Researcher Information

Jun Masamune

Professor

From Micro to Macro

Department of Mathematics, Mathematics

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Theme

The relationships between the micro, mezzo, macro structures of spaces

FieldGlobal Analysis
KeywordLaplacian, Heat Kernel, Essential selfadjointness, Markov uniqueness, Stochastic complete, Liouville Property

Introduction of Research

The main direction of my research is investigation of the global properties of solutions to elliptic and parabolic equations in connection with the geometry "in the large" and the "singularity" of the underlying space. Here are some examples of such properties: essential selfadjointness of operators, heat kernel, Liouville properties, recurrence and non-explosion of the heat semigroup.

Self Introduction

I am from Tokyo. My research area is Global Analysis. My hobby is reading and listening to music, and I am trying to walk ahead quickly in order to keep my health.

Academic background1999 Ph.D., GSIS Tohoku University
2001 Rome University, Visiting Associate Professor
2003 London Imperial Collete, Research Fellow
2009 Penn State, Assistant Professor
2013 GSIS Tohoku University, Associate Professor
2016 Hokkaido University, Professor
Affiliated academic societyMathematical Society of Japan

Department of Mathematics, Mathematics

Jun Masamune

Professor

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What made you decide to become a researcher?

Surrounded by scientists in my childhood, it was natural for me since I was a small child to investigate something deeply. I decided to become a mathematician when I solved a problem on the Markov uniqueness of the Laplacian on a Riemannian manifold when I was a graduate course student.

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What is the research theme that you are currently focusing on?

The main direction of my research is investigation of the global properties of solutions to elliptic and parabolic equations in connection with the geometry “in the large” and the “singularity” of the underlying space. Here are some examples of such properties: stochastic characterizations of essential selfadjointness of operators, Liouville properties of manifolds with ends, recurrence and non-explosion of the heat semigroup and their generalizations.

Recently, I am also interested in the theories of homogenization and shape optimizations.

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What is your dream that you want to achieve through your research?

Frankly speaking, one of the main goals of my research is to discover the principle of the interrelationship between the structures at the different levels: Here are some examples of such phenomena: homogenization, stochastic phenomena and its average, the investigation of “infinity” through Brownian motion.

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What do you usually do when your research work gets stuck?

Just be persistent. Not like in the real life, it is a good sign that you stuck in the middle of your research.

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Please tell us about yourself; things you are good at, your favorites, hobbies, and daily routines.

I like mountains. I moved to HU just a few years ago, and I am very much looking forward to enjoy its great nature.