Akira Sakai

My major research field is mathematical physics (probability and statistical mechanics). The topics I have been most fascinated with are phase transitions and critical phenomena, as well as associated scaling limits. For example, the Ising model, a statistical-mechanical model of ferromagnetism, is known to take on positive spontaneous magnetization as soon as the temperature of the system is turned down below the critical point. Various other observables also exhibit singular behavior around the critical point, due to cooperation of infinitely many interacting variables. To fully understand such phenomena, it would require development of a theory beyond the standard probability theory. This is a challenging and intriguing problem, towards which I would love to make even a tiny contribution.

The mathematical models I have been studying are

· the Ising model,

· the φ⁴ model (in lattice scalar-field theory),

· self-avoiding walk (a model for linear polymers),

· percolation (for random media),

· the contact process (for the spread of an infectious disease),

· random walk with reinforcement.

II. Research papers

1. A. Sakai. Hyperscaling for oriented percolation in 1+1 space-time dimensions. Preprint. arXiv:1709.08291.

2. S. Handa, M. Heydenreich and A. Sakai. Mean-field bound on the 1-arm exponent for Ising ferromagnets in high dimensions. Preprint. arXiv:1612.08809.

3. T. Arae, S. Isai, A. Sakai, K. Mineta, M. Yokota-Hirai, Y. Suzuki, S. Kanaya, J. Yamaguchi, S. Naito and Y. Chiba. Coordinated regulations of mRNA synthesis and decay during cold acclimation in arabidopsis cells. Plant Cell Physiol. 58 (2017): 1090–1102.

4. Y. Chino and A. Sakai. The quenched critical point for self-avoiding walk on random conductors. J. Stat. Phys. 163 (2016): 754–764. arXiv:1508.01262.

5. A. Sakai. Application of the lace expansion to the φ⁴ model. Commun. Math. Phys. 336 (2015): 619–648. The published version incorporates a few corrections to arXiv:1403.5714.

6. L.-C. Chen and A. Sakai. Critical two-point functions for long-range statistical-mechanical models in high dimensions. Ann. Probab. 43 (2015): 639–681. arXiv:1204.1180.

7. L.-C. Chen and A. Sakai. Asymptotic behavior of the gyration radius for long-range self-avoiding walk and long-range oriented percolation. Ann. Probab. 39 (2011): 507–548. arXiv:1002.0875.

8. A. Sakai. Large-time asymptotics of the gyration radius for long-range statistical-mechanical models. RIMS Kokyuroku Bessatsu B21 (2011): 53–62. arXiv:0912.5117.

9. R. van der Hofstad and A. Sakai. Convergence of the critical finite-range contact process to super-Brownian motion above the upper critical dimension: The higher-point functions. Electron. J. Probab. 15 (2010): 801–894. arXiv:0809.1712.

10. L.-C. Chen and A. Sakai. Critical behavior and the limit distribution for long-range oriented percolation. II: Spatial correlation. Probab. Theory Related Fields 145 (2009): 435–458. arXiv:0804.2039.

11. A. Sakai. Applications of the lace expansion to statistical-mechanical models. A chapter in Analysis and Stochastics of Growth Processes and Interface Models (P. Mörters et al. eds., Oxford University Press, 2008).

12. M. Heydenreich, R. van der Hofstad and A. Sakai. Mean-field behavior for long- and finite range Ising model, percolation and self-avoiding walk. J. Stat. Phys. 132 (2008): 1001–1049. arXiv:0712.0312.

13. L.-C. Chen and A. Sakai. Critical behavior and the limit distribution for long-range oriented percolation. I. Probab. Theory Related Fields 142 (2008): 151–188. arXiv:0703455.

14. A. Sakai. Diagrammatic bounds on the lace-expansion coefficients for oriented percolation. arXiv:0708.2897.

15. M. Holmes and A. Sakai. Senile reinforced random walks. Stoch. Proc. Appl. 117 (2007): 1519–1539.

16. A. Sakai. Lace expansion for the Ising model. Commun. Math. Phys. 272 (2007): 283–344. arXiv:math-ph/0510093.

17. R. van der Hofstad and A. Sakai. Critical points for spread-out self-avoiding walk, percolation and the contact process above the upper critical dimensions. Probab. Theory Related Fields 132 (2005): 438–470. arXiv:math/0402050.

