[geometry-ml:03512] Tokyo one-day workshop on stochastic analysis and geometry

[Asuka TAKATSU]

幾何学分科会メーリングリストの皆様、

慶應義塾大学の河備 浩司先生より、下記の研究集会の広報の依頼を受けましたので転送いたします。

高津飛鳥

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幾何学MLの皆様

(重複して受け取られる方もいらっしゃいますでしょうが,
ご容赦ください。)

11月23日 (金)に研究集会
「Tokyo one-day workshop on stochastic analysis and geometry」を
東京大学で開催しますので, ご案内致します。

なお講演終了後に渋谷周辺にて懇親会を予定しております。
人数を把握したいと思いますので, ご参加いただける方は
11月16日 (金) までに河備までメールでお知らせください。

皆様のご参加をお待ち致しております。

連絡先：
会田 茂樹  (東京大学大学院数理科学研究科 aida (AT) ms.u-tokyo.ac.jp )
河備 浩司  (慶應義塾大学経済学部  kawabi (AT) keio.jp )

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研究集会「Tokyo one-day workshop on stochastic analysis and geometry」

日時：2018年11月23日（金: 祝日）13:00~17:40
場所：東京大学大学院数理科学研究科126号室

                                                 プログラム

13:00~14:00  厚地 淳 (慶應義塾大学)
            Default functions and value distribution of holomorphic maps

14:10~15:10  Robert Neel (Lehigh University, USA)
            Minimal submanifolds and surfaces and associated martingales

15:30~16:30  正宗 淳 (北海道大学)
            On convergence of elliptic operators on a Riemannian manifold

16:40~17:40  会田 茂樹 (東京大学)
            Weak Poincare inequalities on path spaces: non-explosion case

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厚地氏の講演概要：
Recently default functions are playing important roles in the theory of 
mathematical finance. We consider another aspect of the functions, 
specially we consider a function theoretic aspect. We show the vanishing of 
default functions of the Dirichlet processes generated by a class of subharmonic 
functions implies Liouville type theorems. Consequently we will see some value 
distributional properties of holomorphic maps. 
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Neel氏の講演概要：
We first discuss a class of degenerate martingales (which we will call rank-n 
martingales) that arises naturally as the diffusion associated with 
minimal submanifolds and, more generally, mean curvature flow. 
This provides a unified approach to “coarse” properties, such as transience, 
of such structures, via methods which naturally generalize those used to study 
the long-time behavior of Brownian motion on Cartan-Hadamard manifolds. 
We then specialize to minimal surfaces in R^{3}, in which case the associated 
rank-2 martingale (which is just Brownian motion on the surface, viewed as 
a process in R^{3}) has the additional property that the tangent plane also 
evolves as a martingale. Taking advantage of this extra structure, we develop 
an extrinsic analogue of the mirror coupling of two Brownian motions. 
This allows us to study finer geometric and analytic properties of minimal surfaces, 
such as intersection results (strong halfspace-type theorems) and Liouville properties. 
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正宗氏の講演概要：
In this talk we study the asymptotic behavior of second-order uniformly 
elliptic operators on weighted Riemannian manifolds. We appeal to the notion of 
H-convergence introduced by Murat and Tartar. In our main result we establish 
an H-compactness result that applies to elliptic operators with measurable, 
uniformly elliptic coefficients on weighted Riemannian manifolds. 
This is a joint work with Helmer Hoppe and Stefan Neukamm. 
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会田氏の講演概要：
We prove weak Poincare inequalities on path spaces over a complete 
Riemannian manifolds. Feng-Yu Wang and his collaborators proved 
the inequality under certain assumption on the Ricci curvature which 
implies naturally non-explosion of the Brownian motion. 
We explain how to prove such an inequality under the non-explosion 
of the Brownian motion. 
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