Research

Current Work: 

I am currently completing my dissertation in Integral p-adic Hodge Theory. More specifically, I am interested in computing simi-simple mod p reductions of irreducible, two-dimensional crystalline representations of absolute Galois groups of unramified p-adic extensions with some restrictions on their labeled Hodge-Tate weights.

Publications:

• Guzman A., Kansal K., Kountouridis K., Savoie B., Wang W. Smoothness of Components of the Emerton-Gee Stack for GL_2. In preparation, arXiv:2209.09439 [PDF]

Past Work:

In the summer of 2017, I participated in a NSF-REU at the Rochester Institute of Technology. I worked with Ryan Vogt and Professor Laura Muñoz in mathematical biology and dynamical systems. The result was the following two papers:

• Guzman A., Vogt R., Charron C., Pusarla K., Muñoz L. Observability Analysis and State Observer Design for a Cardiac Ionic Cell Model. Computers in Biology and Medicine, vol. 125, p. 103910, 2020.

• Vogt R., Guzman A., Charron C., Muñoz L. Controllability and state feedback control of a cardiac ionic cell model. Computers in Biology and Medicine, vol. 139, p 104909, 2021