Education, Licensure and Certification (2)
Ph.D.: Mathematics, Ohio State University 2021
B.S.: Mathematics, Ohio State University 2015
Duncan Clark holds a Ph.D. in Mathematics from Ohio State University. His main research interests are algebraic topology and homotopy theory. More specifically, Clark is interested in Goodwillie's calculus of homotopy functors: including structure inherent to the derivatives of functors, and applications of the theory to categories of structured ring spectra.
Areas of Expertise (3)
Outstanding Graduate Associate Teaching Award (professional)
2017 College of Arts and Sciences, Ohio State
First Year Teaching Award (professional)
2016 Dept. of Mathematics, Ohio State
- American Mathematical Society : Member
Event and Speaking Appearances (3)
An intrinsic operad structure for the derivatives of the identity
University of Regina Topology Seminar
An Intrinsic Operad Structure for the Derivatives of the Identity
EPFL Topology Seminar
An operad structure for the Goodwillie derivatives of the identity functor in structured ring spectra
Graduates Reminiscing Online On Topology
Selected Publications (2)
On the Goodwillie derivatives of the identity in structured ring spectraarXiv:2004.02812
The aim of this paper is three-fold: (i) we construct a naturally occurring highly homotopy coherent operad structure on the derivatives of the identity functor on structured ring spectra which can be described as algebras over an operad in spectra, (ii) we prove that every connected -algebra has a naturally occurring left action of the derivatives of the identity, and (iii) we show that there is a naturally occurring weak equivalence of highly homotopy coherent operads between the derivatives of the identity on -algebras and the operad .
The partition poset complex and the Goodwillie derivatives of the identity in spacesarXiv:2007.05440
We produce a canonical highly homotopy-coherent operad structure on the derivatives of the identity functor in spaces via a pairing of cosimplicial objects, providing a new description of an operad structure on such objects first described by Ching. In addition, we show the derived primitives of a commutative coalgebra in spectra form an algebra over this operad.