Algebraic Geometry in Spectral Theory

منتهي الصلاحية
التواريخ : 24 فيفري 2023 » 26 فيفري 2023

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الجهة المنظمة : ICERM

الرياضيات والإحصاء; الفيزياء;
الكلمات المفتاحية: Algebra, Geometry, Mathematical Physics, Physics
تفاصيل :

Discrete periodic Schrodinger operators describe the behavior of individual electrons in "ideal" crystals in the tight-binding model of solid state physics. Spectra of such operators have the usual band-gap structure, and the corresponding dispersion relations are algebraic varieties. In the 1990's Gieseker, Knorrer, and Trubowitz used toroidal compactifications to solve questions such as irreducibility of Bloch and Fermi varieties and the density of states, for a class of mono-atomic models. Their work showed that while spectral theory is focused on the real part of the Bloch variety, the study of complex singularities and compactifications is crucial for describing formation of bands and gaps. After a gap of 30 years, spectral theory is again interacting with algebraic geometry. Recently, W. Liu gave an algebraic method to obtain more general proofs of irreducibility for Fermi surfaces, Kravaris used free resolutions to study density of states, and Kuchment and coauthors used toric varieties and numerical nonlinear algebra to study spectral edges. These and other developments have led to the realization that many open questions in spectral theory may be studied using modern tools in algebraic geometry. These include the relation of reducibility/irreducibility with physical symmetries of the crystals, the structure of spectral band edges, and Dirac cones. These methods can also be applied to quantum graphs, such as graphene-type structures, and to obtain existence and non-existence theorems for embedded eigenvalues. The goal of this workshop is to bring together experts from spectral theory, mathematical physics, and algebraic geometry to understand, apply, and advance these new methods and interactions. A significant aspect of these reemerging interactions involves computation. A key recent development in algebraic geometry is computation, both symbolic and numerical. Computation and experimentation using tools from algebraic geometry have already been important in two recent papers by Sottile on this subject, and we expect it to become a useful tool for studying periodic operators. Speakers in this workshop are firmly rooted in the uses of computation and experimentation in applications of Algebraic Geometry, and many are familiar with exploiting the atmosphere and facilities of the ICERM to initiate collaboration.


ICERM organises its event entitled Algebraic Geometry in Spectral Theory to be held from 24 فيفري 2023 to 26 فيفري 2023 in Providence, Rhode Island, الولايات المتحدة. It covers various areas of الرياضيات والإحصاء including 0. For more information, visit the website of the conference or contact the organizer.
أضف الى المذكرة 2023-02-24 2023-02-26 Europe/London Algebraic Geometry in Spectral Theory https://www.sciencedz.net/ar/conference/94786-algebraic-geometry-in-spectral-theory Providence, Rhode Island - الولايات المتحدة ICERM

الأقسام ذات الصلة:

مؤتمرات، ملتقيات علمية و ندوات في Rhode Island
مؤتمرات، ملتقيات علمية و ندوات في الولايات المتحدة
مؤتمرات، ملتقيات علمية و ندوات في الولايات المتحدة في2023
مؤتمرات، ملتقيات علمية و ندوات في الرياضيات والإحصاء
مؤتمرات، ملتقيات علمية و ندوات في الرياضيات والإحصاء في2023
مؤتمرات، ملتقيات علمية و ندوات في الرياضيات والإحصاء فيالولايات المتحدة
مؤتمرات، ملتقيات علمية و ندوات في الرياضيات والإحصاء فيالولايات المتحدة في2023
كل المؤتمرات والملتقيات
ملتقيات حسب البلد

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