## Office Hours

I graduated with a B.S. in Mathematics in 1999 from Sharif University of Technology, Tehran, Iran, and with a Ph.D. in Mathematics from Stony Brook University in 2005. I joined Siena College in 2011 after visiting positions at the University of Oregon (Eugene, OR) and Trinity College (Hartford, CT).

Degree | Program | University |
---|---|---|

Ph.D. | Mathematics | SUNY Center Stony Brook |

B.S. | Mathematics | Sharif University of Technology |

## My Siena Experience

### My Teaching Philosophy

The core of my teaching philosophy is *problem solving*. I encourage my students to improve their mathematical skills and understanding through group projects and presentations. I am also a believer in* Inquiry Based Learning* methodology after attending two workshops and implementing the IBL techniques in several of my classes.

### What I Love About Siena

I love my students and appreciate their hard work in my classes. I value the fact that my students take my classes seriously and do their best. Siena College is a vibrant institution with many bright students and faculty.

### My Favorite Courses to Teach

My favorite course to teach at Siena is Euclidean and Non Euclidean Geometry. I run this course as an inqury based learning course, where student presentations are the major part of our meetings.

## My Professional Experience

Year | Title | Organization |
---|---|---|

2021 - Now | Professor | Siena College, School of Science |

2015 - 2021 | Associate Professor | Siena College |

2011 - 2015 | Assistant Professor | Siena College |

2008 - 2011 | Harold L. Dorwart Visiting Assistant Professor | Trinity College |

2005 - 2008 | Paul Olum Visiting Assistant Professor | University of Oregon |

### Current Research

### Articles & Book Reviews

- The Distribution of Fibonacci Numbers Modulo Primes

American Mathematical Monthly, vol. 129

2022 - Upper Bound Residues of the Fibonacci Sequence Modulo Primes

Journal is not in list - being petitioned, vol. 60

2022 - Permutations with a distinct divisor property

Journal is not in list - being petitioned

2021 - Complete Generalized Fibonacci Sequences Modulo Primes

Moscow Journal of Combinatorics and Number Theory, vol. 9

2020 - On Sets Closed Under the Cross Product and a Property of the Octahedron

American Mathematical Monthly, vol. 127

2020 - On the subgroup generated by solutions of Pell's equation

Journal of Number Theory, vol. 194

January, 2019 - A note on polynomial sequences modulo integers

Journal of Integer Sequences, vol. 22

2019 - Cyclic composition operators on separable locally compact metric spaces

Topology and Its Applications, vol. 258

2019 - Loxodromes on hypersurfaces of revolution

INVOLVE Journal, vol. 10

2017 - Projective partitions of vector spaces

Electronic Journal of Linear Algebra, vol. 32

2017 - On transitive polynomials modulo integers

Notes on Number Theory and Discrete Mathematics, vol. 22

July, 2016 - Cycle double covers of infinite planar graphs

Discussiones Mathematicae Graph Theory, vol. 36

2016 - The Correlation Numerical Range and Trace-Positive Complex Polynomials

Operators and matrices, vol. 10

2016 - Dynamics of semigroups of linear fractional transformations

Dynamical Systems, vol. 29

2014 - Hypercyclic and topologically transitive semigroups of composition operators

Topology and Its Applications, vol. 164

2014 - Maximally transitive semigroups of nxn matrices

Journal of Mathematical Analysis and Applications, vol. 401

2013 - A Collatz-type conjecture on the set of rational numbers

Journal of Number Theory, vol. 132

2012 - Dense 2-generator subsemigroups of 2x2 matrices

Journal of Mathematical Analysis and Applications, vol. 387

2012 - Semigroups of matrices with dense orbits

Dynamical Systems, vol. 26

2011 - On a property of plane curves

Journal of Mathematical Analysis and Applications, vol. 361

2010 - Rigidity of conformally compact manifolds with the round sphere as the conformal infinity

