Ph.D. in Mathematics, University of Pittsburgh
B.S. in Mathematics, Temple University
- Office Hours
- Mondays: 3:00 - 4:00 p.m.
Tuesdays: 1:15 - 2:15 p.m.
Wednesdays: 9:00 - 10:00 a.m.
Thursdays: 1:30 - 2:30 p.m.
Growing up in West Chester, Pennsylvania, math was my least favorite subject. Until my junior year of high school, I was 100% certain that I would study something where I could be creative and weave together complicated bits of information to tell a coherent, compelling story; I was sure I would major in history or English. In my junior year, however, I was told about a topic in calculus called "Taylor series," and I couldn't fathom how the ideas behind Taylor series could be true. My disbelief became a determination to understand, and I was very surprised to find that the same passions which made me sure that I would study history or English found a natural outlet in mathematics.
I went on to earn my B.S. in Mathematics from Temple University in Philadelphia, where I worked in the math tutoring center and as a teaching assistant in Temple's Summer Bridge program for conditional-acceptance students. From 2010-2016, I pursued my Ph.D. at the University of Pittsburgh under the supervision of Professor Chris Lennard. During my time there, I had various educational roles: Teaching Assistant, Instructor-of-Record, Graduate Student Teaching Mentor, and Graduate Student Coordinator for the math tutoring center. These experiences solidified my passion for teaching and connecting with students, which has become a major focus in my career. From 2016-2019, I was a Visiting Assistant Professor in the math department at Bucknell University, and I'm very happy to be a part of Monmouth's math department as of Fall 2019!
Outside of teaching and researching in math, I love to read, cook, play and listen to music, play and watch soccer and hockey (go Flyers), solve the New York Times crossword every day, play with our 2-year-old daughter, and play video games. I'm happy to discuss any of these things (especially math), so if you have questions please stop by my office and we can chat!
- Research Interests
My research is in fixed point theory and it blends techniques from functional analysis, topology, and geometry to answer questions of the form "if f(x) is a function, when can we find an x for which f(x) = x?" My research has primarily focused on fixed point properties for so-called mean-nonexpansive mappings, and I am looking for undergraduate students to work with on some projects related to this line of research (more details can be found on the research page of my personal site, found above).
- Scholarly Articles
“A weak convergence theorem for mean nonexpansive mappings.” Rocky Mountain J. Math., 47 (2017), pp. 2167-2178. https://projecteuclid.org/euclid.rmjm/1514084423
“Mean nonexpansive mappings are mean isometries if and only if they are isometries” with C. Lennard. J. Nonlinear Convex Anal., 18 (2017), pp. 73-94. http://www.ybook.co.jp/online2/jncav18-2.html
“Fixed point results for a new mapping related to mean nonexpansive mappings.” Adv. Oper. Theory, 2 (2017), pp. 1-16. http://dx.doi.org/10.22034/aot.1610.1029
“Averaging and fixed points in Banach spaces” (Ph.D. thesis). http://d-scholarship.pitt.edu/28750/
“The demiclosedness principle for mean nonexpansive mappings,”
J. Math. Anal. Appl., 439 (2016), pp. 832-842. http://dx.doi.org/10.1016/j.jmaa.2016.03.029
“Weak compactness is not equivalent to the fixed point property in c,” with C. Lennard & R. Popescu. J. Math. Anal. Appl., 431 (2015), pp. 271-281. http://dx.doi.org/10.1016/j.jmaa.2015.05.050
- Presentations/Invited Talks
“Recent results for mean nonexpansive mappings.” 16 January 2019. AMS/MAA Joint Mathematics Meeting 2019 (Baltimore, MD).
“An overview of mean nonexpansive mappings.” 29 September 2018. AMS Fall Sectional Meeting – Univ. Delaware.
“Iterates, invariance, and chaos.” 22 February 2018. Bucknell University Student Talk.
“A brief history of fixed point theory with modern developments.” 4 May 2016. Bucknell University Colloquium.
“A brief history of fixed point theory.” 3 March 2016. Washington & Jefferson College Undergrad Math Seminar.
“Applying to and succeeding in grad school.” 17 November 2014. Duquesne University Undergraduate Math Seminar.
“Selection type results and fixed point property for affine bi-Lipschitz maps” with Cleon Barroso.
“Averaging mappings” with M. Japón Pineda and C. Lennard.
“New fixed point free nonexpansive mappings in K(l2) and related spaces”
with M. Japón Pineda, C. Lennard, and A. Stawski.
E. Baranger Teaching Award (hon. mention), University of Pittsburgh (2015)
TA Teaching Excellence Award, University of Pittsburgh (2014)
Christopher W. Copple Award For Excellence In The Field Of Mathematics, Temple University (2010)