Curriculum Vitæ — Clark Barwick Massachusetts Institute of Technology Department of Mathematics, E17-332 77 Massachusetts Avenue Cambridge, MA 02139-4307 Web http://www.math.mit.edu/∼clarkbar/ Email [email protected] or [email protected] Citizenship United States Employment History 2013– Massachusetts Institute of Technology (Cambridge, MA, USA). Cecil and Ida Green Career Development Assistant Professor of Mathematics. 2010–13 Massachusetts Institute of Technology (Cambridge, MA, USA). Assistant Professor. 2008–10 Harvard University (Cambridge, MA, USA). Benjamin Peirce Lec- turer. 2007–08 Institute for Advanced Study (Princeton, NJ, USA). Visitor, Term I; Member, Term II. New connections of representation theory to al- gebraic geometry and physics. Project leader: R. Bezrukavnikov. 2006–07 Matematisk Institutt, Universitetet i Oslo (Oslo, Norway). YFF Postdoctoral fellow. Geometry and arithmetic of structured ring spec- tra. Project leader: J. Rognes. 2005–06 Mathematisches Institut Göttingen (Göttingen, Germany). DFG Postdoctoral fellow. Homotopical algebraic geometry. Project leader: Yu. Tschinkel. Education 2005 University of Pennsylvania (Philadelphia, PA, USA). Ph.D, Math- ematics. Thesis advisor: Tony Pantev. 2001 University of North Carolina at Chapel Hill (Chapel Hill, NC, USA). B.S., Mathematics. 1 Papers in progress 22. Algebraic K-theory of Thom spectra (with J. Shah). In progress. 21. Equivariant higher categories and equivariant higher algebra (with E. Dotto, S. Glasman, D. Nardin, and J. Shah). In progress. 20. Higher plethories and chromatic redshift. In progress. 19. On the algebraic K-theory of algebraic K-theory. In progress. 18. Spectral Mackey functors and equivariant algebraic K-theory (III). In progress. 17. Cyclonic and cyclotomic spectra (with S. Glasman). In progress. 16. Spectral Mackey functors and equivariant algebraic K-theory (II). In progress. Publications and prepublications 15. Dualizing cartesian and cocartesian fibrations (with S. Glasman and D. Nardin). Submitted to International Mathematics Research Notices. arXiv:1409.2165 14. Spectral Mackey functors and equivariant algebraic K-theory (I). Submitted to Advances in mathematics. arXiv:1404.0108 13. Regularity of structured ring spectra and localization in K-the- ory (with T. Lawson). Submitted to Journal für reine und angewandte Mathematik. arXiv:1402.6038 12. Multiplicative structures on algebraic K-theory. Submitted to Documenta mathematica. arXiv:1304.4867 11. From operator categories to topological operads. Submitted to Geometry and topology. arXiv:1302.5756 10. On the Q construction for exact ∞-categories (with J. Rognes). Preprint. arXiv:1301.4725 9. On exact ∞-categories and the Theorem of the Heart. Submit- ted to Compositio mathematica. arXiv:1212.5232 2 8. Quillen theorems Bn for pullbacks of (∞; k)-categories. To ap- pear in Homotopy, Homology, and Applications (with D. M. Kan). arXiv:1101.4879 / arXiv:1028.1777 7. On the algebraic K-theory of higher categories. Submitted to Journal of topology. arXiv:1204.3607 6. On the unicity of higher categories (with C. Schommer–Pries). Submitted to Annals of mathematics. arXiv:1112.0040 5. From partial model categories to ∞-categories (with D. M. Kan). Submitted to Homotopy, Homology, and Applications. arXiv:1101.4879 / arXiv:1102.2512 4. n-relative categories: A model for the homotopy theory of n- fold homotopy theories. Homotopy, Homology, and Applications, vol. 15 (2013), no. 2, pp. 281–300 (with D. M. Kan). 3. A characterization of simplicial localization functors and a dis- cussion of DK equivalences (with D. M. Kan). Indagationes Math- ematicæ 23 (2012), pp. 69–79. 2. Relative categories: Another model for the homotopy theory of homotopy theories (with D. M. Kan). Indagationes Mathemat- icæ 23 (2012), pp. 42–68. 1. On left and right model categories and left and right Bous- field completions. Homotopy, Homology, and Applications, vol. 12 (2010), no. 2, pp. 245–320. Selected Invited Presentations Summer 2015 Hausdorff trimester on homotopy theory, manifolds, and field theories: TBD. March 2015 Oberwolfach workshop on homotopy theory: TBD. August 2014 CUNY workshop on differential cohomologies: Absolute non- commutative motives. April 2014 MSRI Workshop on reimagining the foundations of algebraic topology: Redshift and higher categories. March 2014 Berkeley topology seminar: (Equivariant) algebraic K-theory of rings and ring spectra. 