# Murat Akman

I am currently Evarist Giné Assistant Research Professor at the University of Connecticut. Before arriving at UConn I was a postdoctoral researcher at the Instituto de Ciencias Matematicas, Madrid, Spain where I worked with José María Martell. I did my PhD at the University of Kentucky with John Lewis in 2014. I also received postdoctoral researcher fellowship from Institut Mittag-Leffler, Stockholm, Sweden to attend the Evolutionary Problems semester in the fall of 2013. During the spring semester of 2017, I was a postdoctoral fellow at the Mathematical Sciences Research Institute, Berkeley, CA to participate in the Harmonic Analysis program where my mentor was Tatiana Toro.

My research interests are Analysis of PDEs, Potential Theory, Geometric Measure Theory.

You can find my CV here or my Google Scholar page. -- Email: murat.akman "at" uconn.edu.

This year, I am co-organizer for the Analysis Learning Seminar at UConn. I am also co-organizing the AMS Special section on Regularity of PDEs on Rough Domains at Northeastern University, Boston, MA April 21-22, 2018.

• ### Publications and Preprints

• ### Research Interests

• My researchs lie in the interface of analysis of linear and nonlinear elliptic PDEs, Potential Theory, and Geometric Measure Theory. My interests are

1. Variational methods for (non)linear elliptic PDEs with p-Laplacian.
2. Regularity and free boundary regularity for (non)linear elliptic PDEs in non-smooth domains.
3. Conformal densities and Hausdorff dimension of harmonic, $p$-harmonic, and elliptic measures.
4. The Brunn-Minkowski inequality for nonlinear capacity and stability of these inequalities.
5. A Minkowski problem for nonlinear capacity and its connection with Monge-Ampere equation.

I defended my thesis in May 2014. Title:On the Hausdorff dimension of a certain measure arising from a positive weak solution to a divergence type PDE.