Nikolai Roussanov
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Rutgers Mathematics Department VIGRE /DIMACS Center REU Program

Topic: Young Tableaux and Quantum Cohomology of the Grassmanian

Advisor: Chris Woodward
VIGRE graduate students: Michael Weingart, Pieter Blue, and Aaron Lauve.

The project deals with applications of Young tableaux to the study of quantum cohomology of the Grassmanian (Quantum Littlewood-Richardson Rule). The problem we are currently working on is twofold:

a) to find the multiplicity-free products in the quantum cohomology ring (i.e. the sets of triples (\lambda, \mu, \nu) such that the quantum Littlewood-Richardson coefficients c(\lambda, \mu, \nu)(k,l) equal either 0 or 1);

b) give a combinatorial reason for the non-negativity of the Littlewood-Richardson coefficients.

Questions and comments are welcome.