Blake Mellor

**Mailing Address**: Loyola Marymount
University

University Hall

1 LMU Drive, Suite 2700

Los Angeles, CA
90045-2659

**Phone**: (310) 338-5775

**E-mail**: blake.mellor@lmu.edu

**URL**: http://myweb.lmu.edu/bmellor

**Positions Held**

2012-present: Professor of Mathematics, Loyola
Marymount University

2007-2012:
Associate Professor of Mathematics, Loyola Marymount University

2002-2007:
Assistant Professor of Mathematics, Loyola Marymount University

1999-2002:
Assistant Professor of Mathematics, Honors College, Florida Atlantic
University

1994-1999:
Graduate Student Instructor, University of California, Berkeley

**Education**

1999: Ph.D. Mathematics, University of California,
Berkeley

Dissertation: ÒFinite
Type Link Homotopy Invariants,Ó under Professor Robion Kirby

1993: B.A., Mathematics, magna cum laude, Harvard
University

Thesis: ÒHeegaard
Splittings and Casson's Invariant,Ó under Professor Clifford Taubes

**Peer-reviewed Papers**

- ÒRecent Developments
in Spatial Graph Theory,Ó with E. Flapan, T. Mattman, R. Nikkuni and R.
Naimi, 2016, to appear in
*Proceedings of the AMS Special Sessions on Algebraic and Combinatorial Structures in Knot Theory and Spatial Graphs* - ÒAlexander and writhe
polynomials for virtual knots,Ó
*J. Knot Theory Ramif.*, vol. 25, no. 8, 2016 - ÒColorings,
determinants and Alexander polynomials for spatial graphs,Ó with T. Kong,
A. Lewald and V. Pigrish,
*J. Knot Theory Ramif.*, vol. 25, no. 4, 2016 - ÒTopological symmetry
groups of complete bipartite graphs,Ó with K. Hake and M. Pittluck,
*Tokyo J. Math*, vol. 39, 2016, pp. 133-156 - ÒThe forbidden number
of a knot,Ó with A. Crans and S. Ganzell,
*Kyungpook Mathematical Journal*, vol. 55, no. 2, 2015, pp. 485-506 - ÒThe Mathematics of
Symmetry and Attitudes towards Mathematics,Ó in
*Doing the Scholarship of Teaching and Learning in Mathematics*, ed. C. Bennett and J. Dewar, MAA Notes no. 83, 2015, pp. 157-169 - ÒComplete bipartite
graphs whose topological symmetry groups are polyhedral,Ó
*Tokyo J. Math*, vol. 37, no. 1, 2014, pp. 135-158 - ÒSymmetries of
embedded complete bipartite graphs,Ó with E. Flapan, N. Lehle, M. Pittluck
and X. Vongsathorn,
*Fundamenta Mathematicae*, vol. 226, 2014, pp. 1-16 - ÒClassification of
topological symmetry groups of
*K*,Ó with E. Flapan, R. Naimi, and M. Yoshizawa,_{n}*Topology Proceedings*, vol. 43, 2014, pp. 209-233 - ÒCounting Links and
Knots in Complete Graphs,Ó with L. Abrams and L. Trott,
*Tokyo J. Math*, vol. 36, no. 2, 2013, pp. 429-458 - ÒUsing tiling theory
to generate angle weaves with beads,Ó with G. Fisher,
*Journal of Mathematics and the Arts*, vol. 6, no. 4, 2012, pp. 141-158 - ÒSpatial Graphs with
Local Knots,Ó with E. Flapan and R. Naimi,
*Revista Matem‡tica Complutense*, vol. 25, no. 2, 2012, pp. 493-510 (DOI: 10.1007/s13163-011-0072-9) - ÒStudent Surveys: What
Do They Think?Ó with H. Zullo, K. Cline, et. al., in
*Teaching Mathematics with Classroom Voting: With and Without Clickers*, ed. K. Cline and H. Zullo, Mathematical Association of America, 2011 - ÒComplete graphs whose
