Duncan A. Clark, Ph.D.

Instructor

Milwaukee WI UNITED STATES
Mathematics

Dr. Duncan Clark's main research interests are algebraic topology and homotopy theory.

Contact

Education, Licensure and Certification

Ph.D.

Mathematics

Ohio State University

2021

B.S.

Mathematics

Ohio State University

2015

Biography

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

Calculus

Algebraic Topology

Homotopy Theory

Accomplishments

Outstanding Graduate Associate Teaching Award

2017

College of Arts and Sciences, Ohio State

First Year Teaching Award

2016

Dept. of Mathematics, Ohio State

Affiliations

American Mathematical Society : Member

Event and Speaking Appearances

An intrinsic operad structure for the derivatives of the identity

University of Regina Topology Seminar

2021-01-21

An Intrinsic Operad Structure for the Derivatives of the Identity

EPFL Topology Seminar

2020-10-20

An operad structure for the Goodwillie derivatives of the identity functor in structured ring spectra

Graduates Reminiscing Online On Topology

2020-03-09

Selected Publications

On the Goodwillie derivatives of the identity in structured ring spectra

arXiv: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 spaces

arXiv: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.