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Title: Analytic smoothing effect in the incompressible Navier-Stokes system
Speaker: Professor Jean-Yves Chemin (Sorbonne University)
Time: 2019-5-28, 15:00-17:00
Place: 110

 

 

Title: Closed immersions of toroidal compactifications of Shimura varieties
Speaker: Prof. Kai-Wen Lan (University of Minnesota)
Time: 2019-5-31, 10:00-11:00
Place: 110
Abstract: We shall begin with a brief review on Shimura varieties and their toroidal compactifications, and investigate the question of whether a closed immersion between Shimura varieties defined by some morphism of Shimura data extends to a closed immersion (rather than just a morphism) between their toroidal compactifications. We shall pin down some sufficient conditions on the associated cone decompositions, and explain whether they can be satisfied up to refinements. If time permits, we shall also discuss the analogous question for integral models.

 

 

Title: Duality of Drinfeld Modules and P-adic Properties of Drinfeld Modular Forms
Speaker: Shin Hattori (Tokyo City University)
Time: 2019-6-5, 16:30-17:30
Place: 110 (Video)
Abstract: Let p be a rational prime, q>1 a p-power and P a non-constant irreducible polynomial in F_q[t]. The notion of Drinfeld modular form is an analogue over F_q(t) of that of elliptic modular form. Numerical computations suggest that Drinfeld modular forms enjoy some P-adic structures comparable to the elliptic analogue, while at present their P-adic properties are less well understood than the p-adic elliptic case. In 1990s, Taguchi established duality theories for Drinfeld modules and also for a certain class of finite flat group schemes called finite v-modules. Using the duality for the latter, we can define a function field analogue of the Hodge-Tate map. In this talk, I will explain how the Taguchi's theory and our Hodge-Tate map yield results on Drinfeld modular forms which are classical to elliptic modular forms e.g. P-adic congruences of Fourier coefficients imply p-adic congruences of weights.

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