# Helene R. Tyler

## Helene R. Tyler

### Associate Professor

### Department : Mathematics

### Email : helene.tyler@manhattan.edu

### Phone : 718-862-7365

### Office : RLC 2FL

## 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

- Markus Schmidmeier & Helene R. Tyler (2014) The Auslander–Reiten Components in the Rhombic Picture, Communications in Algebra, 42:3, 1312-1336, http://dx.doi.org/10.1080/00927872.2012.738341
- 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

- "String algebras with one cycle - the rhombic picture", Canadian Mathematical Society Winter Meeting, Ottawa, ON, December 2013.
- "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

## Other

Member, Carus Monograph Series Editorial Board

## Courses Taught/Teaching

MATH 153 Linear Math Analysis

MATH 154 Calculus for Business Decisions

MATH 185 Calculus I

MATH 187 Calculus I (Honors)

MATH 186 Calculus II

MATH 188 Calculus II (Honors)

MATH 243 Foundations for Higher Mathematics

MATH 272 Linear Algebra I

MATH 285 Calculus III

MATH 286 Differential Equations

MATH 287 Honors Calculus III

MATH 377 Algebra I

MATH 471 Linear Algebra II

MATH 478 Algebra II

MATH 490 Complex Analysis

MATH 492 Topics in Applied Network Theory

MATH 492 Elementary Number Theory

MATH 499 Independent Study: Complex Analysis II

MATH 499 Independent Study: Linear Algebra III

MATH 499 Independent Study: Intro to Representation Theory of Algebras