Objective Sometimes in the sciences there are different yet complementary descriptions for the same object. This extends to the particle-wave duality of quantum mechanics; one mathematical analog of this duality is the Fourier transform. Questions that are difficult when formulated in one language of science may become simple when interpreted in another. The Langlands conjecture posits the existence of a correspondence between problems in arithmetic and in Representation Theory. The Langlands conjecture has only been proven for a limited number of cases, but even this has solved problems such as the famous Fermat conjecture. The aim of this project is to continue study of the "classical" aspects of the Langlands conjecture and to extend the conjecture to the quantum geometric Langlands correspondence, higher-dimensional fields, Kac-Moody groups (with D.Gaitsgory: quantum Langlands correspondence; D.Gaitsgory and E. Hrushevsi: groups over higher-dimensional fields; A. Braverman: Kac-Moody groups; R. Bezrukavnikov, S.Debacker Y.Varshavsky: classical aspects of the correspondence; A. Berenstein: geometric crystals and crystal bases). The quantum case is much more symmetric than the classical case and can lead in the limit q->0 to new insights into the classical case. The quantum case is also related to the multiple Dirichlet series. New results in the quantum case would lead to progress in understanding important Number Theoretic questions. Extending the Langlands correspondence to groups over higher-dimensional fields could substantially enlarge its applicability. Studying Kac-Moody groups would provide tools for the new important class of L-functions. This progress could lead to a proof of the existence of the analytic continuation of classical L-functions. The geometric Langlands correspondence is closely related to T-symmetry in 4-dimensional gauge theory and the understanding of this relation is important for both Mathematics and Physics. Fields of science natural sciencesphysical sciencesquantum physicsnatural sciencesmathematicspure mathematicsarithmeticsL-functions Programme(s) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Topic(s) ERC-AG-PE1 - ERC Advanced Grant - Mathematical foundations Call for proposal ERC-2009-AdG See other projects for this call Funding Scheme ERC-AG - ERC Advanced Grant Host institution THE HEBREW UNIVERSITY OF JERUSALEM EU contribution € 1 277 060,00 Address EDMOND J SAFRA CAMPUS GIVAT RAM 91904 Jerusalem Israel See on map Activity type Higher or Secondary Education Establishments Administrative Contact Hani Ben-Yehuda (Mr.) Principal investigator David Kazhdan (Prof.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data Beneficiaries (1) Sort alphabetically Sort by EU Contribution Expand all Collapse all THE HEBREW UNIVERSITY OF JERUSALEM Israel EU contribution € 1 277 060,00 Address EDMOND J SAFRA CAMPUS GIVAT RAM 91904 Jerusalem See on map Activity type Higher or Secondary Education Establishments Administrative Contact Hani Ben-Yehuda (Mr.) Principal investigator David Kazhdan (Prof.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data
