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Curriculum Vitae
Masato Mimura
Assistant Professor at Mathematical Institute, Tohoku University.
From 1, April, 2011 to 30, April, 2012, I was a JSPS (Japan Society for the Promotion of Sciences) PostDoctoral fellow at University of Tokyo, Graduate School of Mathematical Sciences. My postdoctoral advisor is Masahiko Kanai. In March, 2011, I finished my Ph.D. course there (my Ph.D. advisor: Taka Ozawa, currently at RIMS)
When I was at University of Tokyo, Graduate School of Mathematical Sciences, I belonged to The Geometry Group and also to The Operator Algebra Group (Here is the link to the website of Yasu Kawahigashi) at Tokyo.
I am currently taking a long stay at EPFL (Lausanne, Switzerland) (again--see below) for the period 25, Aug, 2016--24, Aug, 2018 by the JSPS Postdoctoral Fellowship for Research Abroad . The mentor is Professor Nicolas Monod.
I took a long stay at the University of Neuchatel from 17, April, 2012 to 11, September, 2012 to work with Professor Alain Valette.
I took a long stay at EPFL (Lausanne, Switzerland) for the period 15, Feb, 2010--11, Jan, 2011, with the financial support from JSPS. The purpose of that stay was an entrustment of the guidance of my study to Professor Nicolas Monod.
Research interests
Citizenship
Japanese
Education
- Bachelor of Sciences, at University of Tokyo, March 2006
- Master of Mathematical Sciences, at University of Tokyo, March 2008
- Advisor
- Associate Professor Narutaka Ozawa
- Thesis' title
- A generalization of property (T) of SL(n,R)
- Master of Mathematical Sciences, at University of Tokyo, March 2008
- Advisor
- Associate Professor Narutaka Ozawa
- Thesis' title
- A generalization of property (T) of SL(n,R)
- Ph.D. of Mathematical Sciences, at University of Tokyo, March 2011
- Advisor
- Associate Professor Narutaka Ozawa
- Thesis' title
- Rigidity theorems for universal lattices and symplectic universal lattices
(For details and links, see below.)
Academic Employment
- JSPS Research Fellowship for Young Scientists DC1 (No. 20-8313) (under supervision by Professor Narutaka Ozawa), Japan Society for the Promotion of Science, 1, Apr, 2008-30, Mar, 2011
- JSPS Research Fellowship for Young Scientists PD (No. 23-247) (under supervision by Professor Masahiko Kanai), Japan Society for the Promotion of Science, 1, Apr, 2011-30, Apr, 2012
- Assistant Professor at Tohoku University, Mathematical Institute, 1, May, 2012--present
Awards
- Award for Best Contribution, for the conference "Affine Isometric Actions of Discrete Groups", Centro Stefano Franscini Conferences 2009, ETH Zurich, July 2009
- JSPS Research Fellowship for Young Scientists DC1 (No. 20-8313), Japan Society for the
Promotion of Science, 2008-2011
- JSPS, Excellent Young Researchers Overseas Visit Program (No. 20-8313), Japan Society for the
Promotion of Science, 15, Feb, 2010--11, Jan, 2011
- Dean Prize for Ph.D. thesis, the University of Tokyo, March 2011
- JSPS Research Fellowship for Young Scientists PD (No. 23-247), Japan Society for the
Promotion of Science, 2011-2014
- JSPS Postdoctoral Fellowship for Research Abroad (No. 28-291), Japan Society for the
Promotion of Science, 25, Aug, 2016--present (by 24, Aug, 2018)
My Ph.D. Thesis
Rigidity theorems for universal lattices and symplectic universal lattices.
the Graduate School of Mathematical Sciences, the University of Tokyo, 2011, March
Abstract
Cohomological rigidity theorems (with Banach coefficients) for some matrix groups G over general rings are obtained. Main examples of these groups are (finite index subgroups of) universal lattices SL_m(Z[x1,...,xk]) for m at least 3 and symplectic universal lattices Sp_{2m}(Z[x1,...,xk]) for m at least 2 (where k is finite). The results includes the following for certain large m (for instance, for m at least 4):
- (1) The first group cohomology vanishing with any isometric Lp or p-Schatten coefficients, where p is any real on the open interval (1,infinity). This is strictly stronger than having Kazhdan's property (T).
- (2) The injectivity of the comparison map in degree 2 from bounded to ordinary cohomology, with coefficients as in item (1) not containing trivial one.
As a corollary, homomorphim rigidity (, namely, the statement that every homomorphism from G has finite image) is established with the following targets: circle diffeomorhisms with low regularity; mapping class groups of surfaces; and outer automorhisms of free groups. These results can be regarded as a generalization of some previously known rigidity theorems for higher rank lattices (Bader--Furman--Gelander--Monod; Burger--Monod; Farb--Kaimanovich--Masur; Bridson--Wade) to the case of certain general matrix group cases, which are not realizable as lattices in algebraic groups. Note that G above does not usually satisfy the Margulis finiteness property.
Finally, quasi-homomorphims are studied on special linear groups over euclidean domains. This concept has relation to item (2) above for trivial coefficient case, and to the conception of the stable commutator length. In particular, a question of M. Abert and N. Monod, which was for instance stated at ICM 2006, is answered for large degree case, and a new example of groups with the following intriguing features is provided: having infinite commutator width; but the stable commutator length vanishing.