 31st July 2012, An upper bound on Reidmeister moves.
• Invited Address Topology Seminar, University of California at Santa Barbara, 29th May 2012, Topological and physical link theory are distinct.
• Invited Conference Address The 46th Spring Topology and Dynamics Conference, Mexico City, 22nd March 2012, Topological and physical link theory are distinct.
• Invited Conference Address Redbud Topology Conference, Oklahoma State University, 3rd March 2012, Topological and physical link theory are distinct.
• Invited Address Topology Seminar, UC Riverside, 14th February 2012, Unknotting crossing changes and circular Heegaard splittings.
• Invited Address Topology Sominar, University of Texas at Austin, 31st October 2011, Crossing changes and circular Heegaard splittings.
• Invited Conference Address 2011 AMS Spring Central Section Meeting, Special Session on Thin Position, 19th March 2011, Crossing changes and circular thin position.
• Invited Conference Address 54th annual meeting of the Australian Mathematical Society, Special session on Topology and Geometry, Brisbane, Australia, 27th September 2010, An upper bound on Reidemeister moves.
• Invited Address Differential Geometry Seminar, University of Cambridge, 19th May 2010, An upper bound on Reidemeister moves.
• Invited Address Topology Seminar, Durham University, 19th May 2010, An upper bound on Reidemeister moves.
• Invited Address Geometry and Topology Seminar, University of Warwick, 28th January 2010, 19th May 2010, An upper bound on Reidemeister moves.
• Invited Conference Address Computational and Algorithmic Geometry, William Rowan Hamilton Geometry and Topology Workshop, September 2009, An upper bound on Reidemeister moves.
• Invited Conference Address Geometric Topology in 3 and 4 Dimensions, Conference in honour of Martin Scharlemann, UC Davis, 25th June 2009, An upper bound on Reidemeister moves.
• Invited Address Topology Seminar, University of California at Berkeley, 1st April 2009, Unknotting genus one knots.
• Invited Address Topology/Geometry Seminar, University of California at Davis, 3rd February 2009, Unknotting genus one knots.
• Invited Address Topology Seminar, University of California at Santa Barbara, 29th January 2009, Unknotting genus one knots.
• Invited Conference Address Joint Mathematics Meetings, AMS Special Session on Teichmller Theory and Low-Dimensional Topology, Washington DC, 6th January 2009, Unknotting genus one knots.
• Invited Address Topology/Geometry Seminar, University of California at Davis, 21st October 2008, Detecting the bridge number of hyperbolic knots.
• Contributed Talk Meeting of London Mathematical Society, 4th July 2008, Algorithms and hyperbolic 3-manifolds.
• Invited Conference Address The 25th Annual Workshop in Geometric Topology, Park City, Utah, 27th June 2008, Detecting the bridge number of hyperbolic knots.
• Invited Conference Address Warwick symposium, Workshop on 3-manifold geometry and topology, 11th July 2007, Detecting the bridge number of hyperbolic knots.
• Invited Address Topology Seminar, Oxford University, 30th April 2007, Detecting the bridge number of hyperbolic knots.
Service
• Referee of many papers for journals such as Journal of Topology, Geometry and Topology, Pacific Journal of Mathematics, Topology and its Applications, Algebraic and Geometric Topology and Geometriae Dedicata.
• Fall 2011. Organizer of the Topology and Geometry Seminar, UC Davis.
• Summer 2011. Supervised an NSF funded undergraduate REU, UC Davis.
• Fall 2008. Designed and delivered new graduate course ‘Knots and surfaces in 3- manfolds’, UC Davis, Fall 2008.
• Winter 2009. Organized advanced class on the Gordon Conjecture, UC Davis.
• Summer 2011. Faculty instructor, UC Davis COSMOS program.
• Summer 2010. Faculty instructor, UC Davis COSMOS program.
• Summer 2009. Teacher fellow, UC Davis COSMOS program.
Teaching
University of California at Davis
• Taught the following undergraduate classes:
– Fall 2008. 16A - Short calculus.
– Winter 2009. 22B - Differential equations.
– Spring 2009. 16C - Short calculus.
– Fall 2010. 22B - Differential equations.
– Spring 2011. 16B - Short calculus.
– Spring 2011. 147 - Topology.
– Fall 2011. 21D - Vector calculus.
– Spring 2012. 21C - Calculus.
• June 2012. Awarded the UC Davis G. Thomas Sallee Mathematics Teaching Award for the best teaching of lower-division mathematics over the previous year.
• June 2012. Nominated for the ASUCD (official student government of UC Davis) ‘Educator of the Year’ award.
• Fall 2008. Designed and taught graduate course ‘Knots and Surfaces in 3-manifolds’.
• Spring 2008. Organized and taught advanced class on the Scharlemann-Qui proof of the Gordon conjecture.
University of Oxford
• Spring 2006. Class tutor for the fourth year course ‘Analytic Topology’.
• Fall 2009. Lecturer and class tutor for the fourth year course ‘Topology and Groups’.
• Fall 2009. Class tutor for the fourth year course ‘Graph Theory’.
• Summer 2010. Wrote and examined Section C finals paper ‘C3.1a Topology and Groups’. Th´ai Nguyˆen University, Vietnam
• Since 2011. Extensive service to Th´ai Nguyˆen University in Vietnam, in undergraduate instruction, curriculum development, teacher training and outreach. St. Catherine’s College, University of Oxford
• 2004 -2008. College lecturer and tutor of mathematics at St Catherine’s College. Taught all areas of undergraduate pure mathematics in tutorials and classes, organized and graded examinations and interviewed applicants.