ANDREW DOUGLAS, PH.D.

Contact Full Professor Doctoral Faculty Information Department of Mathematics and Physics Programs NYC College of Technology The Graduate Center City University of New York City University of New York 300 Jay Street 345 Fifth Avenue Brooklyn, NY 11201 New York, NY 10016 B [email protected] T 347.374.1896

Nationality American and Canadian citizen

Research Representation theory, Lie , Lie groups, mathematical physics, computational . Interests

Education 2006 Doctor of Philosophy, University of Toronto, Canada, Mathematics. 2001 Master of Arts, York University, Canada, Mathematics. 2000 Master of Education, Lakehead University, Canada, Education. 1999 Bachelor of Education, Lakehead University, Canada, Education. 1997 Bachelor of Science, University of Toronto, Canada, Mathematics.

Employment & 2016 to Present Full Professor, Department of Mathematics, Appointments New York City College of Technology, CUNY. 2016 to Present Faculty Member, Department of Mathematics, CUNY Graduate Center. 2012 to Present Faculty Member, Department of Physics, CUNY Graduate Center. 2012 to 2016 Associate Professor, Department of Mathematics, New York City College of Technology, CUNY. 2007 to 2012 Assistant Professor, Department of Mathematics, New York City College of Technology, CUNY. Spring and Summer Postdoctoral Fellow, Department of Mathematics and Statistics, 2007 University of Saskatchewan, Canada. Summer and Fall Postdoctoral Fellow, Department of Mathematics and Statistics, 2006 University of Regina, Canada.

Recent Visiting • University of Toronto, Department of Mathematics, Toronto, Canada. Visiting Professor. Fall Positions 2016 and Spring 2017. Collaborator: Professor Joe Repka. • University of Trento, Department of Mathematics, Trento, Italy. May 31-June 7, 2017. Visiting Researcher. Collaborator: Professor Willem de Graaf. • University of Milan, Department of Mathematics, Milan, Italy. May 24-May 31, 2017. Visiting Researcher. Collaborator: Professor Paolo Casati.

Publications 20. Douglas, A., et al., A comparison of two classifications of solvable Lie algebras, Journal of Mathematical Physics 59 (2018) 121701. Note: This article was done with 11 freshman under- graduate students at the University of Toronto. 19. Douglas, A., and Repka, J., Subalgebras of the rank two semisimple Lie algebras, Linear and Multilinear Algebra, (2017) DOI: 10.1080/03081087.2017.1383350.

1 18. Douglas, A., and Repka, J., The subalgebras of the symplectic sp(4, C), Linear Algebra and its Applications, 527 (2017) 303-348. 17. Douglas, A., and Repka, J., The subalgebras of so(4, C), Communications in Algebra, 44(12) (2016) 5269-5286.

16. Douglas, A., and Repka, J., A classification of the subalgebras of A2, Journal of Pure and Applied Algebra, 220(6), (2016) 2389-2413. 15. Douglas, A., and Repka, J., Levi decomposable algebras in the classical Lie algebras, Journal of Algebra, 428 (2015) 292-314.

14. Douglas, A., and Repka, J., The Levi decomposable subalgebras of C2, Journal of Mathematical Physics 56 (2015) 051703.

