Status | Confirmed |
Seminar Series | MATH-IHES |
Subjects | math |
Date | Tuesday 9 April 2024 |
Time | 14:30 |
Institute | IHES |
Seminar Room | Amphithéâtre Léon Motchane |
Speaker's Last Name | Solomon |
Speaker's First Name | David |
Speaker's Email Address | |
Speaker's Institution | University College London & IHES |
Title | SICs, Heisenberg Groups and Starks Conjectures |
Abstract | SICs are configurations of equiangular complex lines in C^d which have been objects of interest to workers in Quantum Information Theory and Design Theory since the 1970's. They are conjectured to exist for all d > 3. Computer calculations show that: all known SICs but one admit an action of the discrete Heisenberg group over Z/dZ, and the inner products of SIC vectors determine Stark units in abelian extensions of the real quadratic field k= Q (√((d-3)(d+1) )) These units `solve' the celebrated conjectures of Harold Stark on special values of Artin L-functions. Their general existence would lead to a solution of Hilbert's 12th Problem over an important class of number fields. After explaining SICs in more detail, I will sketch a programme to put them in a context of p-adic integration and Z_p-extensions, with the aim of elucidating the number Theory involved. If time allows, I will explain some other intriguing, recent links between Physics, SICs and Stark's conjectures. |
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