topological symmetry groups are polyhedral,Ó with E. Flapan and R. Naimi,
*Algebraic and Geometric Topology*, vol. 11, 2011, pp. 1405-1433 - ÒDrawing a triangle on
the Thurston model of hyperbolic space,Ó with C. Bennett and P. Shanahan,
*Math. Mag.*, vol. 83, 2010, pp. 83-99 - ÒCounting Links in
Complete Graphs,Ó with T. Fleming,
*Osaka J. Math.*, vol. 46, 2009, pp. 1-29 - ÒIntrinsic
linking and knotting are arbitrarily complex,Ó with E. Flapan and R.
Naimi,
*Fundamenta Mathematicae*, vol. 201, no. 2, 2008, pp. 131-148 - ÒTree Diagrams for
String Links II: Determining Chord Diagrams,Ó
*J. Knot Theory Ramif.*, vol. 17, no. 6, 2008, pp. 649-664 - ÒWeight Systems for
Milnor Invariants,Ó
*J. Knot Theory Ramif.*, vol. 17, no. 2, 2008, pp. 213-230 - ÒVirtual Spatial
Graphs,Ó with T. Fleming,
*Kobe J. Math.*, vol. 24, no. 2, 2007, pp. 67-85 - ÒAn Introduction to
Virtual Spatial Graph Theory,Ó with T. Fleming, in
*Proceedings of the International Workshop on Knot Theory for Scientific Objects*, OCAMI Studies, Vol. 1 (A. Kawauchi, editor), Osaka Municipal Universities Press, 2007 - ÒThree dimensional
finite point groups and the symmetries of beaded beads,Ó with G. Fisher,
*Journal of Mathematics and the Arts*, vol. 1, no. 2, 2007, pp. 85-96 - ÒIntrinsic Linking and
Knotting in Virtual Spatial Graphs,Ó with T. Fleming,
*Algebr. Geom. Topol.*, vol. 7, 2007, pp. 583-601 - ÒTree Diagrams for
String Links,Ó
*J. Knot Theory Ramif.*, vol. 15, no. 10, 2006, pp. 1303-1318 - ÒIntrinsic linking and
knotting of graphs in arbitrary 3-manifolds,Ó with E. Flapan, H. Howards
and D. Lawrence,
*Algebr. Geom. Topol.*, vol. 6, 2006, pp. 1025-1035 - ÒIntersection Graphs
for String Links,Ó
*J. Knot Theory Ramif.*, vol. 15, no. 1, 2006, pp. 53-72 - ÒOn the Topology of
Celtic Knot Designs,Ó with G. Fisher,
*Proceedings of the 7*, 2004 (also in^{th}Annual BRIDGES Conference*Visual Mathematics*, vol. 7, no. 1, 2005) - ÒA few weight systems
arising from intersection graphs,Ó
*Michigan Math. J.*, vol. 51, no. 3, 2003, pp. 509-536 - ÒA geometric
interpretation of Milnor's triple invariants,Ó with P. Melvin,
*Algebr. Geom. Topol.*, vol. 3, 2003, pp. 557-568 - ÒOn the existence of
finite type link homotopy invariants,Ó with D. Thurston,
*J. Knot Theory Ramif.*, vol. 10, no. 7, 2001, pp. 1025-1040 - ÒFinite Type Link
Homotopy Invariants II: Milnor's invariants,Ó
*J. Knot Theory Ramif.,*vol. 9, no. 6, 2000, pp. 735-758 - ÒFinite Type Link
Concordance Invariants,Ó
*J. Knot Theory Ramif.,*vol. 9, no. 3, 2000, pp. 367-385 - ÒThe Intersection
Graph Conjecture for Loop Diagrams,Ó
*J. Knot Theory Ramif.*, vol. 9, no. 2, 2000, pp. 187-211 - ÒFinite Type Link
Homotopy Invariants,Ó
*J. Knot Theory Ramif.*, vol. 8, no. 6, 1999, pp. 773-787

**Other Papers and Articles**

- Review of
*Viewpoints: Mathematical Perspective and Fractal Geometry in Art,*by Marc Frantz and Annalisa Crannell,*Journal of Mathematics and the Arts*, vol. 5, no. 4, 2011, pp. 221-222 - ÒThe Exhibition of Mathematical Art at the 2008 Joint
Mathematics Meetings,Ó
*Journal of Mathematics and the Arts*, vol. 2, no. 1, 2008, pp. 39-45

