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Explore the fascinating intersection of polymer topology and electrostatic interactions in this 34-minute conference lecture from the Workshop on "Charged Soft Matter: Bridging Theory and Experiment." Delve into the unique rheological properties of ring polymer solutions that arise from their circular topology and distinctive self-organization patterns. Examine the physics of short minirings where persistence length becomes comparable to contour size, and discover how electric charge distribution along polymer backbones influences their behavior. Learn about recent research findings on semiflexible ring-shaped polyelectrolytes that form cluster glasses in concentrated solutions, where rheological properties can be precisely controlled through counterion concentration and valency - with multivalent counterions acting as stiffening agents while monovalent counterions promote melting. Investigate the behavior of ribbon-shaped rings and understand how pH variations enable local tuning of the twist/writhe balance along polymer backbones, leading to charge-regulated coexistence between writhe-rich and twist-rich domains. Gain insights into cutting-edge research on topology-controlled microphase separation and the interconversion of twist and writhe domains in supercoiled annealed polyelectrolytes, supported by recent publications in ACS Nano and Physical Review Letters.