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Last updated : February 12, 2020

## Ikkei HOTTA

Associate Professor
Department of Applied Science
Yamaguchi University
Ube 755-8611, Japan [map]

ihotta (at) yamaguchi-u.ac.jp

## Education & Experience

 B.Sc. (2004) Tokyo Metropolitan University, Japan M.Sc. (2007) Tokyo Metropolitan University, Japan Ph.D. (2010) Tohoku University, Japan

 Apr. 2010 - Sep. 2010 Research Student at Tohoku University, Japan Oct. 2010 - Dec. 2010 Lecturer at The State School of Higher Education in Chełm, Poland Jan. 2010 - Mar. 2011 Invited Lecturer at Maria Curie-Skłodowska University, Poland Apr. 2011 - Mar. 2013 DAAD Postdoctoral Fellow at University of Würzburg, Germany Apr. 2013 - Mar. 2014 Guest Researcher at University of Würzburg, Germany Apr. 2013 - Mar. 2015 JSPS Postdoctoral Fellow at Tokyo Institute of Technology, Japan Apr. 2015 - Mar. 2019 Lecturer (full-time) at Yamaguchi University, Japan Apr. 2019 - present Associate Professor at Yamaguchi University, Japan

## Research Interests (key words)

Loewner Theory
• Evolution families and semigroups of holomorphic functions
• The Loewner differential equations
• Schramm-Loewner Evolutions
• Relation to non-commutative (quantum) probability theory
Geometric Function Theory
• Quasiconformal extensions of univalent functions
• Special classes of univalent functions
Teichmüller Theory
• Universal Teichmüller spaces (Bers model)
• Schwarzian derivatives and pre-Schwarzian derivatives

## Grants

• 2013 -- 2014, Grant-in-Aid for JSPS Fellows (No.13J02250)
• 2014 -- 2016, JSPS Grant-in-Aid for Young Scientists (B) (No.26800053)
• 2017 -- 2019, JSPS Grant-in-Aid for Young Scientists (B) (No.17K14205)
• 2020 -- 2023, JSPS Grant-in-Aid for Scientific Research(C) (No.20K03632)

## Publications

Papers (refereed):
1. Explicit quasiconformal extensions and Löwner chains,
Proc. Japan Acad. Ser. A Math. Sci. 85 (2009), no. 8, 108--111.
[fulltext]
2. Ruscheweyh's univalence criterion and quasiconformal extensions,
Kodai Math. J. 33 (2010), no. 3, 446--456.
[fulltext]
3. On strongly starlike and convex functions of order $\alpha$ and type $\beta$ (with Mamoru Nunokawa),
Mathematica 53(76) (2011), no. 1, 51--56.
[fulltext, preprint]
4. Boundedness, univalence and quasiconformal extension of Robertson functions (with Li-Mei Wang),
Indian J. Pure Appl. Math., 42(4) (2011), 239--248.
[fulltext, preprint]
5. Löwner chains with complex leading coefficient,
Monatsh. Math. 163 (2011), no. 3, 315--325.
[fulltext]
6. Ahlfors's quasiconformal extension condition and $\Phi$-likeness,
Publ. Math. Debrecen 82 (2013), no. 2, 473--483.
[fulltext, preprint]
7. Locally one-to-one harmonic functions with starlike analytic part (with Andrzej Michalski),
Bull. Soc. Sci. Lett. Łódź Sér. Rech. Déform., vol. 64, no. 2 (2014), 19--27.
[fulltext, preprint]
8. Quasiconformal extendibility of integral transforms of Noshiro-Warschawski functions (with Li-Mei Wang),
Rocky Mountain J. Math. 47 (2017), no. 1, 185–204.
[fulltext, preprint]
9. Chordal Loewner chains with quasiconformal extensions (with Pavel Gumenyuk),
Math. Z. 285 (2017), no. 3-4, 1063–1089.
[fulltext, preprint]
10. Some remarks on Schur's theorem for bounded analytic functions (with Andrzej Michalski)
Bull. Soc. Sci. Lett. Łódź Sér. Rech. Déform., vol. 67, no. 2 (2018), 93-99.
[fulltext]
11. Tightness results for infinite-slit limits of the chordal Loewner equation (with Andrea Del Monaco and Sebastian Schleißinger)
Comput. Methods Funct. Theory 18 (2018), no. 1, 9–33.
[fulltext, preprint]
12. On a numerical algorithm for the solution of the radial Loewner equation (with Hirokazu Shimauchi)
Math. Methods Appl. Sci. 41 (2018), no. 2, 714–723.
[fulltext]
13. Hydrodynamic Limit of Multiple SLE (with Makoto Katori)
J. Stat. Phys. 171 (2018), no. 1, 166–188.
[fulltext, preprint]
14. Loewner theory for quasiconformal extensions: old and new,
Interdiscip. Inform. Sci. 25 (2019), no. 1, 1--21.
[fulltext]
15. Loewner chains with quasiconformal extensions: an approximation approach,
J. Anal. Math., to appear.
[preprint]
16. Univalent functions with quasiconformal extensions: Becker's class and estimates of the third coefficient (with Pavel Gumenyuk)
Proc. Amer. Math. Soc., to appear.
[preprint]
17. Limits of radial multiple SLE and a Burgers-Loewner differential equation (with Sebastian Schleißinger)
J. Theoret. Probab., to appear.
[preprint]

