Trust in modern AI systems hinges on understanding how they learn—and, increasingly, how they can forget. This talk develops a geometric view of trustworthiness that unifies structure-aware optimization, stability analysis, and the emerging science of unlearning. I will begin by revisiting the role of sharpness and flatness in shaping both generalization and sample sensitivity, showing how the geometry of the loss landscape governs what models remember. Building on these insights, I will present recent results on Sharpness-Aware Machine Unlearning, a framework that characterizes when and how learning algorithms can provably erase the influence of specific data points while preserving accuracy on the rest. The discussion connects theoretical guarantees with empirical findings on the role of data distribution and loss geometry in machine unlearning—ultimately suggesting that the shape of the optimization landscape is the shape of trust itself. About the speaker: Rajiv Khanna is an Assistant Professor in the Department of Computer Science. His research interests span various subfields of machine learning including optimization, theory and interpretability.Previously, he held positions of Visiting Faculty Researcher at Google, postdoctoral scholar at Foundations of Data Analystics Institute at University of California, Berkeley and a Research Fellow in the Foundations of Data Science program at the Simons Institute also at UC Berkeley. He graduated with his PhD from UT Austin.