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.

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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.