A note on the Global Langlands Conjecture Erez

Langlands Functoriality Conjecture

Functoriality conjecture is one of the central and influential subjects of the present day mathematics. Functoriality is the profound lifting problem formulated by Robert Langlands in the late 1960s in order to establish nonabelian class field theory. In this expository article, I describe the Langlands-Shahidi method, the local and global Langlands conjectures and the converse theorems which a...

Lecture Note on Local Langlands Conjecture

A note on Fouquet-Vanherpe’s question and Fulkerson conjecture

‎The excessive index of a bridgeless cubic graph $G$ is the least integer $k$‎, ‎such that $G$ can be covered by $k$ perfect matchings‎. ‎An equivalent form of Fulkerson conjecture (due to Berge) is that every bridgeless‎ ‎cubic graph has excessive index at most five‎. ‎Clearly‎, ‎Petersen graph is a cyclically 4-edge-connected snark with excessive index at least 5‎, ‎so Fouquet and Vanherpe as...

Shtukas for Reductive Groups and Langlands Correspondence for Functions Fields

This text gives an introduction to the Langlands correspondence for function fields and in particular to some recent works in this subject. We begin with a short historical account (all notions used below are recalled in the text). The Langlands correspondence [Lan70] is a conjecture of utmost importance, concerning global fields, i.e. number fields and function fields. Many excellent surveys a...

The Thurston’s program derived from the Langlands global program with singularities

The seven geometries H , S , H × R , S × R , PSL2(R ) , Nil and Sol of the Thurston’s geometrization program are proved to originate naturally from singularization morphisms and versal deformations on euclidean 3 -manifolds generated in the frame of the Langlands global program. The Poincare conjecture for a 3 -manifold appears as a particular case of this new approach of the Thurston’s program.