Date : Monday, August 31, 2015 – Friday, September 4, 2015

Venue: Sakura Hall, Katahira Campus, Tohoku University

Website : http://www.nagaoka-ct.ac.jp/~tawara/ge_jp2015/

Hosted by

Mathematical Institute, Tohoku University

Supported by

Japan Society for the Promotion of Science (JSPS Kakenhi)

Tohoku Forum for Creativity

#### Event Organizers

Shigeki Aida (Tohoku University)

Hiroshi Kawabi (Okayama University)

Seiichiro Kusuoka (Tohoku University)

Kazumasa Kuwada (Tokyo Institute of Technology)

Yuichi Shiozawa (Okayama University)

Masayoshi Takeda (Tohoku University)

#### Speakers

Sebastian Andres (University of Bonn)

Martin Grothaus (TU Kaiserslautern)

Martin Hairer (University of Warwick)

Fumio Hiroshima (Kyushu University)

Walter Hoh (University of Bielefeld)

Martin Huesmann (University of Bonn)

Yuzuru Inahama (Nagoya University)

Naotaka Kajino (Kobe University)

Hiroshi Kawabi (Okayama University)

Panki Kim (Seoul National University)

Seiichiro Kusuoka (Tohoku University)

Kazumasa Kuwada (Tokyo Institute of Technology)

Kazuhiro Kuwae (Fukuoka University)

Xiangdong Li (Chinese Academy of Science)

Xue-Mei Li (University of Warwick)

Song Liang (University of Tsukuba)

Wolfgang Löhr (University of Duisburg-Essen)

Jun Masamune (Tohoku University)

Yukio Nagahata (Niigata University)

Nobuaki Naganuma (Tohoku University)

Makoto Nakashima (University of Tsukuba)

Stefan Neukamm (TU Dresden)

Max von Renesse (University of Leipzig)

Michael Röckner (University of Bielefeld)

Nikola Sandrić (TU Dresden)

Ichiro Shigekawa (Kyoto University)

Yuichi Shiozawa (Okayama University)

Karl-Theodor Sturm (University of Bonn)

Ryokichi Tanaka (Tohoku University)

Hideki Tanemura (Chiba University)

Gerald Trutnau (Seoul National University)

Masaki Wada (Tohoku University)

#### Time Schedule

- Monday, August 31, 2015
- 9:00 – 10:15
- Registration

- 10:15 – 10:50
- Michael Röckner (University of Bielefeld)
- Infinite dimensional continuity and Fokker-Planck-Kolmogorov equations

- 11:00 – 11:35
- Ichiro Shigekawa (Kyoto University)
- The logarithmic Sobolev inequality and the convergence of a semigroup in the Zygmund space

- 11:45 – 12:20
- Panki Kim (Seoul National University)
- Minimal thinness for jump processes

- 12:20 – 13:40
- Lunch break

- 13:40 – 14:15
- Jun Masamune (Tohoku University)
- Variational convergence on Riemannian manifolds

- 14:25 – 15:00
- Ryokichi Tanaka (Tohoku University)
- Random walks on hyperbolic groups: entropy and speed

- 15:10 – 15:45
- Xiangdong Li (Chinese Academy of Science)
- W-entropy formulas and rigidity theorems on Wasserstein space over Riemannian manifolds

- 16:05 – 16:40
- Kazumasa Kuwada (Tokyo Institute of Technology)
- A dimensional Wasserstein contraction characterizing the curvature-dimension condition

- 16:50 – 18:30
- Poster session

- 18:30 –
- Banquet

- Tuesday, September 1, 2015
- 10:15 – 10:50
- Kazuhiro Kuwae (Fukuoka University)
- Analytic characterization of gaugeability for generalized Feynman-Kac functionals and its applications

- 11:00 – 11:35
- Nikola Sandrić (Technical University of Dresden and University of Zagreb)
- Long-time behavior of Lévy-type processes: transience, recurrence and ergodicity

- 11:45 – 12:20
- Masaki Wada (Tohoku University)
- Large time asymptotics of Feynman-Kac functionals for symmetric α-stable processes

- 12:20 – 13:40
- Lunch break

- 13:40 – 14:15
- Yuichi Shiozawa (Okayama University)
- Escape rate of symmetric Markov processes

- 14:25 – 15:00
- Walter Hoh (University of Bielefeld)
- Markov processes with jumps and nonlocal generators

- 15:10 – 15:45
- Hideki Tanemura (Chiba University)
- Systems of infinitely many Brownian motions with long ranged interaction

- 16:05 – 16:40
- Martin Grothaus (Technical Univesity of Kaiserslautern)
- On the stochastic heat equation with sticky reflected boundary condition

- 16:50 – 17:25
- Song Liang (University of Tsukuba)
- Stochastic Newton equation with absorbing area

