Noah Snyder

How to contact me: nsnyder math columbia edu 626 Math building Application materials CV Research Statement Teaching Statement Publication List Me on the internet: Secret Blogging Seminar Math Overflow

About me:

Teaching:

Papers and Preprints:

• Subfactors of index less than 5, part 3: quadruple points accepted by Communications in Mathematical Physics (with Masaki Izumi, Vaughan Jones, and Scott Morrison).
• Quantum subgroups of the Haagerup fusion categories accepted by Communications in Mathematical Physics (with Pinhas Grossman).
• Subfactors of index less than 5, part 2: quadratic tangles and triple points accepted by International Journal of Mathematics (with Scott Morrison, David Penneys, and Emily Peters)

• Subfactors of index less than 5, part 1: the principal graph odometer accepted by Communications in Mathematical Physics (with Scott Morrison)
• Cyclotomic integers, fusion categories, and subfactors Communications in Mathematical Physics 303 (2011), no. 3, 845--896 (with Scott Morrison and Frank Calegari)
• Knot polynomial identities and quantum group coincidences Quantum Topology 2 (2011), no. 2, 101--156(with Scott Morrison and Emily Peters)
• Non-cyclotomic fusion categories accepted by Transactions of the AMS (with Scott Morrison)

• Constructing the extended Haagerup planar algebra accepted by Acta Mathematica (with Stephen Bigelow, Scott Morrison and Emily Peters)

• The half-twist for U_q(g) representations Algebra & Number Theory. Volume 3 no. 7, p. 809-834, 2009 (with Peter Tingley)
• Skein theory for the D2n planar algebras J. Pure Appl. Algebra 214 (2010), no. 2, 117--139 (with Emily Peters and Scott Morrison)

• Mednykh's formula via lattice topological quantum field theories not intended for publication
• Groups with a character of large degree Proc. Amer. Math. Soc. 136 (2008), no. 6, 1893-1903.
• Cartan subalgebras of root-reductive Lie algebras J. Algebra 308 (2007), no. 2, 583-611.(with Elizabeth Dan-Cohen and Ivan Penkov)
• An alternate proof of Mason's theorem Elem. Math. 55 (2000), no. 3, 93--94)

Writing in progress:

• 3-dimensional topology and finite tensor categories (with Chris Douglas and Chris Schommer-Pries).
  Applying the cobordism hypothesis, we generalize the Turaev-Viro TFT in three ways: extending the TFT down to points, getting 3-framed TFTs from non-spherical fusion categories, and getting noncompact 3d TFTs from non-semisimple finite tensor categories.
  ETA: November 2011.
• The Brauer-Picard groupoid of the Asaeda-Haagerup categories (with Pinhas Grossman).
  We compute the Brauer-Picard groupoid of the Asaeda-Haagerup categories. Like in the Haagerup case there is a new third fusion category Morita equivalent to the other two, but unlike in the Haagerup case the group of Morita autoequivalences is nontrivial.
  ETA: Fall 2011
• Kashaev-Reshetikhin Knot Invariants (with Scott Morrison).
  We clarify some details of Kashaev-Reshetikhin's construction of invariants of knots together with a flat SL(2) connection and compute these invariants for some small examples.
  ETA: Spring 2011. (Answers to calculations available by request.)

Slides for talks (some made by Scott Morrison):

• Finite quantum groups
• Classification of subfactors with index at most 5
• How to recognize U_q(g_2) or S_t
• Fusion categories and subfactors Part 1 and Part 2
• Extended Haagerup exists!
• Coincidences of tensor categories
• Kashaev-Reshetikhin knot invariants

Application materials