Explore a computer science seminar that delves into the complexity theory of Constraint Satisfaction Problems (CSP) and their efficient solvability. Learn about the algebraic dichotomy theorem which establishes that polynomial time algorithms exist for CSPs when their solution spaces are closed under non-trivial local operations called polymorphisms, while other cases are NP-complete. Examine the extension of this polymorphic principle to promise CSPs - problems where relaxed constraint satisfaction is permitted, including applications like approximate graph coloring and discrepancy minimization. Discover the emerging theoretical framework for characterizing tractability of promise CSPs, the effectiveness of linear and affine relaxation algorithms, and the ongoing challenges in this field. Through this lecture from UC Berkeley's Venkatesan Guruswami, gain insights into how mathematical structure determines computational complexity and the potential for efficient algorithmic solutions.