Mathematics
I recently completed a year as a Visiting Assistant Professor of mathematics at Furman University. I received my Ph.D. from UC Irvine in 2013, and continued to teach at UCI through summer of 2015. My bachelors degree is in math and physics, which I obtained at Colby College in 2007.
My mathematical research is in the field of set theory. My research primarily investigates infinite combinatorics at small singular cardinals, large cardinals, and the consistency results which relate these subjects. A primary tool used in this work is forcing, a technique for constructing outer models of the axioms of mathematics. Recently I have also looked at generalizations of cardinal characteristics to partially-ordered sets.
I was advised by Dr. Martin Zeman on my thesis “On the Consistency of Square.” This work looks at the consistency strength of the failure of the principle \( \square( \aleph_{\omega+1},<\omega )\) as well as the separation of the \(\square_{\kappa,n}\) principles for singular cardinals \(\kappa.\) An in-depth statement about my research can be viewed here.
Talks
- Square at Singular Cardinals (pdf)
- Feb. 2013, UC Irvine, Logic in Southern California talk
- A Friendly Introduction to Large Cardinals and Consistency Strength
- Feb. 2013, UC Irvine, Math Graduate Student Colloquium series
- Combinatorics at \(\aleph_{\omega+1}\) in Prikry-type extensions (pdf)
- Jan. 2013, Joint Mathematics Meeting, Contributed talk
- Silver’s model for failure of SCH
- Oct. 2012, UC Irvine, Seminar
- Kappa-Suslin sets, semiscales and scales I and II
- Apr. 2010, UC Irvine, Seminars
Conferences
- Present, since Fall 2011 - Logic in Southern California quarterly conferences (Caltech, UC Irvine, UCLA)
- January 6-9, 2016 - Joint Mathematics Meeting (Seattle)
- November 2014 - Southern California-Nevada Section Meeting (Pomona College)
- January 2013 - Joint Mathematics Meeting (San Diego)
- June 2012 - Graduate Summer School in Set Theory - Large cardinals, inner models, and fine structure (UC Irvine)