Speaker: Zhihan Wang (Cornell)Title: Shape of Mean Curvature Flow Passing Through a Non-degenerate SingularityAbstract:A central question in geometric flow is to understand the change of geometry and topology after passing through singularities. In this talk, I will focus on mean curvature flow, the negative gradient flow of area functional, and explain how the local dynamics influence the shape of the flow near a singularity, as well as how the geometry and topology of the flow change after passing through a singularity with generic dynamics. This talk is based on the joint work with Ao Sun and Jinxin Xue.

Speaker: Thomas Hameister (Boston College)Title: Relative Duality for Hitchin SystemsAbstract: The Hitchin fibration for a reductive group G is a certain generalized abelian fibration, which admits remarkable duality properties. Namely, the "semi-classical limit" of geometric Langlands asserts that the Hitchin fibrations for G and for its Langlands dual Gv are generically dual abelian fibrations. In this talk, we will explore a relative form of this duality, in the sense of Ben-Zvi, Sakellaridis, and Venkatesh. We associate to a spherical variety or symplectic representation particular sheaves on the Hitchin moduli spaces for G and Gv which we conjecture to be Fourier-Mukai dual, generalizing a conjecture of Hitchin. We will show how this duality reduces to simple calculations in invariant theory, which are confirmed in many examples in our work and which have been proved in the strongly tempered case in the forthcoming work of Ben-Zvi, Sakellaridis, and Venkatesh. This is based on joint work with Zhilin Luo and Benedict Morrissey.

Title: TBD

Talk Title: When worlds collide: porous polymer synthesis and simulation

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