Noah Snyder
Advisors:
Mathematical interests:
Quantum groups at roots of unity and higher category theory with a view towards low dimensional topology
Research papers and preprints:
Braiding for quantum groups at roots of unity (in preparation)
In this paper we extend the results of Kashaev and Reshetikhin from sl_2 to a general simple quantum group. This paper is coauthored with Nicolai Reshetikhin and is supported by several of his grants and the hospitality of CTQM at Aarhus.
A rapid proof of Mednykh's formula (in preparation)
In this note we give a quick application of the theory of lattice TQFTs to prove Mednykh's formula for characters of finite groups. We modify this theory slightly to prove a related result for unoriented surfaces due to Frobenius and Schur.
Cartan subalgebras of root reductive Lie algebras (to appear in J. Algebra, arxiv preprint)
In this paper we extend the results of Karl-Hermann Neeb and Ivan Penkov in "Cartan subalgebras of gl_\infty" (Canad. Math. Bull. 46 (2003), no. 4, 597--616) to an arbitrary root reductive Lie algebra. We also give a description of the conjugacy classes of Cartan subalgebras of simple root reductive Lie algebras.
This paper is coauthored with Ivan Penkov and Elizabeth Dan-Cohen. The research for this paper was supported in part by two National Science Foundation Research Fellowships and in part by another NSF grant.
Groups with a character of large degree (tentatively accepted, arxiv preprint)
Let G be a finite group of order n and V an irreducible representation over the complex numbers of dimension d. For some nonnegative number e, we have n=d(d+e). If e is small, then the character of V has unusually large degree. We fix e and attempt to classify such groups. For e=1 or 2 we give a complete classification. For any other fixed e we show that there are only finitely many examples.
The research for this paper was done under the advice of Hendrik Lenstra Jr., and was supported by a National Science Foundation Research Fellowship.
My senior year of high school Serge Lang mentioned Mason-Stother's theorem (the polynomial version of the famous ABC conjecture) to me. This brief paper gives a simple short proof of this result. It has also appeared in Lang's Math Talks for Undergraduates.
Talks and Seminars
In Fall 2005 I organized a weekly seminar on Topological Invariants and Quantum Algebra and gave half of the talks. Here are the notes.
In Spring 2005 Jennifer Berg and I organized a weekly seminar on representation theory under the supervision of Vera Serganova.
In seminars at Berkeley I have given expository talks on the following subjects:
Expository papers and teaching notes:
In the fall of 2003 I wrote a final paper called "Automorphism Groups of Curves" for Robin Hartshorne's class on algebraic curves. Here it is in pdf.
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.
Other interests
