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The University of Colorado Center for Number Theory has interests spanning number theory, from analytic to algebraic.  There is a focus on arithmetic geometry, including arithmetic dynamics, elliptic curves and higher genus curves.  Another theme is cryptography and coding theory, including elliptic curve cryptography and lattice-based cryptography.  On the analytic side, there is a focus on automorphic forms, analytic number theory and harmonic analysis.  The group also has a long tradition in Diophantine approximation.