Member, Hausdorff Research Institute for Mathematics, Bonn, June July Concurrently/supported by Max Planck Institute for Mathematics.

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1 Dept of Mathematical Sciences Wilson Hall Bozeman, MT RYAN E GRADY Employment Assistant Professor,, Bozeman, Montana. August 2016-present. Postdoctoral Fellow, Perimeter Institute for Theoretical Physics, Waterloo, Ontario, September 2015-August Instructor and Postdoctoral Faculty Fellow, Boston University, Boston, Massachusetts, July 2012-June Research Visits Visitor, Université Montpellier, France, June Member, Hausdorff Research Institute for Mathematics, Bonn, June July Concurrently/supported by Max Planck Institute for Mathematics. Visitor, Perimeter Institute for Theoretical Physics, Waterloo, Ontario, January Education Ph.D. in Mathematics, University of Notre Dame, Notre Dame, Indiana, May Advisor: Stephan Stolz B.S. in Mathematics, Colorado School of Mines, Golden, Colorado May With honors. Published or Accepted Homotopy RG flow and the non-linear σ-model. Contemporary Mathematics (to appear). Joint with B. Williams. Lie algebroids as L spaces. J. Inst. Math. Jussieu (to appear). Joint with O. Gwilliam. The Â-genus as a projective volume form on the derived loop space. Math. Phys. Anal. Geom. 21 (2018), no. 2, Art. 13. BV quantization and the algebraic index. Adv. Math, 317 (2017) Joint with Qin Li and Si Li. L -spaces and derived loop spaces, New York J. Math, 21 (2015) Joint with O. Gwilliam. One-dimensional Chern-Simons and the Â-genus, Algebr. Geom. Topol., 14 (2014) Joint with O. Gwilliam. On geometric aspects of topological quantum mechanics, Ph.D. thesis, Univ of Notre Dame, Covers, Laplacians, and heat kernels of directed graphs, Electron. J. Combin., 16 (2009) no. 1, Research Paper 31. Joint with C. Brasseur and S. Prassidis. Books Edited Topology and Quantum Theory in Interaction, Contemporary Mathematics, American Mathematical Society, Providence, RI, 2018 (in press). Edited with David Ayala and Dan Freed.

2 Submitted Drafts Parametrized L -spaces. 15 pages. arxiv: Kazhdan s property (T) for graphs. 13 pages. arxiv:math Joint with C. Brasseur and S. Prassidis. A one-dimensional AKSZ σ-model and sheaves of twisted differential operators, in preparation, Joint with O. Gwilliam and B. Williams. Boundary observables and Koszul duality, in preparation, Joint with B. Williams. Honors and Grants NSF Infrast. Grant: Topological and Geometric Methods in QFT # , Dec 2016 Nov A NSF-CBMS regional conference held at MSU (Bozeman). Co-Principal Investigator, with PI David Ayala. NSF Standard Grant: Geometric Analysis and Topology # , July 2013-June Co-Principal Investigator on the project Geometric Aspects of Quantum Field Theory and Topological Strings. The Principal Investigator is Si Li (Boston). MAA Section NExT Fellow, Member, Center for Faculty Excellence,, Faculty Excellence Grant,, Fall U.S. Junior Oberwolfach Fellow, May 2016, June AMS Travel Grant, August Heidelberg Laureate Forum, Participant/Workshop Organizer, September Conferences Higher Structures in Topological Data. SIAM Central States Fall Meeting, Fort Collins, CO, September 30, Observables in Courant σ-models. Gone Fishing Poisson Conference, Notre Dame, IN, May 5, Topological invariants via local-to-global constructions of QFT. Texas Geometry and Topology Conference, Lubbock, TX, February 16, Algebras and modules from boundary QFT. AMS Fall Central Sectional Meeting, Minneapolis, MN, October 30, Observables in effective BV theory. (2 of 6 talks in a lecture series.) Oberwolfach: Factorization Algebras and Functorial Field Theory, May 8 14, Perturbative QFT from derived stacks. Mathematics of Quantum Field Theory, IBS-CGP, Pohang, Korea, January 14, Moduli/β-functions for BV theories. Homological Methods in QFT, Simons Center for Geometry and Physics, September 30, Factorization algebras and an application to algebraic index theory. Special Session on Mathematical Physics, Operad Theory, Algebraic Topology and Higher Categories, Mathematical Congress of the Americas, Guanajuato, Mexico, Aug 8, Ricci flow and the space of quantum field theories. Quantum Theory s Influences on Topology, Analysis, and Geometry; Center for Deformation and Symmetry, Copenhagen, May 27, 2013.

