|Fall 2014:||Math 311 (Advanced Calculus I) Sec. 5 (Prof. Sesum)|
|Office:||Hill 628, Busch Campus|
|Office Hours:||Thursdays, Noon - 1.00 PM|
|E-mail (for students):||firstname.lastname@example.org|
Research Interests -
|Vertex operator algebras, affine Lie algebras, partition identities|
IdentityFinder and some new identities of Rogers-Ramanujan type, to appear.
S. Kanade, M. C. Russell
The Rogers-Ramanujan identities and various analogous identities (Gordon, Andrews-Bressoud, Capparelli, etc.) form a family of very deep identities concerned with integer partitions. These identities (written in generating function form) are typically of the form "product side" equals "sum side," with the product side enumerating partitions obeying certain congruence conditions and the sum side obeying certain initial conditions and difference conditions (along with possibly other restrictions). We use symbolic computation to generate various such sum sides and then use Euler's algorithm to see which of them actually do produce elegant conjectured product sides. We not only rediscover many of the known identities but also discover some apparently new ones, as conjectures supported by strong mathematical evidence.
Ghost series and a motivated proof of the Andrews-Bressoud Identities, to appear.
S. Kanade, J. Lepowsky, M. C. Russell, A. V. Sills
We present what we call a ``motivated proof'' of the Andrews-Bressoud partition identities for even moduli. A ``motivated proof'' of the Rogers-Ramanujan identities was given by G. E. Andrews and R. J. Baxter, and this proof was generalized to the odd-moduli case of Gordon's identities by J. Lepowsky and M. Zhu. Recently, a ``motivated proof'' of the somewhat analogous G\"ollnitz-Gordon-Andrews identities has been found. In the present work, we introduce ``shelves'' of formal series incorporating what we call ``ghost series,'' which allow us to pass from one shelf to the next via natural recursions, leading to our motivated proof. We anticipate that these new series will provide insight into the ongoing program of vertex-algebraic categorification of the various ``motivated proofs.''
A motivated proof of the Gollnitz-Gordon-Andrews Identities, to appear.
B. Coulson, S. Kanade, J. Lepowsky, R. McRae, F. Qi, M. C. Russell, C. Sadowski
We present what we call a ``motivated proof'' of the Gollnitz-Gordon-Andrews Identities identities. A similar motivated proof of the Rogers-Ramanujan identities was previously given by G. E. Andrews and R. J. Baxter, and was subsequently generalized to Gordon's identities by J. Lepowsky and M. Zhu. We anticipate that the present proof of the Gollnitz-Gordon-Andrews Identities identities will illuminate certain twisted vertex-algebraic constructions.
|Notre Dame University:||Algebra Seminar, Dec 2014|
|CUNY Graduate Center:||New York Applied Algebra Colloquium, Oct 2014|
|Rutgers University:||Experimental Mathematics Seminar, Oct 2014||Video: 1, 2; Chalkboard (Thanks to Matthew Russell!)|
|Rutgers University:||Lie groups and Quantum Mathematics Seminar, Sept 2014||Slides|
|Spring 2013:||Graduate Students' Vertex Operator Algebra Seminar|
|Fall 2012:||Graduate Students' Vertex Operator Algebra Seminar|
|Summer 2014:||Instructor||Math 354 (Linear Optimization)|
|Spring 2014:||TA||Math 311 (Advanced Calculus I)|
|Fall 2013:||TA||Math 251 (Calculus III)|
|Summer 2013:||Instructor||Math 250 (Linear Algebra)|
|Spring 2013:||TA||Math 244 (Differential Equations)|
|Fall 2012:||Head TA||Math 152 (Calculus II)|
|Summer 2012:||Instructor||Math 477 (Theory of Probability)||Course web page|
|Spring 2012:||Head TA||Math 152 (Calculus II)|
|Fall 2011:||Head TA||Math 151 (Calculus I)|
|Summer 2011:||Instructor||Math 152 (Calculus II)||Course web-page|
|Spring 2011:||TA||Math 135 (Calculus I)|
|Fall 2010:||TA||Math 135 (Calculus I)|