**Preprints**

- ÒThe Alexander
polynomial for virtual twist knots,Ó with I. Benioff, 2015, available at
*arXiv:1508.06670* - ÒChord Diagrams and
Gauss Codes for Graphs,Ó with T. Fleming, 2006, available at
*arXiv:math.CO/0508269*

**Work in Progress**

- ÒQuandles of 2-bridge knots,Ó with A. Crans and
P. Shanahan

**Grants and Awards**

Recognizes
articles of expository excellence published in *Mathematics Magazine*.
Awarded for ÒDrawing a triangle on the Thurston model of hyperbolic
space,Ó with C. Bennett and P. Shanahan.

ÒTopological
symmetries and intrinsic properties of graphs embedded in 3-spaceÓ

CASTL Institute Scholar, 2005

LMU Summer Research Grant, 2003

NSF Grant DUE-0088211, 2001-2004, Co-PI, $187,054

ÒDiscovery
Based Science and Math in an Environmental ContextÓ

Florida Atlantic University Research Initiation Award,
#RIA-19, 2000

Project NExT Fellow, 1999-2000

Department of Education National Needs Fellowship,
1993-1994

**Conference Presentations and Panels and
Seminar/Colloquium Talks**

2. ÒColoring Spatial Graphs,Ó International Workshop on
Spatial Graphs 2013, Tokyo Christian WomenÕs University, Tokyo, Japan, August
14, 2013

3. ÒColoring Spatial Graphs,Ó Spatial Graphs Conference, Loyola
Marymount University, June 9, 2013

4. ÒFlipping Precalculus,Ó Teaching with Technology Day,
Loyola Marymount University, January 18, 2013

5. ÒIntrinsic Properties of Spatial Graphs,Ó The
Undergraduate Knot Theory Conference, Denison University, July 16, 2012
(Invited Talk)

6. ÒTopological Symmetry Groups of Complete Graphs,Ó Joint
Mathematics Meetings, Boston, January 4, 2012

7. ÒTopological Symmetry Groups of Complete Graphs,Ó USC
Mathematics Colloquium, January 19, 2011 (Invited Talk)

8. ÒTopological Symmetry Groups of Complete Graphs,Ó
International Workshop on Spatial Graphs 2010, Waseda University, Tokyo, August
17-21, 2010

9. ÒIntrinsic linking and knotting are arbitrarily
complex,Ó 1039^{th} meeting of the AMS, Claremont McKenna College, May
4-5, 2008 (Invited Talk)

10. ÒHow Does a Course in the Mathematics of Symmetry
Affect Students in the Liberal Arts?,Ó
MAA MathFest, San Jose, August 2007

11. ÒMathematics of Symmetry, an Experimental Core
Mathematics Course,Ó BIRS Workshop on Innovations in Mathematics Education via
the Arts, Banff, Canada, January 22, 2007

12. ÒMultiple Facets of Quantitative Literacy,Ó
International Society for the Scholarship of Teaching and Learning, November 9,
2006 (panel presentation with Jacqueline Dewar, Curtis Bennett, Suzanne Larson
and Thomas Zachariah)

13. ÒMathematics of Symmetry, an Experimental Core
Mathematics Course,Ó LMU Center for Teaching Excellence, October 26, 2006

14. ÒIntrinsic linking and knotting in virtual spatial
graphs,Ó USC Geometry and Topology Seminar, April 17, 2006 (Invited Talk)

15. ÒIntrinsically linked and knotted graphs,Ó Claremont
Mathematics Colloquium, February 22, 2006 (Invited Talk)

16. ÒWeight systems for Milnor invariants,Ó Joint
Mathematics Meetings, San Antonio, January 11-15, 2006

17. ÒIntrinsic Linking and Knotting in Virtual Spatial
Graphs,Ó Claremont Topology Seminar, November 29, 2005 (Invited Talk)

18. ÒSurviving the First Few Years in an Academic Job,Ó
Panel discussion, Southern California section meeting of the MAA, October 8,
2005 (Invited Participant)

19. ÒEffects of Core Classes on Attitudes and Beliefs
towards Mathematics,Ó CASTL Institute, Columbia College, Chicago, June 9-11,
2005 (Institute Scholar)

