# Clark Barwick

> Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Clark_Barwick
> Markdown URL: https://mediated.wiki/source/Clark_Barwick.md
> Source: https://en.wikipedia.org/wiki/Clark_Barwick
> Source revision: 1344164135
> License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/)

**Clark Edward Barwick** (born January 9, 1980) is an American mathematician and [professor](/source/Academic_ranks_in_the_United_Kingdom) of pure mathematics at the [University of Edinburgh](/source/University_of_Edinburgh). His research is centered around [homotopy theory](/source/Homotopy_theory), [algebraic *K*-theory](/source/Algebraic_K-theory), [higher category theory](/source/Higher_category_theory), and related areas.

## Early life and education

Barwick grew up in [North Carolina](/source/North_Carolina), and in 2001 completed his [BS](/source/Bachelor_of_Science) in mathematics at the [University of North Carolina at Chapel Hill](/source/University_of_North_Carolina_at_Chapel_Hill).[1][2] Barwick was then a graduate student at the [University of Pennsylvania](/source/University_of_Pennsylvania), and received his [PhD](/source/Doctor_of_Philosophy) in mathematics in 2005 under the direction of Tony Pantev.

## Career

Barwick held [postdoctoral fellowships](/source/Postdoctoral_Fellow) at the [Mathematisches Institut Göttingen](/source/University_of_G%C3%B6ttingen) (2005–2006) and at the [Matematisk Institutt, Universitetet i Oslo](/source/University_of_Oslo) (2006–2007).[2] Barwick spent the year 2007–2008 at the [Institute for Advanced Study](/source/Institute_for_Advanced_Study), and from 2008–2010 was a [Benjamin Peirce](/source/Benjamin_Peirce) Lecturer at [Harvard](/source/Harvard_University). In 2010 Barwick became an [assistant professor](/source/Assistant_professor) at [MIT](/source/Massachusetts_Institute_of_Technology), and in 2013 he became the Cecil and Ida Green Career Development Assistant Professor of Mathematics. In 2015 Barwick was a [Fulbright](/source/Fulbright_Program) visiting professor at the [University of Glasgow](/source/University_of_Glasgow) and was promoted to Cecil and Ida Green Career Development [Associate Professor](/source/Associate_professor) of Mathematics at MIT, a position which he held until he became a reader at the University of Edinburgh in 2017.[3][4] In 2020, Barwick was promoted to a professor at the University of Edinburgh.[5]

## Research and notable works

A theme in Barwick's work is the homotopy theory of higher categories. In his early career, he frequently collaborated with [Dan Kan](/source/Daniel_Kan); much of their work was concerned with models for the homotopy theory of homotopy theories. In his joint work with Chris Schommer-Pries, Barwick proved a unicity theorem for the homotopy theory of [(∞,*n*)-categories](/source/(%E2%88%9E,_n)-category).

Barwick has also made contributions to algebraic *K*-theory. In particular, Barwick defined higher-categorical generalizations of [Waldhausen categories](/source/Waldhausen_category) and Waldhausen's [*S*-construction](/source/S-construction) and used these to extend [Waldhausen's](/source/Friedhelm_Waldhausen) *K*-theory to the setting of [(∞,1)-categories](/source/Quasi-category). Using this new theory, he proved the Theorem of the Heart for Waldhausen *K*-theory. In joint work with [John Rognes](https://no.wikipedia.org/wiki/John_Rognes), he generalized [Quillen's](/source/Daniel_Quillen) [*Q*-construction](/source/Q-construction) to the higher-categorical setting, providing higher-categorical generalizations of [Quillen's Theorem B](/source/Quillen's_theorems_A_and_B) as well as Quillen's dévissage argument in the process. Much of his recent work has concerned [equivariant algebraic *K*-theory](/source/Equivariant_algebraic_K-theory) and [equivariant homotopy theory](/source/Equivariant_algebraic_topoloy). Barwick won the 2019 [Berwick Prize](/source/Berwick_Prize) of the [London Mathematical Society](/source/London_Mathematical_Society) for his paper "On the algebraic *K*-theory of higher categories" where he "proves that Waldhausen's algebraic K-theory is the universal homology theory for ∞-categories, and uses this universality to reprove the major fundamental theorems of the subject in this new context."[6][7]

In 2019 Barwick with his student Haine introduced the theory of [pyknotic objects](/source/Pyknotic_object). Which was published coincidentally and is very closely related to that of [condensed sets](/source/Condensed_mathematics), with the main differences being set-theoretic in nature: pyknotic theory depends on a choice of [Grothendieck universes](/source/Grothendieck_universe), whereas condensed mathematics can be developed strictly within [ZFC](/source/ZFC).[8]

## References

1. ["Clark Barwick | School of Mathematics"](http://www.maths.ed.ac.uk/school-of-mathematics/people?person=589). *www.maths.ed.ac.uk*. Retrieved 2018-04-18.

1. Barwick, Clark. ["Curriculum Vitæ of Clark Barwick"](http://www.maths.ed.ac.uk/~cbarwick/papers/cv_public.pdf). Retrieved 2018-04-18.

1. ["University of Glasgow – Schools – School of Mathematics & Statistics – About us – Information for current students and staff – Newsletter Archive – October 15 – Meet Fulbright Professor Clark Barwick"](https://web.archive.org/web/20180421030858/http://www.glasgowheart.org/schools/mathematicsstatistics/about/studentstaff/newsletterarchive/october15/headline_425779_en.html). *www.glasgowheart.org*. Archived from [the original](http://www.glasgowheart.org/schools/mathematicsstatistics/about/studentstaff/newsletterarchive/october15/headline_425779_en.html) on 2018-04-21. Retrieved 2018-04-18.

1. ["US-UK Fulbright Commission"](https://web.archive.org/web/20180421062335/http://188.65.115.112/about/meet-our-fulbrighters/clark-barwick/1111). *188.65.115.112*. Archived from [the original](http://188.65.115.112/about/meet-our-fulbrighters/clark-barwick/1111) on 2018-04-21. Retrieved 2018-04-18.

1. The University of Edinburgh Senatus Academicus, 27 May 2020. [www.ed.ac.uk/files/atoms/files/20200527agendapapers.pdf](https://www.ed.ac.uk/files/atoms/files/20200527agendapapers.pdf). Retrieved 2021-03-03

1. ["LMS Prize Winners 2019 – London Mathematical Society"](https://www.lms.ac.uk/news-entry/28062019-1621/lms-prize-winners-2019). 2019-06-28. Retrieved 2019-06-29.

1. Barwick, Clark (2016). "On the algebraic *K*-theory of higher categories". *[Journal of Topology](/source/Journal_of_Topology)*. **9** (1): 245–347. [arXiv:1204.3607](https://arxiv.org/abs/1204.3607). [doi:10.1112/jtopol/jtv042](https://doi.org/10.1112/jtopol/jtv042). MR 3465850. [S2CID 119160499](https://api.semanticscholar.org/CorpusID:119160499)

1. ["Pyknotic sets"](https://ncatlab.org/nlab/show/pyknotic+set). *nLab*

## External links

- [Official website](http://www.maths.ed.ac.uk/~cbarwick/)
- [Clark Barwick](https://www.genealogy.math.ndsu.nodak.edu/id.php?id=93010) at the [Mathematics Genealogy Project](/source/Mathematics_Genealogy_Project)

---
Adapted from the Wikipedia article [Clark Barwick](https://en.wikipedia.org/wiki/Clark_Barwick) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Clark_Barwick?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.