Research

Publications:

  1. Topology and arithmetic of resultants, II: the resultant = 1 hypersurface (with an appendix by C. Cazanave) (with Benson Farb). Algebraic Geometry, vol. 4, no. 1, 2017, pp. 337-352.
  2. Relative Tate Objects and Boundary Maps in the K-Theory of Coherent Sheaves (with Oliver Braunling and Michael Groechenig). Homology, Homotopy and Applications, vol. 19, no. 1, 2017, pp. 341-369.
  3. Modular Operads of Embedded Curves (with Satoshi Kondo and Charles Siegel). Geometry & Topology, vol. 21, no. 2, 2017, pp. 903-922.
  4. Operator Ideals in Tate Objects (with Oliver Braunling and Michael Groechenig). Mathematical Research Letters, vol. 23, no. 6, 2016, pp. 1565-1631.
  5. Geometric and Analytic Structures on the Higher Adeles (with Oliver Braunling and Michael Groechenig). Research in the Mathematical Sciences, Special Collection in Celebration of the Research of Fedor Bogomolov on the Occasion of his 70th Birthday, vol. 3, no. 1, 2016, article 22.
  6. Topology and arithmetic of resultants, I (with Benson Farb). New York Journal of Mathematics, vol. 22, 2016, pp. 801-821
  7. Tate Objects in Exact Categories (with an appendix by J. Stovicek and J. Trlifaj)  (with Oliver Braunling and Michael Groechenig). Moscow Mathematical Journal, vol. 16, no. 3, 2016, pp. 433-504.
  8. Descent for n-Bundles. Advances in Mathematics, vol. 288, 2016, pp. 527-575.

Pre-prints:

  1. Derived \ell-adic zeta functions (with Jonathan Campbell and Inna Zakharevich). Submitted for publication.
  2. Coincidences of homological densities, predicted by arithmetic (with Benson Farb and Melanie Matchett Wood). Submitted for publication.
  3. Hochschild coniveau spectral sequence and the Beilinson residue (with Oliver Braunling). Submitted for publication.
  4. The A_\infty-Structure of the Index Map (with Oliver Braunling and Michael Groechenig). Submitted for publication.
  5. Etale homological stability and arithmetic statistics (with Benson Farb). Submitted for publication.
  6. A Generalized Contou-Carrere Symbol and its Reciprocity Laws in Higher Dimensions (with Oliver Braunling and Michael Groechenig). Submitted for publication.
  7. The Index Map in Algebraic K-Theory (with Oliver Braunling and Michael Groechenig). Submitted for publication.

Thesis:

  1. Descent for n-Bundles, Tate Objects in Exact Categories, and the Index Map and Reciprocity Laws

Research Talks:

