# Clark Barwick

### Research Interests

My work is broadly classified as homotopy theory, and I'm particularly interested in its interactions with algebraic geometry and algebra. Much of my work has involved algebraic K-theory and higher categories.

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#### Research Groups

### Current and Recent PhD Students

Current:

Haine, Peter

Johansen, Rasmus

Former:

Ph.D 2017 – Nardin, Denis. 'Stability and distributivity over orbital ∞-categories'

Ph.D 2017 – Shah, Jay. 'Parametrized higher category theory'

Ph.D 2015 – Glasman, Saul. 'Day convolution and the Hodge filtration on THH'

### Recent Conference and Workshop Involvement

July 2020 – Institut des Hautes Études Scientifiques. Motivic, equivariant, and non-commutative homotopy theory (speaker)

Spring 2020 – Thematic program at Mathematical Sciences Research Institute: Higher categories and categorification (organiser)

Dec. 2018 – Isaac Newton Institute for Mathematical Sciences. Homotopy harnessing higher structures (session organiser)

June 2018 – Sabhal Mor Ostaig. International conference on manifolds, groups and homotopy (speaker)

May 2018 – Casa Matemática Oaxaca. ∞-categories, ∞-operads, and their applications (speaker)

Sep. 2016 – Purdue University. Midwest topology seminar. speaker: 'How to rationalize an exact category'

June 2016 – American Institute of Mathematics. Equivariant derived algebraic geometry. speaker: 'Parametrized higher category theory and higher algebra'

June 2016 – MATRIX. Higher structures in geometry and physics. speaker: 'Parametrized higher category theory'

May 2016 – Caesarea Workshop. plenary speaker: 'Parametrized higher category theory'

Dec. 2015 – University of Glasgow. Scottish topology seminar. plenary speaker: 'Transfers in equivariant stable homotopy theory' / 'Equivariant stable homotopy theory and parametrized higher category theory'

Sep. 2015 – Clay Mathematics Institute. Algebraic topology: Manifolds unlocking higher structures. speaker: 'Modes of equivariance'

May 2015 – Ohio State University. K-theory: Future directions. speaker: 'Equivariant algebraic K-theory'

Aug. 2014 – City University of New York. Differential cohomologies. speaker: 'Absolute noncommutative motives'

Apr. 2014 – Mathematical Sciences Research Institute. Reimagining the foundations of algebraic topology. speaker: 'Redshift and higher categories'

### Biographical Statement

Clark became interested in mathematics as a youngster in North Carolina, where he would remain to receive his 2001 B.S. His 2005 Ph.D from the University of Pennsylvania preceded a string of postdoctoral positions – Göttingen, Oslo, the Institute for Advanced Study, and finally Harvard. Clark joined the faculty at the Massachusetts Institute of Technology in 2010 as Assistant Professor; in 2015 he was promoted to Associate Professor. But during his time as Fulbright Visiting Professor at the University of Glasgow, Clark and his partner Alexandra became smitten with Scotland, and now they merrily return as he takes up a post as Reader in Mathematics at the University of Edinburgh.

### Education Background

Ph.D 2005 – University of Pennsylvania

B.S. 2001 – University of North Carolina at Chapel Hill

### Previous Employment

2015–17 – Massachusetts Institute of Technology : Cecil and Ida Green Career Development Associate Professor of Mathematics

2013–15 – Massachusetts Institute of Technology : Cecil and Ida Green Career Development Assistant Professor of Mathematics

2010–13 – Massachusetts Institute of Technology : Assistant Professor

2008–10 – Harvard University : Benjamin Peirce Lecturer

2007–08 – Institute for Advanced Study : Visitor / Member. Programme: New connections of representation theory to algebraic geometry and physics

2006–07 – Matematisk Institutt, Universitetet i Oslo : Postdoctoral Fellow. Programme: Geometry and arithmetic of structured ring spectra

2005–06 – Mathematisches Institut Göttingen : Postdoctoral Fellow. Programme: Homotopical algebraic geometry