18. A. Sakai. Mean-field behavior for the survival probability and the percolation point-to-surface connectivity. J. Stat. Phys. 117 (2004): 111–130.

19. R. van der Hofstad and A. Sakai. Gaussian scaling for the critical spread-out contact process above the upper critical dimension. Electron. J. Probab. 9 (2004): 710–769. arXiv:math/0402049.

20. M. Holmes, A.A. Járai, A. Sakai and G. Slade. High-dimensional graphical networks of self-avoiding walks. Canad. J. Math. 56 (2004): 77–114.

21. A. Sakai. Hyperscaling inequalities for the contact process and oriented percolation. J. Stat. Phys. 106 (2002): 201–211.

22. A. Sakai. Mean-field critical behavior for the contact process. J. Stat. Phys. 104 (2001): 111–143.

III. Recent public talks

Year 2017

1. Hyperscaling for oriented percolation in 1+1 space-time dimensions.

· NTU Math Colloquium (November 27). National Taiwan University, Taiwan.

2. 強磁性イジング模型の相転移・臨界現象に関する研究の最近の動向（Recent progress in researches on phase transitions and critical behavior for Ising ferromagnets).

· MSJ Fall Meeting (September 11–14). Yamagata University, Japan.

3. 有向パーコレーションの臨界現象：厳密な立場より（Critical behavior for oriented percolation: From a mathematically rigorous standpoint).

· Summer School in Mathematical Physics (August 25–27). The University of Tokyo, Japan.

4. The lace expansion for self-avoiding walk and percolation on the BCC lattice.

· Seminar on Probability (July 18). Osaka University, Japan.

5. Mean-field bound on the 1-arm exponent for high-dimensional Ising ferromagnets.

· Physical and Mathematical Approaches to Interacting Particle Systems – In Honer of 70^th Birthday of Herbert Spohn (January 11–12). Tokyo Institute of Technology, Japan.

Year 2016

1. Mean-field bound on the 1-arm exponent for Ising ferromagnets in high dimensions.

· 3^rd Workshop on Probability Theory and its Applications (December 13–16). Korea Institute for Advanced Study, South Korea.

· 2016 TMS Annual Meeting (December 11–12). National Dong Hwa University, Taiwan.

· 15^th Stochastic Analysis on Large Scale Interacting Systems (November 2–4). The University of Tokyo, Japan.

· International Conference on Probability Theory and Statistical Physics (March 25–27). NYU Shanghai, China.

· 2016 Spring Probability Workshop (March 7–9). Academia Sinica, Taiwan.

2. The lace expansion for the nearest-neighbor models on the BCC lattice.

· MSJ Fall Meeting (September 15–18). Kansai University, Japan.

· The BIRS Workshop “Random Structures in High Dimensions” (June 26–July 1). Casa Matemática Oaxaca, Mexico.

3. Rigorous analysis of critical behavior for statistical-mechanical models of polymers.

· Hokkaido Young Polymer Scientists Workshop (September 2–3). Jozankei View Hotel, Japan.

4. Random walk and its dimensional dependence.

· Science Globe for New Students (June 15). Hokkaido University, Japan.

5. Self-avoiding walk on random conductors.

· The IMI Workshop “Mathematical Quantum Field Theory and Related Topics” (June 6–8). Kyushu University, Japan.

· NCU Probability Seminar (March 11). National Central University, Taiwan.

· NZ Probability Workshop 2016 (January 3–9). Scenic Hotel Bay of Islands, New Zealand.

Previous years

IV. Workshops

1. The 1-day workshop “Recent Progress in Probability Theory and Its Applications” (July 28, 2017). Hokkaido University, Japan.

2. 2017 Spring Probability Workshop (March 6–8, 2017). Academia Sinica, Taiwan.

3. The 2^nd workshop on Universality and Scaling Limits in Probability and Statistical Mechanics (August 5–9, 2013). Hokkaido University, Japan.

4. International Workshop on Potential Theory (February 4, 2013). Hokkaido University, Japan.

5. The RIMS workshop “Applications of Renormalization Group Methods in Mathematical Sciences” (September 12–14, 2011). Kyoto University, Japan.

