I am a symplectic geometer working in the intersection of dynamical systems, mathematical physics, and algebraic topology.

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I use homology theories stemming from Morse homology and Floer homology — like symplectic cohomology and Rabinowitz Floer homology — to probe dynamics on symplectic manifolds.

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I like studying non-exact symplectic manifolds, understanding dynamics of contact hypersurfaces, and developing mirror-symmetric interpretations and intuition, particularly within quantitative symplectic frameworks.

Publications and preprints

• Symplectic cohomology and complex-analytic mirror symmetry.  In preparation.

   

• Semi-orthogonal decompositions in Fukaya-Seidel mirrors to blowups of toric varieties.  In preparation.  With Catherine Cannizzo.

   

• Rabinowitz Fukaya categories and the categorical formal punctured neighborhood of infinity.  In preparation.  With Sheel Ganatra and Yuan Gao.

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• Periodic leaf-wise intersection points from Lagrangians
  Submitted, arXiv:2105.10021, 35 pages.

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• The quantitative nature of reduced Floer theory. 

  Advances in Mathematics. Volume 383, 2021, 107682, 80 pages.

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• Rabinowitz Floer homology and mirror symmetry
  Journal of Topology. 11 (2018), no. 1, 144--179.

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• Completed Symplectic Cohomology and Liouville Cobordisms 
  PhD Thesis, 2018.

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• Knot projections with a single multi-crossing. 
  With C. Adams, T. Crawford, B. DeMeo, M. Landry, A. Lin, M. Montee, S. Park, F. Yhee 
  Journal of Knot Theory and Its Ramifications, Vol. 24, No. 3 (2015).

Research Talks

• Holomorphic Curves and Symplectic Topology Conference, August 2017, Institut Mittag-Leffler

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• Mathematical Physics Seminar, December 2017, Harvard University CMSA

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• AMS-AWM Special Session on Women in Symplectic and Contact Geometry, January 2018, Joint Math Meetings

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• Geometry/Topology Seminar, April 2018, Stony Brook University

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•  Georgia Topology Conference, June 2018, University of Georgia, Athens

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•  Topology Seminar, October 2018, UC Berkeley

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•  Geometry Seminar, November 2018, UT Austin

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•  Geometry and Physics Seminar, February 2019, Northwestern

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•  Categorical Symplectic Topology Conference, March 2019, Cambridge University

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•  AWM Research Symposium, April 2019, Rice University

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• Homological Algebra, Microlocal Analysis and Symplectic Geometry Conference, June 2019, CRM

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• QMAP Seminar, October 2019, UC Davis

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• Symplectic Geometry and Topology Seminar, October 2019, Stony Brook University

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• Northern California Symplectic Geometry Seminar, November 2019, Stanford University

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• Workshop on Higher Structures in Geometry and Physics, November 2019, The Fields Institute

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• Geometry/Topology/Categorification Seminar, January 2020, USC

   

• Seminário Simplético do Rio, October 2020, Rio de Janeiro

   

• Floer Theory and Hamiltonian Dynamics of Non-Compact Hypersurfaces Conference, January 2021, ETH Zurich.  Slides.

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Notes from working seminars

• Categorical Dynamics.  Columbia University Fall 2014.

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• Low-dimensional Topology and mirror symmetry.  Stanford University Fall 2019.