20. ÒKnots and Graphs,Ó Guest Lecture at UCLA, February
2005

21. ÒKnots and Graphs,Ó LMU Math Dept. Seminar, February
2005

22. ÒOn the Topology of Celtic Knot Designs,Ó 7^{th}
Annual BRIDGES Conference, Southwestern College, Winfield, KS, July 30-August
1, 2004 (with Gwen Fisher, Cal Poly San Luis Obispo)

23. ÒAn Overview of Robertson-Seymour-Thomas,Ó International Workshop on Knots and Links in a Spatial
Graph, Waseda University, Tokyo, July 20-28, 2004

24. ÒCollaborative Learning in Calculus I,Ó PMET Workshop,
SUNY Oswego, NY, June 2004

25. ÒThe Topology of Celtic Knot Designs,Ó MAA Session on
Math and the Arts, Joint Mathematics Meetings, Phoenix, January 7-10, 2004
(with Gwen Fisher, Cal Poly San Luis Obispo)

26. ÒDiscovery-based Science and Mathematics in an
Environmental Context,Ó MAA Poster Session on Projects supported by the NSF
DUE, Joint Mathematics Meetings, Phoenix, January 7-10, 2004 (with Stephanie
Fitchett, Honors College, Florida Atlantic University)

27. ÒIntersection Graphs for String Links,Ó 991^{st}
meeting of the AMS, University of North Carolina, Chapel Hill, October 24-25,
2003 (Invited Talk)

28. ÒDiscovery-based Science and Mathematics in an
Environmental Context,Ó MAA Poster Session on Projects supported by the NSF
DUE, Joint Mathematics Meetings, Baltimore, January 17, 2003 (with Stephanie
Fitchett, Honors College, Florida Atlantic University)

29. ÒTo Have or Have Knot,Ó Mathematics Colloquium,
California Polytechnic University, San Luis Obispo, November 8, 2002 (Invited
Talk)

30. ÒFinite type invariants and intersection graphs,Ó
Claremont Colleges Topology Seminar, October 29, 2002 (Invited Talk)

31. ÒSeifert Surfaces and Milnor's Invariants,Ó 965^{th}
meeting of the AMS, UNLV, Las Vegas, April 21-22, 2001 (Invited Talk)

32. ÒOn the existence of finite type link homotopy
invariants,Ó Joint Mathematics Meetings, New Orleans, January 10-13, 2001

33. ÒA geometric interpretation of ,Ó 959^{th} meeting of the AMS, Columbia University,
New York, November 3-5, 2000

34. ÒThree weight systems arising from intersection
graphs,Ó AMS Mathematical Challenges of the 21^{st} Century, UCLA,
August 7-12, 2000

35. ÒTopological Psychology,Ó MAA Mathfest, UCLA, August
3-5, 2000

36. ÒIntersection graphs and finite type invariants,Ó
Workshop on Low-Dimensional Topology, University of Warwick (UK), July 10-21,
2000

37. ÒFinite Type Link Homotopy Invariants,Ó 949^{th}
meeting of the AMS, UNC Charlotte, October 15-17, 1999

**Conferences Organized**

1. International Workshop on Spatial Graphs 2013, Tokyo
Christian WomenÕs University, Tokyo, Japan, August 2013 (Co-organizer)

2. Conference on Spatial Graphs, Loyola Marymount
University, June 2013 (Co-organizer)

3. International Workshop on Spatial Graphs 2010, Waseda
University, Tokyo, Japan, August 2010 (Co-organizer)

4. Southern California Student Conference on Spatial
Graphs, Caltech, April 2009 (Co-organizer)

5. Building a Community Partnership: Collaborations in Environmental Science,
Education and Conservation, Honors College, FAU, Jupiter, FL, July 2001 (Co-organizer)

**Conference Sessions Organized**

- Special Session on
Spatial Graphs, AMS Western Sectional Meeting, CSU Fullerton, October
24-25, 2015 (Co-organizer)
- ÒLinking Mathematics
with Other Disciplines,Ó MAA Session, Joint Mathematics Meetings,
Baltimore, January 18, 2003 (Co-organizer)
- Panel on ÒStrategies
for Mathematics for Liberal Arts,Ó Project NExT, UCLA, August 3, 2000

