On Nahm's conjecture
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Thu, 18/11/2010 16:00 |
Dr S Zwegers (University College, Dublin) |
Number Theory Seminar  |
L3 |
| We consider certain q-series depending on parameters (A,B,C), where A is a positive definite r times r matrix, B is a r-vector and C is a scalar, and ask when these q-series are modular forms. Werner Nahm (DIAS) has formulated a partial answer to this question: he conjectured a criterion for which A's can occur, in terms of torsion in the Bloch group. For the case r=1, the conjecture has been show to hold by Don Zagier (MPIM and CdF). For r=2, Masha Vlasenko (MPIM) has recently found a counterexample. In this talk we'll discuss various aspects of Nahm's conjecture. | |||