Assistant Professor. Department of Applied Mathematics, National Yang Ming Chiao Tung University, Hsinchu, Taiwan. August 2019 - now.
Postdoctoral fellow, Department of Mathematics and Statistics, University of Jyväskylä, Finland. September 2018 - July 2019, working with Professor Mikko Salo.
※ From August 2016 to August 2018 (2-years), I was working with Professor Gunther Uhlmann.
Postdoctoral fellow, Institute for Advanced Study (IAS), Jockey Club, HKUST, Hong Kong. January 2018 - August 2018.
Postdoctoral fellow, Department of Mathematics, University of Washington, Seattle, United States. March 2017 - December 2017.
Postdoctoral fellow, Institute for Advanced Study (IAS), Jockey Club, HKUST, Hong Kong. August 2016 - February 2017.
Ph.D. in Mathematics, Department of Mathematics, National Taiwan University, Taiwan. September 2012 - June 2016.
M.Sc. in Mathematics, Department of Mathematics, National Taiwan University, Taiwan. September 2008 - June 2010.
B.Sc. in Mathematics, Department of Mathematics, National Taiwan Normal University, Taiwan. September 2004 - June 2008.
Honor and Awards
EAIP Young Scientist Award. Awarded by Eurasian Association on Inverse Problems, 2024.
Humboldt Research Fellowship for Experienced Researchers (德國洪堡基金會資深學者). Awarded by Alexander von Humboldt Foundation, Germany. 2024-2027.
Outstanding Young Scholar Research Award (國立陽明交通大學理學院年輕學者研究獎). Awarded by National Yang Ming Chiao Tung University (NYCU), Taiwan. 2023.
NSTC Young Scholar Fellowship: The Columbus Program (哥倫布計畫2020-2022) and 2030 Cross-Generation Young Scholar Program (國科會2030跨世代年輕學者方案-國際年輕傑出學者2022-2025). Awarded by the National Science and Technology Council (NSTC), Taiwan. 2020-2025.
Travel Award of Simons Foundation: Attend Math+X symposium, Rice University, Texas. Awarded by Simons Foundation Grant, USA. January 23-31, 2019.
Keynote Speaker, 9th International Conference on Inverse Problems and Related Topics, National University of Singapore, Singapore. 2018.
Outstanding Ph.D Thesis Golden Award (台灣數學會傑出博士論文金牌獎). Awarded by Taiwanese Mathematical Society (TMS), Taiwan. 2016.
Research Grants
National Science and Technology Council (2030-NSTC國際年輕傑出學者研究計畫), 113-2628-M-A49-003. February 1, 2024- January 31, 2025 (5/5).
National Science and Technology Council (2030-NSTC國際年輕傑出學者研究計畫), 112-2628-M-A49-003. February 1, 2023 - January 31, 2024 (4/5).
National Science and Technology Council (2030-NSTC國際年輕傑出學者研究計畫), 111-2628-M-A49-002. February 1, 2022 - January 31, 2023 (3/5).
Ministry of Science and Technology Taiwan (MOST哥倫布計畫), MOST 110-2636-M-009-007. February 1, 2021 - January 31, 2022 (2/5).
Ministry of Science and Technology Taiwan (MOST哥倫布計畫), MOST 109-2636-M-009-006. February 1, 2020 - January 31, 2021 (1/5).
PhD Students
Yu-Wei Chen (陳佑威). Graudate on January 2024 (coadvisor with Prof. Daniel Eli Spector)
Pin-Chieh Tseng (曾品傑), current (coadvior with Prof. Ching-Yi Lai)
Conference Invited Talks
Minisympisium on Inverse Problems for Fractional Equations, the 11th international conference Inverse Problems: Modeling and Simulation (IPMS 2024), Malta, May 24-June 1, 2024.
Invited Speaker at One-Day Workshop on Inverse Problems, National Taiwan University, Taiwan, May 10, 2024.
Invited Speaker at 7th East Asia Section of Inverse Problems International Association, Young Scholar Symposium. HKUST, Hong Kong, December 9 – 10, 2023.
Minisymposium on Recent Advances in Inverse Problems for Elliptic and Hyperbolic Equations, Applied Inverse Problems Conference (AIP 2023), Göttingen, Germany, September 4-8, 2023.
Minisymposium on Inverse Problems for Nonlinear Equations, Applied Inverse Problems Conference (AIP 2023), Göttingen, Germany, September 4-8, 2023.
Minisymposium on Recent Advances in Inverse Problems, Hong Kong SIAM Biennial Meeting, Hong Kong, August 28-September 1, 2023.
Minisymposium on Inverse Problems for Anomalous Diffusion, International Congress on Industrial and Applied Mathematics (ICIAM 2023), Waseda University, Tokyo, Japan. August 20-25, 2023.
Minisymposium on Inverse Theoretical and Computational Progress on PDE-based Inverse Problems with Applications, International Congress on Industrial and Applied Mathematics (ICIAM 2023), Waseda University, Tokyo, Japan. August 20-25, 2023.
Inverse Problems Session, 34th International Workshop on Operator Theory and its Applications (IWOTA 2023), Helsinki, Finland, July 31–August 4, 2023.
Invited Speaker at 6th East Asia Section of Inverse Problems International Association, Young Scholar Symposium, The Chinese University of Hong Kong, Hong Kong, March 25-26, 2023.
Invited Speaker at Inverse Problems in the Desert, New York University Abu Dhabi, Abu Dhabi (UAE), December 19-22, 2022.
Invited Speaker at The 1st East and Southeast Asia Workshop on Inverse Problems and Optimal Control (ESEAW: IPOC), August 1st-5th, 2022.
Minisympisium on Inverse Problems for time-fractional PDEs, the 10th international conference Inverse Problems: Modeling and Simulation (IPMS 2022), Malta, May 22-28, 2022.