- Wednesday, September 2, 2015
- 9:30 – 10:05
- Naotaka Kajino (Kobe University)
- Localized upper bounds of heat kernels for diffusions via a multiple Dynkin Hunt formula

- 10:15 – 10:50
- Sebastian Andres (University of Bonn)
- Heat kernel estimates for random walks with degenerate weights

- 11:00 – 11:35
- Makoto Nakashima (University of Tsukuba)
- Phase transitions of random walk pinning model

- 11:45 – 12:20
- Stefan Neukamm (Technical University of Dresden)
- A regularity theory for elliptic systems with random coefficients

- 12:20 –
- Lunch break
- Excursion

- 18:30 –
- Conference dinner

- Thursday, September 3, 2015
- 10:15 – 10:50
- Free discussion

- 11:00 – 11:35
- Fumio Hiroshima (Kyushu University)
- Quantum field theory by Gibbs measures on cadlag path space

- 11:45 – 12:20
- Martin Huesmann (University of Bonn)
- The geometry of multi marginal Skorokhod embedding

- 12:20 – 13:40
- Lunch break

- 13:40 – 14:15
- Xue-Mei Li (University of Warwick)
- Stochastic homogenization in geometry

- 14:25 – 15:00
- Yukio Nagahata (Niigata University)
- Spectral gap for surface diffusion

- 15:10 – 15:45
- Gerald Trutnau (Seoul National University)
- Recurrence criteria for diffusion processes generated by divergence free perturbations of non-symmetric energy forms

- 16:05 – 16:40
- Hiroshi Kawabi (Okayama University)
- Functional CLTs for non-symmetric random walks on crystal lattices

- 16:50 - 17:25
- Wolfgang Löhr (University of Duisburg-Essen)
- Invariance principle for variable speed random walks on trees

- Friday, September 4, 2015
- 9:30 – 10:05
- Max von Renesse (University of Leipzig)
- Modified Arratia flow and Wasserstein diffusion

- 10:15 – 10:50
- Nobuaki Naganuma (Tohoku University)
- Error analysis for approximations to one-dimensional SDEs via perturbation method

- 11:00 – 11:35
- Yuzuru Inahama (Nagoya University)
- Large deviations for rough path lifts of Donsker-Watanabe’s delta functions

- 11:45 – 12:20
- Martin Hairer (University of Warwick)
- Modelling a random rubber band

- 12:20 – 13:40
- Lunch break

- 13:40 – 14:15
- Seiichiro Kusuoka (Tohoku University)
- Continuity and bounds of the density functions of the solutions to pathdependent stochastic differential equations

- 14:25 – 15:00
- Karl-Theodor Sturm (University of Bonn)
- Optimal transport, Brownian motion, and super-Ricci flow for metric measure spaces

#### Poster Session

**Monday, August 31, 2015 16:50 – 18:30**

- Yoshihiro Abe (Kyoto University)

**Maximum and minimum of local times for two-dimensional random walk** - Takafumi Amaba (Ritsumeikan University)

**Convergence implications via dual flow method** - Syota Esaki (Tokyo Institute Technology)

**Infinite particle systems of long range jumps with long range interactions** - Torben Fattler (Technical University of Kaiserslautern)

**Disease spreading models within the framework of two-component configuration spaces in continuum** - Julian Hollender (Technical University of Dresden)

**Unbounded viscosity solutions of non-dominated HJB-equations** - Masato Hoshino (University of Tokyo)

**KPZ equation with fractional derivatives of white noise** - Yu Ito (Osaka University)

**Integration of controlled rough paths via fractional calculus** - Yosuke Kawamoto (Kyushu University)

**Finite particle approximation of interacting Brownian motion** - Kyung-youn Kim (Seoul National University)

**Heat kernel estimates for symmetric Markov processes in C**^{1,ρ}open sets and its application - Eva Kopfer (University of Bonn)

**Minimizing movement scheme for time dependent metrics on probability space** - Franziska Kühn (Technical University of Dresden)

**Existence and estimates of moments for Lévy-type processes** - Katharina von der Lühe (University of Bielefeld)

**Pathwise uniqueness for SDEs with non-regular drift and nonconstant diffusion** - Yusuke Miura (Tohoku University)

**The conservativeness of Girsanov transformed symmetric Markov processes** - Chikara Nakamura (Kyoto University)

**Lamplighter random walks on fractals** - Izumi Okada (Tokyo Institute of Technology)

**Geometry structures of favorite sites of random walk range** - Kohei Suzuki (Kyoto University)

**Convergence of Brownian motions on RCD**^{＊}*(K,N)*spaces - Robert Voßhall (Technical University of Kaiserslautern)

**Interacting particle systems with sticky boundary** - Melchior Wirth (Friedrich Schiller University Jena)

**Diffusion determines the recurrent graph** - Lu Xu (University of Tokyo)

**Central limit theorem for stochastic heat equations in random environments**