Preprints (submitted):
1. Problems related to conformal slit-mappings (with Sebastian Schleißinger)
[preprint]

Papers (unrefereed):
1. Löwner chains and quasiconformal extensions,
The proceedings of the Twelfth conference on real and complex analysis (2008), 47--54.
2. Quasiconformal extensions of univalent functions and Becker's theorem,
RIMS Kokyuroku 1626 (2009), 7--14.
[fulltext, preprint]
3. Normalization of Löwner chains and univalence and quasiconformal extension criteria,
The proceedings of the International Symposium on Geometric Function Theory and Applications 2010, 159--164.
4. On spirallike functions and Robertson functions,
RIMS Kokyuroku 1727 (2011), 10--15.
[fulltext, preprint]
5. Norm estimate of pre-Schwarzian derivatives of nonlinear integral transform for certain analytic functions,
The proceedings of the International Symposium on Geometric Function Theory and Applications 2011, 91--95.
[fulltext]
Notes:
1. Loewner Theory (Japanese/日本語)
A short survey for International Workshop on Conformal Dynamics and Loewner Theory
[fulltext]
2. On a theorem concerning to univalent functions linearly accessible by M. Bienacki
English Translation of "Sur un théorème concernant les fonctions univalentes linéairement accessibles de M. Bienacki" by A. Bielecki and Z. Lewandowski
[fulltext]