13. Douglas, A., and Repka, J., The GraviGUT algebra is not a subalgebra of E8, but E8 does contain an Extended GraviGUT algebra, SIGMA. 10 (2014) 072. 12. Douglas, A., Repka, J., and Joseph, W., The Euclidean algebra in rank 2 classical Lie algebras, Journal of Mathematical Physics, 55 (2014) 061701. 11. Douglas, A., de Guise, H., and Repka, J., The Poincar´e algebra in rank 3 simple Lie algebras, Journal of Mathematical Physics, 54 (2013) 023508. 10. Douglas, A., Kahrobaei, D., and Repka, J., Classification of embeddings of abelian extensions of Dn into En+1, Journal of Pure and Applied Algebra, 217(10), (2013) 1942-1954. 9. Bremner, M.R., and Douglas, A., The simple non-Lie Malcev algebra as a Lie-Yamaguti alge- bra, Journal of Algebra, 358 (2012) 269-291. 8. Douglas, A., Joseph, W., and Repka, J., A classification of the embeddings of the Diamond Lie algebra into sl(3, C) and sp(4, C), and restrictions of irreducible modules, Journal of Math- ematical Physics, 52 (2011) 103507. 7. Douglas, A., and Repka, J., Embeddings of the Euclidean algebra e(3) into sl(4, C) and re- striction of irreducible representations of sl(4, C), Journal of Mathematical Physics, 52 (2011) 013504. 6. Douglas, A., and Repka, J., Indecomposable representations of the Euclidean algebra e(3) from irreducible representations of sl(4, C), Bulletin of the Australian Mathematical Society, 83 (2011) 439-449. 5. Douglas, A., and Repka, J., Indecomposable representations of the Euclidean algebra e(3) from irreducible representations of the symplectic algebra sp(4, C), Journal of Physics: Conf. Ser. 284 (2011) 012022. 4. Douglas, A., and de Guise, H., Some nonunitary, indecomposable representations of the Eu- clidean algebra, Journal of Physics A: Mathematical and Theoretical, 43 (2010). 3. Kahrobaei, D., Douglas, A., and Bencsath, K., Some Residually Solvable One-relator Groups, Bulletin of the Irish Mathematical Society, 65 (2010) 23-31. 2. Douglas, A., On the finite dimensional, indecomposable representations of the Euclidean Al- gebra e(2) having two generators, Journal of Mathematical Physics 47(5) (2006). 1. Douglas, A., and Premat, A., A class of nonunitary, finite dimensional representations of the Euclidean algebra e(2), Communications in Algebra, 35 (2007) 1433-1448.

Preprints • Douglas, A., and de Graaf, W.A., Closed subsets of root systems and regular subalgebras, submitted.

2 Invited talks 27. University of York Algebra Colloquium since 2008 Place: University of York, York, England Date: January 11, 2019 26. Graduate Student Mathematics Colloquium Place: CUNY Graduate Center, New York, NY Date: October 23, 2017 25. Mathematics Colloquium Place: University of Trento, Trento, Italy Date: June 6, 2017 24. Lie Groups and Quantum Mathematics Seminar Place: Rutgers University, New Brunswick, NJ Date: April 8, 2016 23. Universit´e du Qu´ebec `a Montr´eal Mathematics Colloquium Place: Montr´eal, Canada Date: October 2, 2015 22. International Meeting of the American Mathematical Society, European Mathematical Society, and the Portuguese Mathematical Society Place: Universidade do Porto, Porto, Portugal Date: June 10-13, 2015 21. Stony Brook Mathematics Education Research Seminar Place: State University of New York at Stony Brook, Stony Brook, New York Date: February 23, 2015 20. New York Applied Algebra Colloquium Place: CUNY Graduate Center, New York, NY Date: September 19, 2014 19. 30th International Colloquium on Theoretical Methods in Physics Place: Ghent University, Ghent, Belgium Date: July 15, 2014 18. Groups St. Andrews Conference 2013 Place: University of St. Andrews, St. Andrews, Scotland Date: August 7, 2013 17. University of Zaragoza Mathematics Colloquium Place: University of Zaragoza, Zaragoza, Spain Date: June 28, 2013 16. American Mathematical Society-Mathematical Association of America Regional Meeting Special session on Algorithmic Problems of Group Theory and Applications to Information Security Place: Boston, Massachusetts Date: April 6, 2013. 15. American Mathematical Society-Mathematical Association of America National Joint Mathe- matics Meeting Special session on Groups, Algorithms, Complexity, and Theory of Security Place: Boston, Massachusetts Date: January 5, 2012 14. CUNY Representation Theory Seminar Place: CUNY Graduate Center, New York, NY Date: February 3, 2012

