Mark C. Hughes
Contact
Information
Department of Mathematics
312 TMCB
Brigham Young University
Provo, UT 84602
801-422-7416
hughes@mathematics.byu.edu
Citizenship
Canada; US Permanent Resident
Research
Interests
Braided surfaces and their applications in 3 and 4-manifold topology, symplectic topology,
categorifications of quantum link invariants.
Education
Stony Brook University, Stony Brook, NY, USA
Ph.D., Mathematics, 2014
• Thesis: Braiding non-ribbon surfaces and constructing broken fibrations on
smooth 4-manifolds.
• Advisor: Oleg Viro, Ph.D.
University of Waterloo, Waterloo, ON, Canada
M.Math., Pure Mathematics, 2008
• Thesis: Branched covering constructions and the symplectic geography problem.
• Advisor: B. Doug Park, Ph.D.
University of Calgary, Calgary, AB, Canada
B.Sc., Applied Mathematics, 2006
• Minor: Pure Mathematics
• First Class Honours
Employment
Papers
Visiting Assistant Professor
Brigham Young University
Aug 2014 to present
1. “Bounds on the braid rank via Dehornoy orderings.” In preparation.
2. “Constructing broken Lefschetz fibrations via braided surfaces with caps.”
In preparation.
3. “Braiding link cobordisms and non-ribbon surfaces.” To appear in Algebraic &
Geometric Topology. arXiv:1305.2973v3.
4. “A note on Khovanov-Rozansky sl2 -homology and ordinary Khovanov homology.”
J. Knot Theory Ramifications. 23 (2014), no. 12, 1450057 (25 pages).
5. (with A. Akhmedov, and B.D. Park) “Geography of simply connected nonspin
symplectic 4-manifolds with positive signature.” Pacific J. Math. 261 (2013), no.
2, 257-282.
6. “Braiding non-ribbon surfaces and constructing broken fibrations on smooth 4manifolds.” Stony Brook University Ph.D. Thesis.
7. “Branched covering constructions and the symplectic geography problem.”
University of Waterloo M.Math. Thesis.
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Awards and
Recognition
Natural Sciences and Engineering Research Council of Canada
• Postgraduate Scholarship
Sept 2008 to Aug
• Canada Graduate Scholarship (Declined )
Oct
• Canada Graduate Scholarship
Sept 2006 to Aug
• Undergraduate Student Research Award
May to Aug
• Undergraduate Student Research Award
May to Aug
2010
2008
2008
2006
2005
Academic and Leadership Awards
• President’s Graduate Scholarship - University of Waterloo Sept 2006 to Aug 2008
• R.J. Torrence Memorial Scholarship - University of Calgary
Sept 2005
• Joyce MacAlpine Bursary - University of Calgary
Sept 2005
• Louise McKinney Scholarship - Government of Alberta
Sept 2005
• Jason Lang Scholarship - Government of Alberta
Sept 2004
• Student of the Year - Medicine Hat College
Apr 2004
• Alexander Rutherford Scholarship - Government of Alberta
Sept 2000
• Governor General’s Academic Medal - Government of Canada
Jun 2000
Talks
• Braiding knot cobordisms.
Special Session on Knots and 3-Manifolds, AMS Spring Western
Sectional Meeting. University of Nevada, Las Vegas.
• Lefschetz fibrations and the symplectic geography problem.
Topology Seminar. Brigham Young University.
• Bounding the ribbon genus via braided surfaces.
Topology Seminar. Brigham Young University.
• Constructions of broken fibrations on 4-manifolds.
Differential Geometry and Symplectic Topology Seminar. University
of Minnesota.
• A new bound on the ribbon genus of knots via braided surfaces.
Topology Seminar. Georgia Institute of Technology.
• Comparing slice and ribbon genera via braided surfaces.
Knots in Washington XXXVII. George Washington University.
• Constructing broken fibrations on 4-manifolds.
Colloquium. Brigham Young University.
