gmail account: davidayala.math

office: 464C, KAP

See my

My background is in algebraic topology with an emphasis on the homotopy theory of manifolds. My research concerns the differential topology of locally defined entities, such as manifolds, and their moduli as informed by conceptual and computational techniques from (derived) algebraic geometry and homotopy theory. Slightly more specifically, my work characterizes invariants of things like manifolds or links which are obtained from algebraic or categorical data -- the goal is to facilitate the construction of a wealth of robust invariants, equipped with desired local-to-global functorialities, with an eye toward calculations among them. Instances of such local invariants include sheaves, cosheaves, motives, and topological field theories; and proposed examples of such invariants include the Turaev-Viro TFT invariants, versions of Heegaard Floer homology, Rozansky-Witten and Khovanov homology, and finite type knot invariants.

I am not teaching this academic year. In the past I have taught two calculus courses, a basic topology course, and a course on the homotopy theory of manifolds, as well as various teaching assistantships. See my CV for specifics.

I supervised a masters project of Casper Guldberg's (University of Copenhagen) on

I supervised a side PhD project of Emanuele Dotto's (University of Copenhagen) where he is used simplicial techniques to consider

Some

Some photos of

Some modest

Mojave Run

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