**Other Conferences and Workshops Attended**

- Math Circle Mentorship
and Partnership Workshop, Denver, CO, September 2016
- Joint Mathematics
Meetings, San Diego, CA, January 2013
- Joint Mathematics
Meetings, San Francisco, CA, January 2010
- Joint Mathematics
Meetings, San Diego, CA, January 2008
- Park City Mathematics
Institute, Park City, UT, June 2006
- MAA PMET workshop,
Asilomar, CA, June 2006
- Southern California
Topology Conference, Caltech, May 2004
- ISAMA-BRIDGES,
Granada, Spain, July 23-26 2003
- MAA PMET workshop,
SUNY Potsdam, June 8-19 2003
- Southern California
Topology Conference, Caltech, May 2003
- Joint Mathematics
Meetings, San Diego, January 2002
- Project Intermath
Curriculum Workshop, Carroll College, Helena, MT, June 2001
- Georgia International
Topology Conference, University of Georgia, Athens, GA, May 2001
- 31
^{st}Southeastern International Conference on Combinatorics, Graph Theory and Computing, Florida Atlantic University, March 2000 - Joint AMS/MAA/SIAM
Meeting, Washington, D.C., January 2000
- MAA Mathfest,
Providence, R.I., July 1999
- Joint AMS/MAA/SIAM
Meeting, San Antonio, TX, January 1999
- Kirbyfest, MSRI, UC
Berkeley, June 1998
- Joint AMS/MAA/SIAM
Meeting, San Diego, CA, January 1998

**Teaching Experience**

**Theses Directed**

Alec Lewald, ÒColorings and Alexander Polynomials for
Spatial Graphs,Ó Senior Thesis, May 2014

Kate Hake, ÒTopological Symmetry Groups of Complete
Bipartite Graphs,Ó Senior Thesis, May 2012

Katrina Freitag, ÒCycling through Crystals: A Spatial
Analysis of Human Body Movement,Ó Senior Thesis, May 2012

Lowell Trott, ÒGordian: A Mathematical Tool for Spatial Graph
Characterization,Ó Senior Thesis, May 2008

Katie Williams, ÒConstructivist Perspectives on
Problem Solving,Ó MAT Thesis, July 2006

**Loyola Marymount University**

Honors 250 Mathematics of Symmetry (Spring 2015)

Math 102 Quantitative Skills for the Modern World
(Fall 2005; Fall 2008)

Math 112 Math Analysis for Business II (Spring 2004;
Spring 2005)

Math 120 Precalculus (Fall 2008; Fall 2010; Fall 2011;
Fall 2012; Spring 2013; Fall 2014)

Math 190 Workshop in Mathematics I (Fall 2014)

Math 131 Calculus I (Fall 2002; Fall, 2003; Fall 2006)

Math 198 Mathematics of Symmetry (Spring 2006; Spring
2010; Spring 2013)

Math 234 Multivariable Calculus (Spring 2008; Fall
2013)

Math 245 Differential Equations (Spring 2003)

Math 248 Introduction to Proofs (Spring 2004; Fall
2007)

Math 250 Linear Algebra (Spring 2005; Spring 2006; Spring
2012; Spring 2014; Spring 2015)

Math 285 Discrete Mathematics for Engineering (Spring
2007)

Math 302 Mathematical Ideas for Future Teachers II
(Spring 2005; Spring 2006)

Math 321 Real Analysis (Fall 2010; Fall 2011)

Math 366 Discrete Methods (Spring 2003; Spring 2012)

Math 397 Putnam Preparation (co-taught) (Fall 2002-present)

Math 471 Topology (Spring 2007; Spring 2011)

Math 473 Differential Geometry (Fall 2003; Fall 2005)

Math 493 Senior Capstone for Future Teachers (Fall
2005; Fall 2006; Fall 2013)

Math 550 Fundamental Concepts of Geometry (Fall 2007;
Fall 2009; Fall 2012)

Math 598 Transformational Geometry (Spring 2014)

**Honors College, Florida Atlantic
University**

Symmetry (Spring, 2002)

Statistics (Fall, 2001)

Precalculus (Fall, 2000; Fall, 2001)

