Department of Mathematics - Hill Center

Rutgers, The State University Of New Jersey

110 Frelinghuysen Rd.

Piscataway, NJ 08854-8019

My interests include representation theory, algebraic combinatorics, and experimental mathematics. More importantly, I am currently thinking about Verlinde algebras, affine Kac-Moody Lie algebras, theta functions, non-homogeneous symmetric functions, convergence of iterates of a nonlinear operators, representations of double affine Hecke algebras, and undergraduate mathematical proof comprehension.

Hours: 2 - 3 PM Tuesdays

Directions: There are two pairs of elevators in the Hill building. One of them goes up to the fifth floor and the other goes up to the seventh. Choose wisely.

- Prove that for every pair of integers
**a**and**b**(not both zero), every common divisor of**a**and**b**divides the greatest common divisor of**a**and**b**. - Let
**R**be a ring with identity element 1 and let**S**be the set {0,1,2,...,n,n+1,...}. Prove that if**R**is an integral domain and**S**is finite, then**|S|**is prime. - (a) Find examples of commutative rings
**R**(not necessarily with identity) and maximal ideals**m**such that**m**is NOT a prime ideal.

(b) Let**R**be a commutative ring (not necessarily with identity) such that for every x in**R**, x is in**R**x. Prove that all maximal ideals in**R**are prime ideals. - Let p be a prime number. Prove: If
**G**is a group of order p, then**G**is cyclic. Also prove: If**G**is a group of order p^2, then**G**is abelian.

A. Ginory. Twisted Affine Lie Algebras, Fusion Algebras, and Congruence Subgroups

A. Ginory, R. Nussbaum. On the Border of Order-Preserving Maps: A Problem Suggested by Lie Algebra Theory

A. Ginory. Vertex Algebras Conformal Blocks and Zhu's algebra

Simple and Affine Lie Algebras - Computes Cartan matrices, Coxeter numbers, dual Coxeter numbers, and other related data for simple and affine Lie algebras.(in progress)

Lattice Program - Computes dual lattices, bases, sums, intersections and other linear algebra related calculations.(in progress)

Graduate Algebra and Representation Theory Seminar - Fall 2018

Graduate Algebra and Representation Theory Seminar - Spring 2018

Graduate Algebra and Representation Theory Seminar - Fall 2017

Graduate Student Vertex Operator Algebra Seminar - Spring 2017

Graduate Student Vertex Operator Algebra Seminar - Fall 2016

Vertex Operator Algebra Notes (in progress, last update 10/27/16)

The Square Root of 2 is Irrational

The Brouwer Fixed Point Theorem

Counting Factorizations in the Symmetric Group

de Rham's Theorem

Closed Subgroup Theorem (Lie Groups)

Equivalence of 2 Classical Constructions of the p-adic Numbers

Thesis Slides