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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Critical Points Of Discrete Periodic Operators

## Critical Points Of Discrete Periodic OperatorsAdd to your list(s) Download to your calendar using vCal - Frank Sottile (Texas A&M University)
- Tuesday 23 January 2024, 11:45-12:45
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact nobody. EMGW02 - Applied and computational algebraic geometry It is believed that the dispersion relation of a Schrodinger operator with a periodic potential has non-degenerate critical points, for general values of the potential and interaction strengths. In work with Kuchment and Do, we considered this for discrete operators on a periodic graph G, for then the dispersion relation is an algebraic hypersurface. We showed how, for a given periodic graph G, this may be established from a single numerical verification, if we knew the number of critical points for general values of the parameters.With Matthew Faust, we use ideas from combinatorial algebraic geometry to give an upper bound for the number of critical points at generic parameters, and also a criterion for when that bound is obtained. The dispersion relation has a natural compactification in a toric variety, and the criterion concerns the smoothness of the dispersion relation at toric infinity. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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