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Department of Mathematics, National Institute of Technology, Calicut, India

Lie algebras and superalgebras are among the most important algebraic structures with ample applications in modern mathematics like geometry, harmonic analysis, algebra and representation theory, and number theory. Number Theory is one of the oldest and classical branch of mathematics. This conference aims to bring together researchers working in various areas of algebra and number theory to exchange knowledge and further possible collaborations.

Structure and representation theory of finite and infinite dimensional Lie algebras/Lie superalgebras, Number Theory (Algebraic Number Theory/ Modular Forms/ Automorphic Forms/ Diophantine Equations/ Partition Theory), Applications of Lie Theory to Number Theory

Centre International de Mathématiques Pures et Appliquées (CIMPA)

An L-function is a function defined additively by a Dirichlet series with a multiplicative Euler product. The initial work of Dirichlet was generalized to number fields by Hecke and given an adelic interpretation by Tate which paved the way to move from GL(1) to higher degree L functions associated to automorphic forms of GL(n) for a general n . Automorphic L functions are essentially analytic objects and allow translations between arithmetic and analysis. We recall the legendary correspondence in the case of the Riemann-ζ function, the prototype of higher L -functions both analytic and arithmetic-algebraic, between an arithmetic statement on the distribution of primes and an analytic one on the distribution of its zeros. Now there are many more parameters to explore. For example, bounding twisted automorphic forms in terms of conductors help obtain the asymptotics of representations of totally positive integers by ternary quadratic forms. The aim of this school is to prepare the participants to appreciate the contemporary theory of automorphic representations, their L -functions and their surprising links with diverse fields like Fourier analysis, algebraic geometry and theoretical physics.