Research

Research Interests

• Derivators and abstract homotopy theory
• Higher Algebraic K-Theory and category theory

Papers

• Stabilization of derivators revisited, arXiv:1802.04343. Journal of Homotopy and Related Structures, 14 (2019), no. 2, 525-577.
• The K-theory of left pointed derivators, arXiv:2009.09063. Submitted.
• The theory of half derivators, arXiv:2010.12057. Documenta Mathematica, 27 (2022), 655-698.
• Localization, monoid sets and K-theory, arXiv: 2109.03193. To appear in the Journal of Algebra.

Presentations

• “Derivators as an enhancement of triangulated categories”. Seminar of the Department of Algebra, Universidad de Sevilla, 10 July 2017
• “The K-theory of derivators”. Recent developments in noncommutative algebra and related areas, University of Washington, 17 March 2018
• “A brief history of Algebraic K-theory”. Seminar of the Department of Algebra, Universidad de Sevilla, 4 July 2018
• “The K-theory of derivators”. K-theory ICM Satellite, Universidad de Buenos Aires, 27 July 2018
• “The K-theory of derivators”. Topology Seminar, University of Chicago, 22 January 2019
• “The stabilization of pointed derivators”. Workshop on Derivators, Universität Regensburg, 10 April 2019
• “What is a derivator?”. Algebra Seminar, Rutgers University, 9 October 2019
• “The algebraic K-theory of derivators”. AMS Fall Eastern Sectional Meeting, Binghamton University, 12 October 2019
• Cancelled talk on the stabilization of derivators for the AMS Spring Southeastern Sectional Meeting, University of Virginia, 14 March 2020

Older Stuff

Caveat lector! May contain errors, especially when noted.

• An explicit construction of an expander family, Northwestern University Undergraduate Honours Thesis. (PDF file)
• Abelian Patterns and Periods, UNC Greensboro REU Presentation. (Beamer file)
• UCLA Algebra Qualifying Exam Solutions, Fall 2009 - Spring 2014. (PDF File)
• UCLA Geometry/Topology Qualifying Exam Solutions, Spring 2008 - Spring 2014. (PDF File)

Non-mathematical Papers

• Virgil's Aeneid in Neronian Literature, Joseph Clyde Murley Prize Honourable Mention 2013. (PDF file)
• Augustus, Ekphrasis, and the Shield of Aeneas, Joseph Clyde Murley Prize Winner 2012. (PDF file)
• Empowering LGBT Scientists, an article I wrote for the Medill Equal Media Project at Northwestern
• The simple sacral dimple: diagnostic yield of ultrasound in neonates, published in Pediatric Radiology. (PDF file)