Talks and Presentations
This page showcases my academic presentations and seminars records. You will find a brief introduction for each item below. If any presentation piques your interest, please feel free to watch the related video via the provided link.
All videos are also synchronized to my social media account, so you can also view the content directly on my platform. You can visit my Bilibili homepage here: https://space.bilibili.com/366692478. I currently do not maintain separate YouTube or other platform accounts for sharing academic content. If I decide to create additional platform accounts in the future, I will update the links here accordingly. Thank you for your understanding.
Presentations
This seminar delved into the foundational concepts of representable functors and the profound Yoneda Lemma, which stands as a cornerstone of category theory. The discussion illuminated how representable functors bridge abstract categorical structures with concrete sets of morphisms, providing a powerful tool for understanding mathematical objects through their relationships. The Yoneda Lemma was explored in depth, demonstrating its remarkable implication that an object is entirely determined by its interactions with all other objects in the category, thereby offering a fundamentally relational perspective on mathematical entities.
An in-depth exploration of Galois theory, focusing on the fundamental connection between field extensions and group theory. This seminar covered the core principles of polynomial roots, field automorphisms, and the celebrated Galois correspondence, which establishes a beautiful duality between subfields and subgroups. The discussion extended to the insolvability of the quintic equation by radicals, demonstrating the power of Galois theory in resolving classical problems in algebra.