Advances in Mathematics, vol. 224

2010 - Topologically transitive semigroup actions of real linear fractional transformations

Journal of Mathematical Analysis and Applications, vol. 368

2010 - Chord Theorems on Graphs

Proc. Amer. Math. Soc, vol. 137

2009 - Convergence of Ricci flow on R^2 to flat space

Journal of Geometric Analysis, vol. 19

2009 - A generalization of Dirichlet approximation theorem for the affine actions on real line

Journal of Number Theory, vol. 128

2008 - Dirichlet problem on locally finite graphs

Discrete Applied Mathematics, vol. 155

2007 - A new arrangement inequality

Journal of Inequalities in Pure and Applied Mathematics, vol. 7

2006

### Awards & Distinctions

- COTFD Fellowship Award

Category: Research

Siena College, 2016 - COFTD Fellowship Award

Category: Research

Siena College, 2014 - COTFD Fellowship Award

Category: Research

Siena College, 2012 -

Category: Research

Stony Brook University, 2005 -

Category: Teaching

Stony Brook University, 2003 -

Category: Other

Sharif University of Technology, 1999 -

Category: Other

Sharif University of Technology, 1996 -

Category: Other

IMO, 1995 - IPM Fellowship Award

Category: Other

IPM, Iran, 1995

### Presentations

- A Note on Polynomial Sequences Modulo Integers

2020

Joint Mathematics Meetings, Denver, Colorado - Fair partitions of polygons

April, 2018

SUNY Oneonta, Oneonta, New York - Cycle double covers of infinite planar graphs

July, 2017

Mathfest, Chicago, Illinois - Non-existence in Mathematics

March, 2015

Siena College Mathematics Colloquium, Loudonville, New York - Dynamics of semigroups of LFT

January, 2015

Joint Mathematics Meetings, San Antonio, Texas - Continued fractions and other mathematical adventures

November, 2014

Union College Mathematics Colloquium, Union College, Schenectady, New York - Proofs without words

March, 2014

Department of Mathematics Colloquium, Loudonville, New York - Paul Erdos, the traveling mathematician

March, 2013

Department of Mathematics Colloquium, Loudonville, New York - Dense 2-generator subsemigroups of 2x2 matrices

January, 2012

American Mathematical Society and Mathematical Association of America Annual Meeting, Boston, Massachusetts - Maximally transitive semigroups of matrices

2012

The 9th AIMS conference on Dynamical systems, Differential Equations, and Applications, Orlando, Florida - Semigroups of matrices with dense orbits

January, 2010

American Mathematical Society and Mathematical Association of America Annual Meeting, San Francisco, California - Semigroups of real functions with dense orbits

November, 2009

CCSU colloquium, New Britain, Connecticut - Rigidity of conformally compact manifolds with the round sphere as the conformal infinity

April, 2009

AMS central section spring meeting, Urbana, Illinois - On a property of plane curves

January, 2009

American Mathematical Society and Mathematical Association of America Annual Meeting, Washington, District of Columbia - On a property of plane curves

November, 2008

CCSU colloquium, New Britain, Connecticut - Harmonic functions via inverse mean-value theorems

January, 2008

American Mathematical Society and Mathematical Association of America Annual Meeting, San Diego, California - Dirichlet problem on locally finite graphs

November, 2007

University of Oregon Geometry Seminar, Eugene, Oregon - Chord Theorems on Graphs

April, 2007

MAA Pacific northwest section meeting, McMinnville, Oregon - A combinatorial-analysis invariant of graphs

January, 2007

American Mathematical Society and Mathematical Association of America Annual Meeting, New Orleans, Louisiana - Conformally compact Einstein metrics with symmetry in dimension 5

October, 2006

AMS central section fall meeting, Cincinnati, Ohio - Conformally compact Einstein metrics with symmetry in dimension 5

March, 2006

Oregon State University Analysis seminar, Corvallis, Oregon