Talks:
2019
2018
2017
2016
• Dec. 9, 2016, Shimane Univ.;
Matsue Seminar 2016 (Japanese)
"Classical and modern Loewner Theory"
• Nov. 15, 2016, Chuo Univ.;
Seminar on Stochastic Physics and Probability Theory (Japanese)
"Recen burst of the theory of Loewner's equations and applications to stochastic physics"
• Nov. 3, 2016, Hokkaido Univ.;
Monday Analysis Seminar (Japanese)
"Recen burst of the theory of Loewner's equations and related problems"
• Jul. 9, 2016, Kyushu Institute of Technology;
Workshop on Geometry in Kitakyushu (Japanese)
"From the classical Loewner differential equations to the stochastic Loewner evolutions"
• Jun. 29, 2016, The John Paul II Catholic University of Lublin, Poland;
Seminar in Complex Analysis
"On close-to-convex harmonic functions"
• Jun. 27, 2016, The State School of Higher Education in Chełm, Poland;
XVIIIth Conference on Analytic Functions and Related Topics
"Linearly accessibility by flows associated with Loewner’s equations"
• Mar. 18, 2016, University of Stavanger, Norway;
Math. Colloquium
"Applications of the Loewner differential equations"
• Mar. 15, 2016, University of Würzburg, Germany;
Complex Analysis Seminar
"Slit maps for randomly growing domains"
• Mar. 7-11, 2016, University of Seville, Spain;
Series of seminars in Complex Analysis
"Herglotz functions for multiple growing radial slits"
• Jan. 18, 2016, Kyoto Univ.;
Second International ACCA-JP/UK Workshop
"Computational approach to Loewner theory"
2015
• Jul. 13, 2015, Yamaguchi Univ., Japan;
Mathematical Sciences Colloquium
"Loewner theory"
• Aug. 25, 2015, Kyushu Sangyo Univ., Japan;
23rd ICFIDCAA
"Geometric properties of functions whose derivative has a positive real part"
• Sep. 5, 2015, Fukushima, Japan;
50th Summer Seminar on Function Theory
"Introduction to Loewner theory"
2014
• Nov. 22-23, 2014, Tokyo Tech, Japan;
International Workshop on Conformal Dynamics and Loewner Theory
"Introduction to Loewner theory" and "$L^d$-Loewner chains with quasiconformal extensions"
• Sep. 25, 2014, Hiroshima Univ.;
MSJ Autumn Meeting 2014
"$L^d$-Loewner chains with quasiconformal extensions"
• Aug. 21, 2014, Yamaguchi Univ.;
Complex Analysis seminar
"Modern Loewner theory" and "The Loewner differential equation and the dynamics of quasiconformal maps"
• Aug. 8, 2014, Dongguk University, Korea;
22nd ICFIDCAA
"Chordal Loewner chains with quasiconformal extensions"
• Jul. 4, 2014, The John Paul II Catholic University of Lublin, Poland;
Seminar in Complex Analysis
"On $k$-quasiconformal Loewner chains"
• Jul. 2, 2014, The State School of Higher Education in Chełm, Poland;
XVIIth Conference on Analytic Functions and Related Topics
"$L^d$-Loewner chains with quasiconformal extensions"
• Jun. 26, Tokyo Tech., Japan;
Tokyo Tech. Complex Analysis Seminar
"Classical and Modern Loewner Theory"
• Jan. 30, Babeş-Bolyai University, Cluj-Napoca, Romania;
Seminar Talk in Complex Analysis
"Becker's quasiconformal extension criterion for L^d-Loewner chains"
• Jan. 11, Hosei Univ. Tokyo, Japan;
Joint Meeting on Conformal Mappings and Value Distribution Theory
"Chordal Loewner chains with quasiconformal extensions"
2013
2012
• Nov. 12, University of Würzburg, Germany;
Workshop on Riemann-Hilbert Problems, Circle Packing and Conformal Geometry
"Functions generated by families of curves"
2011
• Oct. 10, University of Würzburg, Germany;
Seminar on Function Theory
"Conformal and quasiconformal evolutions and related problems in Geometric Function Theory"
• Sep. 05, Babeş-Bolyai University, Romania;
International Symposium on Geometric Function Theory and Applications 2011
"Norm estimate of pre-Schwarzian derivatives of nonlinear integral transform for certain analytic functions"
• Feb. 15 - Mar. 10, Maria Curie-Skłodowska University, Poland;
Intensive Lecture
"Selected topics in applied complex analysis"
• Mar. 2 & 9, Maria Curie-Skłodowska University, Poland;
Seminar in Complex Analysis
"Conformal evolutions and Loewner differential equations"
2010
• Dec. 17, Maria Curie-Skłodowska University, Poland;
Open Lecture in Mathematics
"Löwner chains and quasiconformal extensions for univalent functions"
• Dec. 15, Rzeszów University of Technology, Poland;
Seminar in Complex Analysis
"Löwner chains and quasiconformal extensions for univalent functions"
• Aug. 27, Bulgarian Academy of Sciences, Sofia, Bulgaria;
International Symposium "Geometric Function Theory and Applications'2010"
"Normalization of Löwner chains and univalence and quasiconformal extension criteria"
• Jul. 14, University of Würzburg, Germany;
Seminar on Function Theory
"Loewner differential equation and quasiconformal extensions for univalent functions"
• May 21, RIMS, Kyoto Univ.;
Applications of Convolutions in Geometric Function Theory
"On spirallike functions and Robertson functions"
• Mar. 06, Keio Univ.;
Session on Function Theory, Meeting of MSJ
"Löwner chains with complex leading coefficient"
"On strongly starlike and convex functions of order α and type β" (joint work with Mamoru Nunokawa)
• Feb. 20, Akita Univ.;
Meeting of Mathematical Society of Japan, Tohoku branch
"Normalization of Löwner chains and univalence and quasiconformal extension criteria"
• Feb. 13, Naruko, Miyagi;
Workshop on the Loewner Equations and SLE
"Chordal and Radial Loewner equation I"
"Chordal and Radial Loewner equation II"
2009
• Dec. 06, Tohoku Univ.;
Joint Meeting on Conformal Mappings and Value Distribution Theory
"Ruscheweyh's univalence criterion and quasiconformal extensions"
• Sep. 26, Osaka Univ.;
Session on Function Theory, Meeting of MSJ
"Ruscheweyh's univalence criterion and quasiconformal extensions"
• May 22, Kinki Univ.;
International Short Workshop; Geometric Function Theory and Applications
"Ruscheweyh's univalence criterion and quasiconformal extensions"
2008
• Dec. 05, Tohoku Univ.;
The Twelfth Conference on Real and Complex Analysis
"Löwner chains and quasiconformal extensions"
• Sep. 24, Tokyo Inst. Tech.;
Session on Function Theory, Meeting of MSJ
"Quasiconformal extensions of univalent functions and Löwner chains"
• May 22, RIMS, Kyoto Univ.;
Study on Non-Analytic and Univalent Functions and Applications
"Quasiconformal extensions of univalent functions and Becker's theorem"