Helene R. Tyler, PHD

Education

PHD, Syracuse University
MS, Syracuse University
BA, Purchase College, SUNY

Research

My main research interests are in the representation theory of finite dimensional algebras. This area was born of a desire to understand how a finite number of linear transformations can act simultaneously on a vector space. Over the last forty years, a well-developed theory has emerged; the Auslander-Reiten theory now understands the representations of an algebra as the study of the classification of the indecomposable modules over that algebra and the homomorphisms between them. My current focus is the relationship between the Auslander-Reiten theory and the recently developed Gabriel-Roiter theory, which provides an alternative classification mechanism for the module category.

Professional Experience

I have served three times as a Volunteer Lecturer at the Royal University of Phnom Penh (RUPP) in Cambodia. During each of my first two visits, I taught a course in Ordinary Differential Equations. My third visit was in June, 2012, when I taught a course in Group Theory. The Volunteer Lecturer Program is supported by the National Academy of Sciences and focuses on scientific capacity-building in Cambodia and other developing countries. Volunteer lecturers from the USA, France, Japan, and other countries collaborate with RUPP to offer a masters program in mathematics. More information about the program can be found on their website: http://sites.nationalacademies.org/pga/biso/IMU/PGA_050583

Publications & Professional Activities

Publications

• M. Schmidmeier, H.R. Tyler, The Auslander-Reiten Components in the Rhombic Picture, preprint, 29 pp, (2012), to appear in Communications in Algebra, http://arxiv.org/pdf/1204.1654v2.pdf
• M. Kleiner, H.R. Tyler, Sequences of reflection functors and the preprojective component of a valued quiver, Journal of Pure and Applied Algebra, 212 (2008) 718-726, http://dx.doi.org/10.1016/j.jpaa.2007.06.014
• M. Kleiner, H.R. Tyler, Admissible sequences and the preprojective component of a quiver, Advances in Mathematics, 192 (2005) 376-402, http://dx.doi.org/10.1016/j.aim.2004.04.006
• D.Gagliardi, H.Tyler, M.Lewinter, Three-colorable maximal planar graphs and self-complementary graphs. Graph Theory Notes of NY XLVII (40-41) 2004.

Selected Presentations

• "The Auslander-Reiten Components in the Rhombic Picture", International Conference on Representations of Algebras, Bielefeld, Germany, August 2012, http://www.math.uni-bielefeld.de/icra2012/presentations/icra2012_tyler.pdf
• "The Auslander-Reiten Components in the Rhombic Picture", Maurice Auslander International Conference, Woods Hole, MA, April, 2012.
• "Auslander-Reiten Layers in the Rhombic Picture of an Algebra," Canadian Mathematical Society Winter Meeting, Toronto, Canada, December, 2011.
• “Auslander-Reiten Layers in the Rhombic Picture,” BIREP Seminar, Bielefeld University, Germany, July, 2011.
• “Gabriel-Roiter Families Occurring in Tubes,”American Mathematical Society Fall Eastern Section Meeting, Syracuse University, October, 2010.
• “A Comparison of Orderings for Preprojective Modules,”Canadian Mathematical Society Summer Meeting, University of New Brunswick at Fredericton, June, 2010.
• “Reflections on Graphs and a Measure for the Position of a Module,”Algebra Seminar, Florida Atlantic University, April, 2010.
• “Slices, Tilting Sets, and Annihilating Sequences of BGP-Reflection Functors,”American Mathematical Society Fall Western Section Meeting, University of California at Riverside, November, 2009.
• “Shortest Annihilating Sequences for Preprojective Quiver Representations,” International Conference on Representations of Algebras and Related Topics, Woods Hole, Massachusetts, April, 2009.
• “Reflection Functors Acting on Systems of Vector Spaces,” Algebra/Cryptology Seminar, Florida Atlantic University, October 2007.
• “Sequences of Reflection Functors and the Preprojective Component of a Valued Quiver,” XII International Conference on Representations of Algebras, Nicolaus Copernicus University, Torun, Poland, August 2007.
• “(+)-Admissible Sequences and the Preprojective Component,” American Mathematical Society Eastern Section Meeting, Northeastern University, October, 2003.

Honors & Awards

• 2003-2004 Exxon-Mobil Project NexT Fellow

Professional Memberships

American Mathematical Society, Mathematical Association of America, Association for Women in Mathematics

Courses Taught/Teaching

MATH 103      Calculus I
MATH 103      Calculus I (Honors)
MATH 104      Calculus II
MATH 105      Linear Math Analysis
MATH 201      Calculus III
MATH 203      Differential Equations
MATH 209      Honors Calculus III
MATH 213      Foundations for Higher Mathematics
MATH 315      Algebra I
MATH 316      Algebra II
MATH 469      Independent Study:Intro to Rep Theor Alg