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## Application materialsCVResearch Statement Teaching Statement Publication List
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Spring 2011 I taught Calculus I.

Fall 2010 I taught group representation theory.

__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)

__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.)

- 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

CV

Research Statement

Teaching Statement

Publication List

Two years ago, I applied for postdocs. Here are my application materials, they are currently out of date but may be of interest to people who are preparing their own applications.

CV

Research Statement

Teaching Statement

AMS Cover Sheet

Cover Letter

Publication List

In the summer of 2002 I taught a tutorial at Harvard on L-functions and zeta functions.

Here are the notes from lectures (in pdf): 1, 2, 3, 4, 5 and 6, 7, 8 and 9, 10

Here are the homeworks (in pdf): 1, 2

Here are the suggested paper topics (in pdf).

In the spring of 2002 I wrote my senior thesis at Harvard under the supervision of Benedict Gross. It was titled "Artin L-Functions: A Historical Approach." It received highest honors from the math department. Here it is in pdf.

In the fall of 2001 I wrote a paper on the distribution of primes in F_p[x] for a seminar taught by Tom Brennan. I received advice on both the content and presentation of this paper from both Tom Brennan and Keith Conrad. Here it is in pdf.