Automorphic Forms and Applications

Introduction Armand Borel, Automorphic Forms on Reductive Groups: Automorphic forms on reductive groups Bibliography L. Clozel, Spectral Theory of Automorphic Forms: Spectral theory of automorphic forms Mostly SL(2) The spectral decomposition of $L^2(G(\mathbb{Q})\backslash G(\mathbb{A}))$: Arthur's conjectures Known bounds for the cuspidal spectrum and the Burger-Sarnak method Applications: Control of the spectrum All reductive adelic groups are tame Bibliography James W. Cogdell, $L$-functions and Converse Theorems for $GL_n$: $L$-functions and converse theorems for $GL_n$ Fourier expansions and multiplicity one Eulerian integrals for $GL_n$ Local $L$-functions Global $L$-functions Converse theorems Converse theorems and functoriality Bibliography Philippe Michel, Analytic Number Theory and Families of Automorphic $L$-functions: Analytic number theory and families of automorphic $L$-functions Analytic properties of individual $L$-functions A review of classical automorphic forms Large sieve inequalities The subconvexity problem Some applications of subconvexity Bibliography Freydoon Shahidi, Langlands-Shahidi Method: Langlands-Shahidi Method Basic concepts Eisenstein series and $L$-functions Functional equations and multiplicativity Holomorphy and boundedness; Applications Bibliography Audrey Terras, Arithmetical Quantum Chaos: Arithmetical quantum chaos Finite models Three symmetric spaces Bibliography David A. Vogan, Jr., Isolated Unitary Representations: Isolated unitary representations Bibliography Wen-Ching Winnie Li, Ramanujan Graphs and Ramanujan Hypergraphs: Ramanujan graphs and Ramanujan hypergraphs Ramanujan graphs and connections with number theory Ramanujan hypergraphs Bibliography.