# Cara Mullen

Math Graduate Student at the University of Illinois at Chicago

## Research

I am interested in Arithmetic Dynamics, Number Theory, and Complex Dynamics - specifically the p-adic analogues of well understood objects and phenomena from Complex Dynamics. My thesis advisor is Professor Laura DeMarco from the Mathematics Department at Northwestern University.

### Preprints

The critical orbit structure of quadratic polynomials in Zp. Submitted for publication, 27 pages. pdf.

### Conferences

I have attended the following conferences and workshops:

I presented a poster at the Midwest Dynamical Systems Meeting in 2013, 2014, and 2015. I also presented a poster at Silvermania in 2015.

### Seminar Talks

I have given the following seminar talks in the Chicago area:

• "The p-adic Mandelbrot Set and Other Peculiarities of Arithmetic Dynamics," Graduate Student Colloquium, University of Illinois at Chicago. (November 2015)
• "The p-adic Mandelbrot Set and Other Peculiarities of Arithmetic Dynamics," Graduate Student Seminar, Northwestern University. (December 2014)
• "An Introduction to Berkovich Space," Graduate Number Theory Seminar, University of Illinois at Chicago. (October 2014)
• "An Introduction to Arithmetic Dynamics," Chicago Number Theory Meeting, Northwestern University. (September 2014)
• "A Further Look into the Critical Orbit Structure of $f_c(z) = z^2 + c$ over $\mathbb{C}_p$," Graduate Number Theory Seminar, University of Illinois at Chicago. (March 2014)
• "Critical Orbit Structure of $f_c(z) = z^2 + c$ over $\mathbb{C}_p$," Graduate Number Theory Seminar, University of Illinois at Chicago. (November 2013)
• "An Introduction to p-adic Dynamics," Number Theory Working Seminar, University of Illinois at Chicago. (May 2013)