Publications:

• The definable content of homological invariants I: Ext and the first derived limit.

Joint with Martino Lupini and Aristotelis Panagiotopoulos.

arXiv copy; journal copy.

• A descriptive approach to higher derived limits.

Joint with Nathaniel Bannister, Justin Tatch Moore, and Stevo Todorcevic.

arXiv copy; journal copy.

• The definable content of homological invariants II: Čech cohomology and homotopical classification.

Joint with Martino Lupini and Aristotelis Panagiotopoulos.

arXiv copy; journal copy.

• Projective well orders and coanalytic witnesses.

Joint with Vera Fischer and Corey Switzer.

arXiv copy; journal copy.

• Simultaneously vanishing higher derived limits without large cardinals.

Joint with Michael Hrušák and Chris Lambie-Hanson.

arXiv copy; journal copy.

• The first omega alephs: from simplices to trees of trees to higher walks.

arXiv copy; journal copy.

• On the additivity of strong homology for locally compact separable metric spaces.

Joint with Nathaniel Bannister and Justin Tatch Moore.

arXiv copy; journal copy.

• Simultaneously vanishing higher derived limits.

Joint with Chris Lambie-Hanson.

arXiv copy; journal copy.

• Ramsey theory for monochromatically well-connected subsets.

arXiv copy; journal copy.

• Ramsey theory for highly connected monochromatic subgraphs.

Joint with Michael Hrušák and Saharon Shelah.

arXiv copy; journal copy.

• Strong homology, derived limits, and set theory.

arXiv copy; journal copy.

Thesis:

• Dimensions of ordinals: set theory, homology theory, and the first omega alephs.

Talks:

• A talk introducing the larger project of which the works An introduction to higher walks and The first omega alephs, above, form a part.

In preparation:

• Manifold classification from the descriptive viewpoint.

Joint with Iian Smythe.

• The cohomology of the ordinals.

Joint with Chris Lambie-Hanson and Jing Zhang.

• Long Wadge games.

Joint with David Chodounsky, Osvaldo Guzmán, and Michael Hrušák.