Curriculum Vitae

Contact info

Office: MW (Math Tower) 650
Office Phone: +1 614 292 0605
Department Fax: +1 614 292 1479

Mailing Address:

Nathan Broaddus
Department of Mathematics
Ohio State University
231 W. 18th Ave.
Columbus, OH 43210-1174


Spring 2021 - Math 2255
Autumn 2020 - Math 1151
Summer 2019 - Math 2255
Autumn 2018 - Math 1161.0X
Summer 2018 - Math 2255
Summer 2018 - Math 2415
Autumn 2017 - Math 1161.01
Autumn 2017 - Math 8110
Summer 2017 - Math 2415
Autumn 2015 - Math 2153
Spring 2015 - Math 4552
Spring 2015 - Math 6802
Autumn 2014 - Math 1151
Spring 2014 - Math 3345
Autumn 2012 - Math 5801
Summer 2012 - Math 1534
Winter 2012 - Math 641
Autumn 2011 - Math 345
Winter 2011 - Math 152.02
Winter 2011 - Math 757
Autumn 2010 - Math 161.01
Winter 2010 - Math 152.02
Autumn 2009 - Math 151.02


Joan Birman
Tara Brendle
Benson Farb
William Menasco
Andy Putman


OSU Topology Seminar
OSU Geometric Group Theory Seminar
Ohio State University Math
University of Chicago Math
Cornell University Math
Columbia University Math

Education and Employment

  • 2015-present, Associate Professor, Ohio State University
  • 2009-2015, Assistant Professor, Ohio State University
  • 2005-2009, L.E. Dickson Postdoctoral Instructor, University of Chicago
  • 2003-2005, H.C. Wang Assistant Professor, Cornell University
  • 1997-2003, Ph.D. Mathematics, Columbia University
  • 1993-1997, B.S. Mathematics, University of Chicago


  • T. E. Brendle, N. Broaddus and A. Putman, The mapping class group of connect sums of S2xS1. Submitted.arXiv |
  • T. E. Brendle, N. Broaddus and A. Putman, The high-dimensional cohomology of the moduli space of curves with level structures II: punctures and boundary. Submitted.arXiv |
  • J. Birman, N. Broaddus and W. Menasco, Finite rigid sets and homologically nontrivial spheres in the curve complex of a surface, J. Topol. Anal. 7 (2015), no. 1, 47—71. | MathSciNet ReviewarXiv |

    The authors answer a question of Aramayona and Leininger on the homological nontriviality of certain “finite rigid” simplicial subcomplexes of the curve complex.

  • N. Broaddus, Homology of the curve complex and the Steinberg module of the mapping class group, Duke Math. J. 161 (2012), no. 10, 1943—1969. | MathSciNet ReviewarXiv |

    Building on the work of Harer, I investigate the virtual dualizing module of the mapping class group which is also the homology group of the complex of curves. The main result is that as a module over the group ring of the mapping class group, the homology of the curve complex is generated by a single element.

  • N. Broaddus, B. Farb and A. Putman, Irreducible Sp-representations and subgroup distortion in the mapping class group, Comment. Math. Helv. 86 (2011), no. 3, 537—556. | MathSciNet ReviewarXiv |

    We develop a general tool for demonstrating exponential distortion of the word metric of a finitely generated subgroup of a finitely generated supergroup. We then use this tool to show that a number of subgroups of the mapping class group of a surface are at least exponentially distorted. In particular the Torelli subgroup of the mapping class group is at least exponentially distorted.

  • J. S. Birman, T. E. Brendle and N. Broaddus, Calculating the image of the second Johnson-Morita representation, in Groups of Diffeomorphisms: in honor of Shigeyuki Morita on the occasion of his 60th birthday, 119—134. (2008)MathSciNet ReviewarXiv |

    The exact homomorphic image of the mapping class group under an extension of the Johnson homomorphism—which had been previously identified by S. Morita up to finite index—is given. This result is part of a program to use representations of the mapping class group to compute invariants of Heegaard splittings of 3-manifolds.

  • N. Broaddus, B. Farb and A. Putman, The Casson invariant and the word metric on the Torelli group, C. R. Math. Acad. Sci. Paris (2007), no. 8, 449—452. | MathSciNet ReviewarXiv |

    The square of the word length in the Torelli group gives a tight upper bound on the size of the Casson invariant of a homology 3-sphere.

  • N. Broaddus, Noncyclic covers of knot complements, Geom. Dedicata 111 (2005), 211—239. | MathSciNet ReviewarXiv |

    An upper bound is given on the number of sheets in the smallest finite noncyclic cover of the complement of a nontrivial knot.