3 13. American Mathematical Society-Mathematical Association of America Regional Meeting Special session on Groups, Computations and Applications Place: New Jersey Institute of Technology, Newark, NJ Date: May 23, 2010 12. Second Mile High Conference on Nonassociative Mathematics Place: University of Denver, Denver, Colorado Date: June 22 to 27, 2009 11. Third Annual Meeting of the Prairie Network for Research in Mathematical Sciences Place: University of Saskatchewan, Saskatoon, Canada Date: April 30, 2009 10. NYCCT Research Conference Place: New York City College of Technology, CUNY, Brooklyn, NY Date: Mach 27, 2009 9. American Mathematical Society-Mathematical Association of America National Joint Mathe- matics Meeting, Special session on Representation Theory and Nonassociative Algebras Place: San Diego, California Date: January 8, 2008 8. Learning Communities Conference of the Atlantic Center for Learning Communities Place: New York City Passionist Retreat Center in Riverdale, NY Date: October 22-24, 2008 7. National Learning Communities Conference Place: Marietta, Georgia Date: November 12-14, 2010 6. New York Algebra Colloquium Place: CUNY Graduate Center, New York, NY Date: April 16, 2010 5. Bronx Community College Mathematics Seminar Place: BCC CUNY, Bronx, NY Date: March 31, 2009 4. Universit´e du Qu´ebec `a Montr´eal Mathematics Colloquium Place: Montr´eal, Canada Date: February 13, 2009 3. New York Algebra Colloquium Place: CUNY Graduate Center, New York, NY Date: December 5, 2008. 2. University of Saskatchewan Mathematics Colloquium Place: Saskatoon, Saskatchewan, Canada Date: August 6, 2008 1. City Tech Math Seminar Series Place: City Tech, CUNY, Brooklyn, New York Date: April 10, 2008

Seminar • Co-Organizer, New York Applied Algebra Colloquium, CUNY Graduate Center, 2008-2017. Organization • Co-Organizer, CUNY Representation Theory Seminar, CUNY Graduate Center, 2010-2017.

4 AMS Conference 7. Fall Eastern Sectional Meeting of the American Mathematical Society Organization Place: Rutgers University, New Brunswick, NJ Title of Special Session Co-organized: Representation Theory, Vertex Operator Algebras, and Related Topics Dates: November 14-15, 2015 6. Fall Eastern Sectional Meeting of the American Mathematical Society Place: Temple University, Philadelphia, PA Title of Special Session Co-organized: Representation theory, combinatorics and categorifica- tion Dates: October 12-13, 2013 5. American Mathematical Society-Mathematical Association of America National Joint Mathe- matics National Meeting Place: San Diego, CA Title of Special Session Co-organized: Representation Theory, Lie algebras and Transforma- tion Groups Dates: January 9-10, 2013 4. Sectional Meeting of the American Mathematical Society Place: University of Nevada, Las Vegas. Title of Special Session Co-organized: Lie Algebras, Algebraic Transformations Groups and Representation Theory. Dates: April 30 and May 1, 2011 3. Sectional Meeting of the American Mathematical Society Place: New Jersey Institute of Technology, Newark, NJ. Title of Special Session Co-organized: Lie Algebras and Representation Theory. Dates: May 22-23, 2010. 2. National Meeting of the American Mathematical Society. Place: San Francisco, CA. Title of Special Session Organized: Nonassociative Algebras and Representation Theory. Dates: January 13-16, 2010. 1. Co-organized Regional Meeting of the Mathematical Association of America Place: City Tech Dates: May 1, 2010.

Grants PSC-CUNY Research Grants. • Position: Principal Investigator • Dates: 2009/2010, 2010/2011, 2011/2012, 2013/2014, 2014/2015, 2015/2016, 2016/2017, 2018/2019.

National Science Foundation Noyce Grant. • Position: Co-Principal Investigator • Title: NOYCE Explorers, Scholars, Teachers (NEST): Fostering the Creation of Exceptional Mathematics and Technology Teachers in New York City. • Amount: $1, 418, 976.00 • Dates: 2014-2019

Primary Service Mathematics Education Program, NYC College of Technology, CUNY This program prepares students to teach mathematics in grades 7-12 in New York State. • Program Director (including directing the creation of the program, and assessment of the program for national accreditation), 2012 - 2016. • Program Advisor and committee member, 2016-Present.

5 • CUNY Teacher Education Council member (a council representing all teacher education pro- grams across CUNY), 2015-2016.

Curriculum Leadership and Development, NYC College of Technology, CUNY • Committee member, Curriculum Committee of the Department of Mathematics, 2007-Present. • Curriculum developer (creating and modifying mathematics and mathematics education courses, writing curriculum proposals, created proposal for Mathematics Eduction program), 2007- Present. • Chair, College Council Curriculum Committee, 2012/2013 academic year.