• Alexander and Markov type theorems for link cobordisms.
Knots in Washington XXXV. George Washington University.
• Topological quandles and link invariants.
Graduate Student Seminar. Stony Brook University.
• Braided link cobordisms.
Graduate Student Topology Conference. Indiana University.
• Braid theory in dimension 4.
Graduate Student Seminar. Stony Brook University.
• Branched covering constructions and the symplectic geography
problem. University of Waterloo.
• Ricker discrete dynamical model with randomized perturbations.
University of Calgary.
• Models of the mechanics and dynamics of the tails of dinosaurs.
P.I.M.S. Industrial Problem Solving Workshop. University of Calgary.
• An analysis of the threat of extinction for Sweden’s wolf population.
P.I.M.S. Mathematical Modeling in Biology Workshop. University
of Alberta.
Conference and • Symposium on the Geometry and Topology of Manifolds.
Workshop
Pacific Institute for the Mathematical Sciences at the University
Participation
of British Columbia.
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Apr 2015
Jan 2015
Sept 2014
Feb 2014
Jan 2014
Jan 2014
Nov 2013
Dec 2012
Apr 2012
Apr 2012
Apr 2010
Jul 2008
Sept 2005
May 2005
May 2005
Jul 2015
• Moab Topology Conference. Moab, Utah.
May 2015
• Geometry and Topology of Symplectic 4-manifolds. University of
Apr 2015
Massachusetts, Amherst.
• Special Session on Knots and 3-Manifolds, AMS Spring Western
Apr 2015
Sectional Meeting. University of Nevada, Las Vegas.
• Knots in Washington XXXVII. George Washington University.
Jan 2014
• Tech Topology Conference. Georgia Institute of Technology.
Dec 2013
• Semester on 4-Manifolds and their Combinatorial Invariants.
May to Jun 2013
Max Planck Institute for Mathematics, Bonn Germany.
• Graduate Student Geometry and Topology Conference.
Apr 2013
University of Notre Dame.
• Knots in Washington XXXV. George Washington University.
Dec 2012
• Workshop and Conference on Holomorphic Curves and LowJul to Aug 2012
Dimensional Topology. Stanford University.
• Panorama of Topology - A conference in Honor of William
May 2012
Browder. Princeton University.
• Cornell Topology Festival. Cornell University.
May 2012
• Graduate Student Topology Conference. Indiana University.
Apr 2012
• Floer Theory and Symplectic Dynamics. Centre de Recherches
May 2008
Mathématiques at the Université de Montréal.
• The Stony Brook Dialogues in Mathematics and Physics
Mar 2008
(Yang & Simons Symposium). Stony Brook University.
• Industrial Problem Solving Workshop. Pacific Institute for the
May 2005
Mathematical Sciences at the University of Calgary.
• Mathematical Modeling in Biology Workshop. Pacific Institute
May 2005
for the Mathematical Sciences at the University of Alberta.
Teaching
Experience
Instructor - Brigham Young University
MATH 313 - Elementary Linear Algebra
MATH 113 - Calculus II
Instructor - Stony Brook University
MAT 127 - Calculus C
MAP 103 - Proficiency Algebra
MAT 118 - Mathematical Thinking
Teaching Assistant - Stony Brook University
MAP 103 - Calculus II
MAT 123 - Introduction to Calculus
MAT 125 - Calculus A
MAT 126 - Calculus B
Teaching Assistant - University of Waterloo
Calculus and Linear Algebra courses
Service
Fall 2014, Winter 2015
Fall 2014
Spring 2012, Summer 2013
Fall 2010, Spring 2013
Summer 2010, 2011, 2012
Spring 2011, Fall
Fall
Fall
Spring
2013
2012
2011
2010
Fall 2006 to Spring 2008
Moab Topology Conference - Co-organizer
Brigham Young University
May 2015
Graduate Student Seminar - Co-organizer
Stony Brook University
Sept 2011 to May 2012
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