Modular Forms, K-theory and Knots
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Fri, 22/01/2010 16:30 |
Professor Don Zagier (Max-Planck Institut) |
Colloquia  |
L2 |
| Many problems from combinatorics, number theory, quantum field theory and topology lead to power series of a special kind called q-hypergeometric series. Sometimes, like in the famous Rogers-Ramanujan identities, these q-series turn out to be modular functions or modular forms. A beautiful conjecture of W. Nahm, inspired by quantum theory, relates this phenomenon to algebraic K-theory. In a different direction, quantum invariants of knots and 3-manifolds also sometimes seem to have modular or near-modular properties, leading to new objects called "quantum modular forms". | |||