3 Conferences (cont.) Seminar & Colloquium Twisted differential operators as observables. BU/Keio Workshop on Geometry, Boston University, September 14, Observables and index theorems. FRG Conference on Topology and Field Theories, University of Notre Dame, June 5, Topological quantum mechanics in the BV formalism. Loop spaces, loop groups, and loop algebras, CIRM, Luminy, May 31, Chern-Simons theory and the Todd genus. AMS Fall Central Sectional Meeting, Notre Dame, IN, November 5, A hierarchy of symplectic σ-models. Mathematical Physics Seminar, University of Illinois (Urbana), October 25, A hierarchy of symplectic σ-models. Geometry, Physics, and Representation Theory Seminar, Northeastern University, October 11, Manifold invariants via Perturbative QFT. Colloquium, Creighton University, April 12, Manifold invariants via Perturbative QFT. GST Seminar, University of Nebraska, April 10, Manifold invariants via Perturbative QFT. Colloquium, Utah State University, November 9, Manifold invariants via Perturbative QFT. Geometry Seminar, Vanderbilt University, October 20, An intro to quantum BV theory. University of the Aegean (Samos), Greece, June 26, An intro to quantum BV theory. Géométrie algébrique, champs et homotopie, Institut de Mathématiques de Toulouse, June 20, An intro to quantum BV theory. Colloquium, University of Montana, Missoula, MT, April 3, Some elementary applications of algebraic topology. Computer Science Seminar, Montana State University, November 21, The BV formalism and some applications to index theory. Topology Seminar, University of Notre Dame, April 5, The BV formalism and some applications to index theory. Math-Physics Joint Seminar, University of Pennsylvania, February 11, Derived geometry as a tool for QFT, QFT as a tool in topology. Topology Seminar, Massachusetts Institute of Technology, March 9, Applications of quantum field theory to geometry and topology. University, January 29, Colloquium, Montana State Applications of quantum field theory to geometry and topology: observables and index theory. IGERT Seminar, Brandeis University, November 12, Derived geometry as a tool for QFT. Topology Seminar, University of Notre Dame, June 26, Ricci flow and the space of quantum field theories. Talks in Mathematical Physics, ETH Zurich, May 21, Factorization algebras and an application to algebraic index theory. Colloquium, University of New Hampshire, May 2, Factorization algebras and an application to algebraic index theory. Geometry Seminar, Brown University, April 3, 2013.

4 Seminar & Colloquium (cont.) Factorization algebras and an application to algebraic index theory. Topology Seminar, University of Illinois, Urbana-Champaign, March 12, Ricci flow and the space of quantum field theories. Topology Seminar, University of Notre Dame, March 7, Twisted differential operators as observables. Algebraic Geometry Seminar, University of Wisconsin, Madison, March 23, On geometry and quantum field theory. Geometry Seminar, Boston University, January 26, Volume forms on the derived loop space. ETH Zurich, January 9, Some observations toward the algebraic index theorem. Topology Seminar, Stanford University, December 6, Some observations toward the algebraic index theorem. GAP Seminar, Penn State University, November 15, Categorical traces and field theories. Geometry/Physics Seminar, Northwestern University, April 28, Characteristic classes in derived geometry. March 31, Felix Klein Seminar, University of Notre Dame, The free fermion in BV theory. University of California Berkeley, January 18, Genera from effective field theory. Topology Seminar, University of Illinois, Urbana-Champaign, November 30, An Introduction to Topological Field Theory. Canisius College, Buffalo, July 17, Graduate Advising Chair, Adam Howard, Ph.D Candidate,. Current. Co-Chair, Eric Berry, Ph.D Candidate,. Current. Committee Member, Eric Fink, Ph.D Candidate,. Current. Committee Member, Daniel Perry, Ph.D Candidate,. Current. Committee Member, Anna Cepek, Ph.D Candidate,. Current. Committee Member, Robin Belton, Ph.D Candidate,. Current. Undergraduate Advising Research Mentor, USP, Fall 2016 & Spring-Fall Research Mentor, Boston University UROP, Spring Undergraduate Mentor, Geometric Group Theory, University of Notre Dame, Spring 2010.

5 Courses Taught Lie Groups (M597), Fall Methods of Proof (M242), Fall Introduction to Differential Equations (M274), Summer Topics in Math: Complex Geometry (M597), Spring Algebraic Topology (M512), Spring 2017 and Spring An Introduction to Topology (M476), Fall Topology (M511), Fall Linear Algebra (M333), Fall Boston University Discrete Mathematics, Fall 2013 and Spring Introduction to Differential Geometry, Fall Calculus 2, Summers Topics in Geometry: Noncommutative Geometry, Spring Introduction to Topology, Spring Calculus 1, Fall University of Notre Dame Calculus B, Spring Abstract Algebra (Honors), Summer Service Colloquium Committee (Mathematical Sciences), Affiliated Faculty/Advisor, Topological Data at MSU, 2016 present. Conference Organizer Topological and Geometric Methods in QFT, A NSF-CBMS Regional Conference, MSU (Bozeman), July 31-Aug 4, QFT on Manifolds with Boundary and the BV Formalism, Perimeter Institute for Theoretical Physics, May 8-12, Deformation Quantization of Shifted Poisson Structures, Perimeter Institute for Theoretical Physics, April 18-22, Homological Methods in Quantum Field Theory, Simons Center for Geometry and Physics, September 29-October 3, Referee/Reviewing Journal of Topology, Letters in Mathematical Physic, Mathematical Physics Studies (Springer), Communications in Mathematical Physics, AMS Mathematical Reviews (MathSciNet), 2012 present. Seminar Organizer MSU Mathematics Seminar, 2016 present. MSU Graduate Student Topology Seminar, 2017 present. Boston University Geometry and Physics Seminar,

Harvard University NSF Postdoctoral Fellow and Instructor, 2016 Mentor: Michael Hopkins

Harvard University NSF Postdoctoral Fellow and Instructor, 2016 Mentor: Michael Hopkins Ben Knudsen Contact information Department of Mathematics 1 Oxford St Cambridge, MA 02138 knudsen@math.harvard.edu scholar.harvard.edu/knudsen Employment Education NSF Postdoctoral Fellow and Instructor,