Calculus I (Spring, 2000; Spring, 2001)

Calculus II (Fall, 2000; Spring, 2002)

Calculus II for Physics (Spring, 2001)

Matrix Theory (Fall, 1999)

Discrete Mathematics (Spring, 2001)

Mathematical Reasoning (Spring, 2000; independent
study)

Topology and Psychology (Spring, 2000; co-taught with
Kevin Lanning)

Introduction to Programming in C (Fall, 1999)

Scientific Writing (Fall, 1999)

**University of California, Berkeley**

Multivariable Calculus (Summer 1997)

Co-Instructor for undergraduate seminar on low-dimensional
topology (Spring 1997)

Teaching Assistant for Calculus, Linear Algebra,
Discrete Mathematics, Differentiable Manifolds (graduate course)

**Professional Service**

Graded
AP Calculus Exams, 2008

Referee for *Topology,
J. Knot Theory Ramif., Illinois J. Math., Proc. AMS, Europ. J. Comb., Am. Math.
Monthly, J. Math. Arts, J. Math. Chemistry, Disc. & Comp. Geom., Discrete
Mathematics, J. Graph Theory*

Proposal
reviewer for the National Science Foundation

Reviewer
for Mathematical Reviews

**University Service: Loyola Marymount
University**

**University
Service**

Core
Curriculum Committee, 2006-2015

á Chair 2009-2011, 2013-2015

á Chair of Quantitative Reasoning Course Criteria
Working Group (2011-2012)

á Chair of Foundations Course Approval Subcommittee
(2012-2015)

á Member of Core Curriculum Steering Group (2012-2013)

á Member of Approval Subcommittee for FYS/Rhetorical
Arts and Information Literacy (2016-2017)

Trustee Committee (Student Life), 2008-2011

University Teacher Education Committee, 2008-2015

MaSTeP
Committee, 2006-2015

Faculty
Senate, 2005-2008

Academic
Leadership Workshop Planning Committee, 2007

Organizer
of Junior Faculty Seminar (aka Cub Club), 2004-2007

Valedictorian
Committee, 2002-2006

**College Service**

Seaver College Third-Year Review Committee (2012-2015;
chair 2014-2015)

Seaver College representative to Advisory Board for
Undergraduate Teacher Preparation Program, 2008-2015

Science
and Engineering Community Outreach Program (SECOP), 2007 and 2008

**Department
Service**

Secondary
Teacher Preparation Program Director for Mathematics, 2007-2015

Math Dept. Teacher Education Committee, 2005-present;
Chair 2005-2011, 2012-2014

Putnam
Team Advisor, 2002-present

Sophomore
Scholarship Committee, 2014-present

Math
Dept. Education Liaison Committee, 2005

Math
Dept. Curriculum Committee, 2002-2004, 2005-2007, 2007-2008 (chair)

**Advising
Student Groups**

Faculty
Advisor for LMU Mixed Martial Arts Club, 2012-present

Faculty
Advisor for LMU Swing and Ballroom Club, 2004-2006

Math
Club Advisor, 2002-2005

**University Service: Honors College,
Florida Atlantic University**

Bylaws
Committee (Chair), 2001-2002

Presiding
Officer, Honors College Faculty Assembly, 2000-01

Screening
Committee for Undergraduate Teaching Award (Chair), 2000-01

FAU
Committee for Undergraduate Teaching Award, 2000-01

Faculty
Committee (Chair), Fall 1999

Admissions
Committee (Chair), 1999-2000

Promotions
and Tenure Guidelines Committee, 1999-2002

Academic
Affairs and Student Life Committee, 1999-2001

Search
Committee for Mathematics, 1999-2000 (Chair), 2000-01

Search
Committee for Physics (Chair), 1999-2000

Search
Committee for French, 1999-2000

FAU
Faculty Council (alternate), 1999-2000

**Community Service**

Assisted with 8^{th} grade Science Fair
projects at Whaley Middle School, Compton, January-February 2005

La Ballona Elementary Math Circle, 2016-present

**Languages**: French, German.

**Computer Languages**: BASIC, Pascal, LISP, C, C++, Java, Unix

**Professional Memberships**

American Mathematical Society

Mathematical Association of America

National Council of Teachers of Mathematics