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Theme for TIFR Centre For Applicable Mathematics, Bangalore

This talk will discuss the periodic unfolding operator in the Heisenberg group.  Analogous to the Euclidean unfolding operator, we prove the integral equality, $L^p$-weak compactness, unfolding gradient convergence, and other related properties. Moreover, we have the adjoint operator for the unfolding operator, which can be recognized as an average operator. We apply the unfolding operator to homogenize an optimal control problem subject to a state equation having high contrast diffusive coefficients.