Other Committee Work and Service • Ongoing referee for mathematics and mathematical physics journals (including Communica- tions in Algebra, Journal of Mathematical Physics, Linear and Multilinear Algebra, Linear Algebra and Its Applications). • Review Panel member for PSC CUNY Research Grants (this is a CUNY internal research grant), 2008-2014. • National Science Foundation, Review panel member, spring 2012. • Committee for Promotion to Associate Professor at NYC College of Technology, CUNY; 2013/2014 Academic Year.

Teaching Undergraduate Courses Taught: Abstract Algebra (Groups, Rings, and Fields); Linear Algebra; Calculus; Precalculus; College Algebra and Geometry; Developmental Mathematics; Technology in Mathematics Education; Discrete Structures and Algorithms; Teaching seminar for mathematics education students; Lie algebras; Real Analysis.

Graduate Courses Taught: Lie groups, Lie algebras, and representation theory with applications to physics.

Peer Evaluations of Teaching

Semester Overall Evaluation by a Senior Professor Fall 2007 Excellent Fall 2007 Excellent Fall 2007 Excellent Spring 2008 Excellent Spring 2008 Excellent Fall 2008 Excellent Spring 2009 Very Good Fall 2009 Excellent Spring 2010 Excellent Fall 2010 Excellent Spring 2011 Excellent Spring 2012 Excellent Fall 2012 Excellent Spring 2012 Excellent Fall 2014 Excellent Fall 2015 Excellent

Note: After becoming a Full Professor in Fall 2016, my teaching is no longer observed by other faculty.

6 Student Evaluations of Teaching

Semester Student Evaluation Course (out of 5) Fall 2007 4.77 MAT 1475 Calculus I Fall 2007 4.69 MAT 1180 Math. Concepts and Applications Spring 2008 4.72 MAT 1475 Calculus I Spring 2008 5.00 MAT 1275 Algebra and Trigonometry Fall 2008 4.87 MAT 1175 Algebra and Geometry Fall 2008 4.91 MAT 1475 Calculus I Spring 2009 4.91 MAT 1175 Algebra and Geometry Spring 2009 4.96 MAT 1175 Algebra and Geometry Fall 2009 4.62 MAT 1175 Algebra and Geometry Fall 2009 4.89 MAT 1475 Calculus I Spring 2010 4.66 MAT 1175 Algebra and Geometry Spring 2010 4.96 MAT 1375 Precalclus Fall 2010 4.86 MAT 1175 Algebra and Geometry Fall 2010 4.94 MAT 2580 Linear Algebra Spring 2011 4.79 MAT 1175 Algebra and Geometry Spring 2011 4.79 MAT 2580 Linear Algebra Spring 2012 4.98 MAT 2580 Linear Algebra Fall 2012 4.93 MAT 1175 Algebra and Geometry Fall 2012 4.86 MAT 1475 Calculus I Spring 2013 4.96 MAT 1175 Algebra and Geometry Spring 2013 4.87 MAT 1475 Calculus I Fall 2013 4.85 MAT 1475 Calculus I Fall 2013 5.00 MEDU 2010 Technology in Math. Education Spring 2014 4.88 MAT 3080 Abstract Algebra Spring 2014 4.94 MAT 1475 Calculus I Fall 2014 4.82 MAT 1475 Calculus I Fall 2014 5.00 MEDU 2010 Technology in Math. Education Fall 2014 5.00 MEDU 4010 Seminar for Student Teachers Spring 2015 4.81 MAT 3080 Abstract Algebra Fall 2015 4.85 MAT 1575 Calculus II Fall 2015 4.95 MEDU 2010 Technology in Math. Education Spring 2018 5.00 MAT 3080 Abstract Algebra Spring 2018 4.92 MAT 1475 Calculus I Fall 2018 4.87 MAT 1475 Calculus I Fall 2018 4.88 MAT 3075 Intro to Real Analysis

Professional Ontario Certified Teacher. This is a professional license to teach in the Canadian province of Ontario. Licensure

Updated: February 14, 2019

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