## Office Hours

I graduated with my B.S. in Mathematics 1999 and Ph.D. in Mathematics in 2005, both degrees from the University of New Hampshire. My doctoral thesis was completed under the supervision of Liming Ge, and contributed to the field of von Neumann algebras.

Joining the Siena faculty as a fresh Ph.D. in 2005, I immediately began working with students on undergraduate research, and am proud to have supervised many undergraduate research projects that have resulted in publications with student authors and coauthors. Our work has led to invitations for me and my students to speak nationally and internationally, from Schenectady to Shanghai.

My teaching philosophy is centered on the idea that a mathematics instructor's main task is to carefully and unobtrusively arrange mathematical experiences that encourage each individual student's inquiry and careful investigation. I'm happy to have had the opportunity to craft and run courses that my students repeatedly affirm "are never just about the grade".

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

Ph.D. | Mathematics | The University of New Hampshire |

B.S. | Mathematics | The University of New Hampshire |

## My Siena Experience

### My Teaching Philosophy

**If it isn't in your head, you can't use it to think.** I believe that students should work hard to conceptualize and internalize concepts so the concepts can be thought about fluently. If technology is to be used, it should be used to help in the construction of a sharp mental model that can be thought about without the technology at hand. I want to combat the unfortunate contemporary belief that we do not need to internalize ideas or information because of calculators or Google. In the classroom I aim to employ active learning methods that encourage constructive thought.

### What I Love About Siena

My colleagues are some of the most dedicated and compassionate people I've ever had the opportunity to know. My students are respectful and try their best. These are my favorite things about Siena.

### My Favorite Courses to Teach

I like to teach Modern Algebra and Real Analysis. In these courses, students get a taste of what it means to be a mathematician.

## My Professional Experience

Year | Title | University |
---|---|---|

2017 - Now | Professor | Siena College |

2011 - Now | Associate Professor, Mathematics | Siena College |

2005 - 2011 | Assistant Professor, Mathematics | Siena College |

2004 - 2005 | Dissertation Fellow, Mathematics | The University of New Hampshire |

1998 - 2004 | Teaching assistant, Mathematics Instructor | The University of New Hampshire |

1995 - 1995 | Research assistant, Physics | The University of New Hampshire |

### Articles & Book Reviews

- On Noncommutative Joinings

International Mathematical Research Notices

2017 - Impact of the Siena College Tech Valley Scholars Program on Student Outcomes

Journal of STEM Education

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

Operators and matrices

2016 - The Modular Symmetry of Markov Maps

Journal of Mathematical Analysis and Applications

2016 - A note on moments in finite von Neumann algebras

INVOLVE Journal

2011 - On the Spectrum of Banach Algebra-Valued Entire Functions

Illinois Journal of Mathematics

2011 - A Non-Residually Finite Hyperlinear One-Relator Group

Proc. Amer. Math. Soc

2010 - A Note on Non-Residually Solvable Hyperlinear One-Relator Groups

INVOLVE Journal

2010 - Some Remarks on Haagerup's Approximation Property

Journal of Operator Theory

2008 - A Folner Invariant for Type II_1 Factors

Expo. Math

2007 - Transitive Families of Projections in Factors of Type II_1

Proc. Amer. Math. Soc

2004

### Presentations

- Correlation Numerical Range

2015

Data Science and Mathematics, Providence, Rhode Island - The correlation numerical range and trace-positive polynomials

2015

1114th Meeting of the AMS (California State University, Fullerton), Fullerton, California - The correlation numerical range and trace-positive polynomials

2015

Union College Mathematics Seminar, Schenectady, New York - Generic Weak Mixing and the Negation of Property (T)

June, 2014

Operator Algebras Seminar, Morningside Institute Chinese Academy of Sciences, Beijing, China-PRC - Joinings and Correspondences

June, 2014

Analysis Seminar, Morningside Institute, Chinese Academy of Sciences, Beijing, China-PRC - The Kadison-Singer Problem

November, 2013

SUNY Albany, Albany, United States of America - Weak Mixing and the Negation of Property T

2013

University of Waterloo Operator Algebra Seminar, Waterloo, Canada-Ontario - Joinings and Correspondences

April, 2012

University of Virginia Operator Algebras and Operator Theory Seminar, Charlottesville, Virginia - A Panoply of Pigeonhole Principle Pranks with a Practical Application

2012

Siena Mathematics Colloquium, Loudonville, New York - Correspondences of Finite von Neumann Algebras and Joinings of Measurable Dynamical Systems

2012

International Conference on Operator Theory and Operator Algebras, Shanghai, China-PRC - Joinings and Correspondences

2012

University of Michigan at Dearborn Analysis Seminar, Dearborn, Michigan - Operator Algebras and Quantum Entanglement

2012

Siena Mathematics Colloquium, Loudonville, New York - Operator Algebras and Quantum Entanglement

2012

Vassar College Mathematics Colloquium, Poughkeepsie, New York - Operator algebras and Quantum Entanglement

2012

Skidmore College Mathematics Colloquium, Saratoga Springs, New York - Joinings and Correspondences

November, 2011

New Hampshire Operator Theory Symposium, Hanover, New Hampshire - Rigidity and Finite von Neumann Algebras

February, 2010

SUNY Albany, Albany, United States of America - Hyperlinearity and One-Relator Groups

2010

SUNY Albany, Albany, New York - On the Closability of Certain L2 Derivations

2009

Vanderbilt University, Nashville, Tennessee - An introduction to free probability

October, 2008

SUNY Albany, Albany, United States of America - Correspondences and Haagerup's Approximation Property

2008

MAA Seaway, Unknown, Unknown - Correspondences and Haagerup's Approximation Property

2008

SUNY Albany, Albany, New York - Haagerup's Approximation Property and Relative Amenability

2008

2008 GPOTS at U. of Cincinnati, Cincinnati, Ohio - The Haagerup Property and Correspondences

2007

Texas A&M University, College Station, Texas - Folner Invariants for II_1 Factors

2006

2006 GPOTS (Great Plains Operator Theory Symposium) at the U. of Iowa, Iowa City, Iowa - A Folner Invariant for II_1 Factors

2005

CRANTS (SUNY Albany), Albany, New York - Burnside Factors, Amenability Defects and Transitive Families of Projections in Factors of Type II_1

2005

Thesis Defense (UNH), Unknown, Unknown - Groups and Rubik's Cube

2005

Siena Mathematics Colloquium, Loudonville, New York - Transitive Families in Finite Factors

2005

Capital Region Algebra and Number Theory Seminar (CRANTS) SUNY Albany, Albany, New York - Burnside Factors

2004

UNH Math Seminar, Durham, New Hampshire - Transitive Families in Factors

2004

Vanderbilt University, Nashville, Tennessee