Jonathan M. Bloom
Moore Instructor / NSF Postdoctoral Fellow
Department of Mathematics
Massachusetts Institute of Technology
jbloom AT math.mit.edu

Curriculum Vitae

Research Interests:
Low-dimensional topology and geometry, knot theory, monopole Floer homology, Heegaard Floer homology, Khovanov homology.

Publications:
The combinatorics of Morse theory with boundary
A link surgery spectral sequence in monopole Floer homology, Advances in Mathematics, doi:10.1016/j.aim.2010.10.014
Odd Khovanov homology is mutation invariant, Mathematical Research Letters 17 (2010), no. 1, p.1-10.

Thesis:
Monopole Floer Homology, Link Surgery, and Odd Khovanov Homology

In Preparation:
A bordered monopole Floer theory (with J. Baldwin).
The Künneth principle in Floer homology (with T. Mrowka and P. Ozsváth).
Khovanov homology and U.

Talks and Figures:
Knots for Novices
Moscow State Seminar
Knots in Washington
Künneth Figures

Graduate Seminar:
Homology theories of knots and links, Spring 2010, MSRI

Instructor:
Knots and Dynamics (Undergraduate Seminar), Spring 2009, Columbia University
Calculus IV, Summer 2008, Columbia University
Calculus II (Math Xb), Spring 2006, Harvard University
Calculus I (Math Xa), Fall 2005, Harvard University
Mater Spei College, Summer 2004, Francistown, Botswana
Colegio Franco-Inglés, Summer 2002, Viña del Mar, Chile
Ross Mathematics Program, Summer 2001, Ohio State University

Teaching Assistant:
Introduction to Probability and Statistics , Jeremy Orloff, Spring 2012, MIT
18.03: Differential Equations, David Jerison, Spring 2011, MIT
Modern Algebra II, Dave Bayer, Fall 2009, Columbia University
Calculus III, Aaron Lauda, Fall 2009, Columbia University
Fixed-point Floer Homology REU, Tim Perutz and Robert Lipshitz, Summer 2009, Columbia University
Algebraic Topology I (Graduate), Tim Perutz, Fall 2008, Columbia University
Modern Geometry II (Graduate), Michael Thaddeus, Spring 2008, Columbia University
Modern Geometry I (Graduate), Michael Thaddeus, Fall 2007, Columbia University
Theory and Practice of Teaching Number Thoery, John Boller, Summer 2003, Harvard University
Theoretical Linear Algebra and Multivariable Calculus (Math 23a), John Boller, Fall 2001, Harvard University

Consultant:
Law and Order: SVU, Hothouse, Season 9. (clip)