  1. University of Chicago Geometry/Topology Seminar – Coincidences of homological densities, predicted by arithmetic – Sept. 29, 2016
  2. 2016 Oberwolfach Topology Meeting – Coincidences of homological densities, predicted by arithmetic – July 21, 2016
  3. 27th Nordic Congress of Mathematicians, Geometry and Topology Session – Counting Problems and Homological Stability – March 17, 2016
  4. Purdue Topology Seminar – Counting Problems and Homological Stability – March 2, 2016
  5. Wayne State Colloquium – Polynomials, Counting Problems and Algebraic Topology – February 22, 2016
  6. IBS-CGP Conference on Homotopical Methods in Quantum Field Theory – Higher Determinants and Double Loop Groups – January 13, 2016
  7. Minnesota Topology Seminar – Counting Problems and Homological Stability – October 26, 2015
  8. Rice Topology Seminar – Counting Problems and Homological Stability – October 19, 2015
  9. Northwestern Topology Seminar – Counting Problems and Homological Stability – October 12, 2015
  10. 2015 AMS Summer Institute in Algebraic Geometry – Topology and Arithmetic of Resultants – July 27, 2015
  11. Midwest Topology Seminar – Topology and Arithmetic of Spaces of Rational Maps – May 10, 2015
  12. Wisconsin Number Theory Seminar – Geometry and Arithmetic of Spaces of Rational Maps – May 7, 2015
  13. UIC Homotopy Algebras Seminar – Modular Operads of Embedded Curves – April 17, 2015
  14. 2015 Arkansas Spring Lecture Series – Spaces of Rational Functions, Representation Stability, and Statistics over Finite Fields – March 5, 2015
  15. Rutgers Algebra Seminar – The Index Map and Reciprocity Laws for Contou-Carrere Symbols – Feb. 4, 2015
  16. Yale Geometry, Symmetry and Physics Seminar – The Index Map and Reciprocity Laws for Contou-Carrere Symbols – Feb. 2, 2015
  17. MIT – Topology Seminar – The Index Map and Reciprocity Laws – Nov. 17, 2014
  18. University of Tokyo – Topology Seminar – The Index Map and Reciprocity Laws for Contou-Carrere Symbols – July 22, 2014
  19. IPMU – Get Together Seminar – A Modular Operad of Embedded Curves – July 3, 2014
  20. Imperial College London MAGIC Seminar – Index Theory and Reciprocity Laws – February 26, 2014
  21. Padua Winter School and Workshop on Higher Structures in Algebraic Analysis – The Index Map in Algebraic K-Theory – February 18, 2014
  22. University of Copenhagen Algebra/Topology Seminar – Index Theory and Reciprocity Laws – December 17, 2013
  23. Nagoya University K-Theory Seminar – Index Theory in Algebraic K-Theory -December 12, 2013
  24. Chuo University – K-Theory Seminar – Index Theory in Algebraic K-Theory – December 3, 2013
  25. IPMU – Get-Together Math Seminar – Index Theory in Algebraic K-Theory and Algebraic Geometry – October 10, 2013
  26. Northwestern Mini-Conference – Determinants, Delooping and Reciprocity – June 12, 2013
  27. Northwestern – Topology Seminar – Descent for n-Bundles – June 3, 2013
  28. Paris – Institute de Mathematiques de Jussieu – Seminaire d’Analyse Algebrique – Descent for n-Bundles – May 21, 2013
  29. Utrecht – Descent for n-Bundles – May 17, 2013
  30. Oxford – Algebraic and Symplectic Geometry Seminar – Descent for n-Bundles – May 7, 2013
  31. EPFL – Topology Seminar – Determinants and Delooping of Algebraic K-Theory – May 3, 2013
  32. EPFL – Geometry Seminar – Determinants, Delooping and Reciprocity – May 1, 2013
  33. Max Planck Institute for Mathematics – Higher Differential Geometry Seminar – “Descent for n-bundles” – April 24, 2013
  34. University of British Columbia – Algebraic Geometry Seminar – “Strictifying Higher Bundles” – Oct. 29, 2012
  35. Notre Dame – Topology Seminar – “Extensions of Lie n-Groups”  – Sept. 27, 2012
  36. 2012 ESI Program on K-Theory and Quantum Fields – “Extensions of Lie n-Groupoids by Strict Lie n-Groups” – June 14, 2012

Other Talks:

  1. IPMU Special Seminar – Nerves and Group Completion for Categories and Operads, A Beginner’s Guide, Parts 1-3 – Aug. 29, Sept. 1 and Sept. 2, 2014
  2. IPMU Conformal Blocks Seminar – Loop Groups and Conformal Blocks – Nov. 19, 2013
  3. MIT Babytop – The Structure of Higher Bundles – Nov. 27, 2012
  4. 2012 Simons Center Graduate Workshop on SUSY Field Theories  – Supermanifolds – March 6, 2012
  5. 2011 Talbot Workshop – Principal Bundles, Real Structures, Toledo Invariant and Milnor-Wood – May 2, 2011
  6. Northwestern Graduate Seminar – The Chern-Weil Construction – April 21, 2011
  7. Northwestern Graduate Seminar – Symmetries of Spaces and Bundles – Jan. 20, 2011
  8. Northwestern Graduate Seminar – Spin Structures – Oct. 7, 2010
  9. Discrete and Continuous Geometries, Northwestern Conference for Undergraduates – The Euler Characteristic – June 23, 2010
  10. 2010 Talbot Workshop – Complex K-Theory – May 23, 2010
  11. Northwestern Graduate Seminar – Introduction to Complex K-Theory – May 18, 2010

Posters:

  1. Newton Institute’s Higher Structure 2013: Operads and Deformation Theory – “Mapping Spaces in Higher Stacks, and Applications” – April 2, 2013