The purpose of this dissertation is to discuss previously known results and prove new criteria / results on affine Deligne-Lusztig varieties. Our explicit criterion on the nonemptiness pattern and dimension formula generalizes a previously known result by removing a large restriction. This new criterion has not been suggested even as a conjecture beforehand. Next, we discuss the connected components of affine Deligne-Lusztig varieties. In this question, we follow a novel approach based on the moduli space of mixed-characteristic shtukas which has not been adapted to conquer the restricted versions of the connected components problem. Finally, we study Hodge-Newton indecomposability and show an identity which gives a multiplicity-one result for special types (finite Coxeter type) of affine Deligne-Lusztig varieties.
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