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. TBA

Abstract. TBA