6. The SPA Satellite workshop “Universality and Scaling Limits in Probability and Statistical Mechanics” (August 30–September 3, 2010). Hokkaido University, Japan.

V. Teaching (April 2017 – February 2018)

2^nd Semester	Monday	Tuesday	Wednesday	Thursday	Friday
8:45 – 10:15	N.A.	N.A.	N.A.	N.A.	N.A.
10:30 – 12:00	Mitobe	N.A.	Handa	N.A.	Calculus (P)
12:00 – 13:00	Lunch	Lunch	Lunch	Lunch	Lunch
13:00 – 14:30	Makita, Mukohara	N.A.	N.A.	N.A.	Calculus (P)
14:45 – 16:15	Mizushiri	N.A.	N.A.	F.S. (P)	Calculus (L)
16:30 – 18:00	N.A.	N.A.	Kamijima	F.S. (L)	Calculus (M)
18:15 – 19:45	N.A.	O.H.	Kamakura, Asano	N.A.	N.A.

(Lectures-Preparation-Marking; Office Hour; Seminars; Not Available )

1. Linear Algebra I (1^st Semester, Mondays 10:30–12:00 @ Multimedia Education Bldg E-301).

2. Basic Mathematical Science (1^st Semester, Fridays 10:30–12:00 @ Science Bldg 5-301).

3. Calculus I (1^st Semester, Fridays 14:45–16:15 @ Multimedia Education Bldg E-311).

4. Freshman Seminar (2^nd Semester, Thursdays 16:30–18:00 @ Multimedia Education Bldg E-305).

5. Calculus II (2^nd Semester, Fridays 14:45–16:15 @ Multimedia Education Bldg N-281).

6. Statistics (2^nd Semester, November 6–9 @ Science Bldg 3-204, November 10 @ Science Bldg 3-205).

7. Seminar on Mathematics (Mondays and Wednesdays @ Science Bldg 4-509).

· B2 Seminar (Makita, Mukohara) on Mathematics in Phase Transitions and Critical Phenomena.

· B3 Seminar (Kamakura, Asano) on Random Walks and Stochastic Calculus.

· B4 Seminar (Mizushiri) on Percolation.

· M2 Seminar (Mitobe) on The Multivariate Black-Scholes Model.

· D1 Seminar (Kamijima) on Random Loop Representations for Quantum Spin Systems.

· D2 Seminar (Handa) on The Ising 1-spin expectation at and below the critical temperature.

VI. Curriculum vitae

· September 2015 – August 2019

Councilor of the Bernoulli Society.

· March 2016

Selected as one of Excellent Teachers 2015.

· March 2014

The Hokkaido University President’s Award for Teaching Excellence 2013.

· March 2013

The Hokkaido University President’s Award for Teaching Excellence 2012.

· March 2012

Selected as one of Excellent Teachers 2011.

· April 2011 – present

Associate professor of the Department of Mathematics, Hokkaido University, Japan.

· March 2008 – March 2011

Tenure-track assistant professor of Creative Research Institution SOUSEI, Hokkaido University, Japan.

· April 2006 – February 2008

Lecturer in Probability of the Department of Mathematical Sciences, the University of Bath, UK.

· April 2004 – March 2006

Postdoctoral researcher of Wiskunde en Informatica, Technische Universiteit Eindhoven (TU/e), the Netherlands.

· January 2003 – March 2004

Postdoctoral researcher of the Interacting-Stochastic-Systems (ISS) group, EURANDOM, the Netherlands.

· January 2001 – December 2002

Postdoctoral researcher of the Department of Mathematics, the University of British Columbia, Canada.

· April 1996 – December 2000

Ph.D. study in Applied Physics, Tokyo Institute of Technology, Japan.

Awarded Ph.D. for the thesis “Analyses of the Critical Behavior for the Contact Process based on a Percolation Structure” supervised by Professor Takashi Hara.

· April 1994 – March 1996

Master study in Applied Physics, Tokyo Institute of Technology, Japan.

Awarded M.Sc. for the thesis “Approach to Fractal Growth Phenomena” supervised by Professor Takashi Hara.

· April 1990 – March 1994

Undergraduate study in Applied Physics, Tokyo Institute of Technology, Japan.

Awarded B.Sc. for the thesis “Recurrent in the Plane, Transient in Space” supervised by Professor Kohei Uchiyama.