Cohomology of Arithmetic Groups, Lattices and Number Theory: Geometric and Computational Viewpoint

ag.algebraic-geometry kt.k-theory-and-homology nt.number-theory rt.representation-theory
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The cohomology of arithmetic groups sits squarely at the intersection of several fields of mathematics. For example, it connects to number theory and arithmetic geometry via Galois representations and Hecke operators, and to representation theory, via its relationship to automorphic forms and automorphic representations. It also has deep connections with geometry, topology, and algebra, through its connections with algebraic K-theory, locally symmetric spaces, reduction theory, and lattices. Explicit calculations have played an increasingly important role in the theoretical development of the subject and its applications. For example, explicitly computing the cohomology gives tools to formulate conjectures about automorphic forms and special values of L-functions, and to try to understand the increasing influence in number theory of the torsion in cohomology. As the scale and complexity of the calculations have increased it has become more and more common for such computations to be performed with the aid of computers. This CIRM conference will bring together international experts with diverse skill sets, and expertise in computational techniques relevant to such calculations and their applications to cohomology of groups, algebraic K-theory, arithmetic geometry, and lattices. The main goals are to foster new collaborations, to introduce young researchers to these topics, and to broaden our theoretical knowledge with a view to extending the scope of computer aided calculations in this area.


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