Abstract. Depending on your mathematical clan, a Grassmannian may be either a smooth manifold, an algebraic variety, or a representable functor. What do Grassmannians mean for a matroid theorist? In this talk, we will consider Grassmannians over unusual algebraic structures. They unify many phenomena in matroid theory and tropical geometry. Even basic notion such as Grassman- nian duality suggests interesting questions that led to pleasant discoveries

Abstract. The Chinese Remainder Theorem is a well-known property of integers illustrating simultaneous approximation. In algebraic geometry, this idea extends to the property of weak approximation for varieties defined over fields. A central question asks which varieties exhibit this property. Around 1978, Vladimir Platonov proposed a conjecture about weak approximation in algebraic groups. In this talk, we will explore this conjecture, trace the major advances over the past decades, and explain how I recently settled it. Time permitting, I will touch upon some related results and future questions suggested by this result.

Abstract. The D-module structure on quantum cohomology encodes all the genus 0 curve counting on an algebraic variety. In this talk, I will discuss how quantum D-modules are related under a simple VGIT wall-crossing. I will also introduce the Reduction Conjecture, which relates the genus 0 curve counting generating series on a variety with a torus action to the series on its quotient. If time permits, using the simple VGIT wall-crossing result, I would also try to show the proof strategy for this conjecture under some smooth assumption.

Abstract. Lie theory traces back to the late 19th century, when folks (particularly its namesake, Sophus Lie) started to look into continuous symmetries. In this talk, I will give a brief overview of Lie theory, including its historical roots and different aspects. I will then discuss several directions related to my own research, including Lie superalgebras, Kac–Moody algebras, and connections with integrable systems. No prior knowledge of Lie theory or representation theory will be assumed.

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Abstract. TBA