3 March 2014 Berkeley topology seminar: Algebraic K-theory as categorified sta- ble homotopy theory. December 2013 Cornell topology and group theory seminar: How unique is the functorial Becker–Gottlieb transfer? November 2013 University of Louisiana Lloyd Roeling Conference: Multiplica- tive structures on K-theory and a Barratt-Priddy-Quillen theorem. October 2013 AMS special session on higher structures in algebra, geometry and physics: The algebraic K-theory of higher categories. April 2013 University of Notre Dame 11th Annual Graduate Student Topology & Geometry Conference: Algebraic K-theory of higher categories. July 2012 Stanford Symposium on algebraic topology: Applications and new directions: Dévissage. July 2012 Thematic session on homotopy theory at the 6th European Congress of Mathematics in Krakow, Poland: Waldhausen K- theory as a Goodwillie derivative. May 2012 Northwestern topology seminar: Waldhausen K-theory as a Goodwillie derivative. May 2012 University of Chicago topology seminar: Waldhausen K-theory as a Goodwillie derivative. May 2012 University of New Mexico conference on Witt vectors in arith- metic, geometry, and topology: Higher λ-structures. November 2011 University of Minnesota topology seminar: Algebraic K-theory as a Goodwillie derivative. November 2011 University of Minnesota colloquium: The Tower of Babel problem in higher category theory. March 2011 University of Iowa, AMS Spring central section meeting: Higher algebraic K-theory of ∞-categories. November 2010 Nagoya Conference on Witt vectors, foliations, and absolute de Rham cohomology: A homotopical perspective on the de Rham– Witt complex. 4 August 2010 Fields Institute Conference on homotopy theory and derived algebraic geometry: Equivariant derived algebraic geometry and K- theory. February 2010 Stanford University topology seminar: Equivariant derived alge- braic geometry and K-theory. August 2009 Loen conference on p-adic geometry and homotopy theory: Equivariant derived algebraic geometry and K-theory. June 2009 Plenary speaker at the i-MATH school of derived algebraic ge- ometry at the Departamento de Matemáticas at the Universi- dad de Salamanca: Applications of derived algebraic geometry to homotopy theory. May 2009 Midwest Topology Seminar: Operator categories and homotopy coherent algebra. March 2008 Banff International Research Station workshop on new topo- logical contexts for Galois theory and algebraic geometry: ∞- categories. December 2007 Max Planck Institut topology seminar: Operator categories and homotopy coherent algebra. October 2007 Massachusetts Institute of Technology topology seminar: Op- erator categories and strictification of homotopy coherent algebraic structures. June 2007 Matematisk Institutt Universitetet i Bergen Norwegian topol- ogy symposium: Operator categories, multicategories, and K- theory. March 2007 Fields Institute thematic program on geometric applications of homotopy theory: Differential calculus in spectral algebraic ge- ometry. November 2006 Essen seminar: A new perspective on Grothendieck–Verdier duality. September 2006 Matematisk Institutt Universitetet i Oslo conference on topo- logical algebraic geometry: Crystals and D-crystals in spectral al- gebraic geometry. July 2006 Oberwolfach workshop on Algebraic K-theory: D-crystals. 5 June 2006 Mathematischen Institut Göttingen conference on algebraic groups: Toward a theory of higher-dimensional chiral algebras. May 2006 Université de Nice – Sophia Antipolis conference on higher stacks in algebraic geometry: An overview of positive characteris- tic topological algebraic geometry. May 2006 Université de Nice – Sophia Antipolis conference on higher stacks in algebraic geometry: Rezk multi-(∞; n)-categories. Grants 2012–2013 NSF DMS–1206449, The Legacy of Daniel Quillen: K-Theory and Homotopical Algebra, 9/1/12–8/31/13: $45,500. 2010-2012 Solomon Buchsbaum AT&T Research Fund, The Chromatic Splitting Conjecture and the Algebraic K-Theory of the Sphere Spectrum, 6/1/10–6/1/15: $50,000. 2009–2010 NSF Collaborative Research Grant DMS–0905950, Homotopy Theory: Applications and New Dimensions with Michael Hop- kins, Jacob Lurie, Haynes Miller, and Mark Behrens, 9/1/09– 8/31/2014(est): $1,160,501.00. Postdoctoral research advising Dotto, Emanuele 2013–, C. L. E. Moore Instructor. Hirsh, Joseph 2013–, NSF Postdoctoral Fellow. Graduate research advising Glasman, Saul Ph.D expected: Spring 2015. Papers: 4. A note on commutative algebras and their modules in quasicategories. Preprint. arXiv:1409.3506. 3. Dualizing cartesian and cocartesian fibrations (with C. Bar- wick and D. Nardin). Submitted to International Mathematics Research Notices. arXiv:1409.2165. 2. A spectrum-level Hodge filtration on topological Hoch- schild homology. Preprint. arXiv:1408.3065. 1. Day convolution for ∞-categories. Submitted to Mathemat- ics Research Letters. arXiv:1308.4940. 6 Nardin, Denis Ph.D expected: Spring 2017. Papers: 1. Dualizing cartesian and cocartesian fibrations (with C. Bar- wick and S. Glasman). Submitted to International Mathematics Research Notices. arXiv:1409.2165. Shah, Jay Ph.D expected: