I’m a Mathematician who is passionate about education and research. I am particularly interested in Symplectic and Contact Geometry as well as Hamiltonian Dynamical Systems. I was most recently a postdoctoral fellow at the Center for Geometry and Physics in Pohang, South Korea. I received my PhD from the University of California at Santa Cruz working under the direction of Viktor Ginzburg. My recent research focuses on question about entropy in Reeb dynamical systems. Other research topics includes Contact Conley Conjecture and related problems in Local Symplectic Homology of Closed Reeb Orbits. My CV is available here and my research statement is available here.
Recent Papers
Barcode entropy for Reeb flows on contact manifolds with Liouville fillings https://arxiv.org/abs/2305.04770
For a complete list see my publications page.
Research Interests
Symplectic and Contact Geometry and Topology.
Hamiltonian Dynamical Systems and their fixed points.
Topological and Barcode Entropy.
Conley Conjecture.
Systolic/Diastolic Ratios.
Morse Theory.
To see a more in depth discussion of my research interests consult my research statement.
Honors and Awards
2020
Chancellor’s Dissertation-Year Fellowship
UC Santa Cruz
2019
Mathematics Year-End Fellowship
UC Santa Cruz Math Department
2016
Hispanic Serving Institution Outstanding Teaching Assistant Award
UC Santa Cruz Division of Student Success
2015
DSB Scholarship for Graduate Study
Washington State Department of Services for the Blind
Teaching and Mentoring
Teaching and mentoring is a rewarding and important part of my journey with mathematics. Passing on the knowledge we gain is as important as its discovery. I am especially concerned with creating an environment which fosters equity, diversity, and trust among my students.
My teaching page has a complete list of my teaching and mentoring experience as well as my teaching statement.