Invited Speaker at Workshop on PDEs and Analysis, Fu Jen Catholic University, Taipei, Taiwan, May 6, 2022.
Invited Speaker at Workshop on PDEs and Geometry, National University of Tainan, Tainan, Taiwan, April 9-10, 2022.
Invited Speaker at 2022 Japan-Taiwan Joint Online Workshop on Numerical Analysis and Inverse Problems, Kyoto University, Kyoto, Japan, March 25, 2022.
Minisymposium on Recent Advances in Inverse Problems and Mathematical Imaging, SIAM Conference on Image Sciences, Berlin, Germany, March 22-25, 2022.
Minisymposium on Monotonicity methods for shape reconstruction, Conference on Mathematics of Wave Phenomena, Karlsruhe, Germany, Febrary 14-18, 2022.
Invited Speaker at Young Dynamics Day, National Taiwan Normal University, Taipei, Taiwan, February 18, 2022.
Invited Speaker at 30th Annual Workshop on Differential Equations, National Chengchi University, Taipei, Taiwan, January 14-15, 2022.
Invited Speaker at online workshop Theory and Practice in Inverse Problems, Research Institute of Mathematical Sciences (RIMS), Kyoto University, Japan, January 5-7, 2022.
Invited Speaker at online workshop 2021 Minjiang Workshop on Applied and Computational Mathematics, Minjiang University, China, December 25-26, 2021.
Invited Speaker at Taiwan-Japan Joint Online Workshop on Inverse Problems, University of Kyoto, Kyoto, Japan, March 12, 2021.
Minisymposium on Advances in Image Reconstruction Algorithms for Tomographic Problems, SIAM Conference on Image Sciences, Toronto, Canada, July 6-9, 2020.
Invited Speaker at 28th Annual Workshop on Differential Equations, Academia Sinica, Taipei, Taiwan, December 26-29, 2019.
Invited Speaker at PDE session, Annual meeting of Taiwan Mathematical Society, National Chung Hsing University, Taichung, Taiwan, December 7-8, 2019.
Plenary Speaker, Workshop for Young Scholars, Control and Inverse Problems on waves, oscillations and flows. Tokyo University of Science, Tokyo, Japan. August 26-27, 2019.
Minisymposium on Inverse Problems in Shape and Geometry, International Congress on Industrial and Applied Mathematics (ICIAM 2019), Valencia, Spain, July 15-19, 2019.
Minisymposium on Geometric structures in wave scattering and applications in inverse problems and material sciences, Applied Inverse Problems Conference (AIP 2019), Grenoble, France, July 8-12, 2019.
Math+X Symposium on Inverse Problems and Deep Learning in Space Exploration, Rice University, USA. January 23-25, 2019.
24th Inverse Days, Aalto University, Helsinki, Finland. Dec 11-13, 2018.
Inverse Problems, PDE and Geometry, University of Jyväskylä, Finland, August 20-23, 2018.
Keynote Speaker, the 9th International Conference on Inverse Problems and Related Topics (ICIP 2018), National University of Singapore, Singapore, August 13-17, 2018.
Minisymposium on Recent Advances in Inverse Scattering and Cloaking, the 9th International Conference on Inverse Problems and Related Topics (ICIP 2018), National University of Singapore, Singapore, August 13-17, 2018.
Minisymposium on Recent developments in inverse boundary value problems and applications (dedicated to 70th anniversary of an outstanding expert in inverse problems Professor Gen Nakamura), the 9th international conference Inverse Problems: Modeling and Simulation (IPMS 2018), Malta, May 21-26, 2018.
Invited Speaker at 3rd Young Scholars East Asia Symposium of Inverse Problems International Association (IPIA 2018), Hong Kong Baptist University, Hong Kong, March 17-18, 2018.
Minisymposium on Inverse Problems and Related Questions, 26th Annual on Differential Equations and Related Topics, National Taiwan University, Taipei, Taiwan, Jan 6-7, 2018.
Minisymposia on Inclusion Detection Methods in Inverse Problems and Visibility and Invisibility for Wave Scatters (2 minisymposia), Applied Inverse Problems (AIP 2017), Zhejiang University, Hangzhou, China, May 29-June 2, 2017
Invited Speaker at Analysis and PDE workshop for 70 years anniversary of the Department of Mathematics, National Taiwan University, Taipei, Taiwan, Jan 14-15, 2017.
Minisymposium on Inverse Problems for Systems of Equations, the 8th International Conference on Inverse Problems and Related Topics (ICIP 2016), Ewha Womens University, Seoul, Korea, June 27-July 1, 2016.
Minisymposium on Inverse Problems, 4th TWSIAM annual meeting, National Chung Hsing University, Taiwan, 2016.
Invited Speaker at 1st Young Scholars East Asia Symposium of Inverse Problems International Association (IPIA 2016), South University of Technology, Shengzhen, China, Feb 29-Mar 1, 2016.
Invited Speaker at East Asia Core Doctoral Forum on Mathematics 2016, Fudan University, Shanghai, China, Jan 9-12, 2016.
Invited Speaker at 2015 Taiwan-Japan Joint Workshop on Inverse Problems and Related Topics, National Taiwan University, Taipei, Taiwan, Nov 21-23, 2015.
Minisymposium on Reconstruction Methods for Inverse Problems, Applied Inverse Problems (AIP 2015), Helsinki University, Finland, May 25-29, 2015.
Invited Speaker at The 6th Taiwan-Japan Joint Workshop for Young Scholars in Applied Mathematics, Meiji University, Tokyo, Japan, Feb 27-28, 2015.
Invited Speaker at East Asian Core Doctoral Forum on Mathematics 2015, National Taiwan University, Taiwan, Jan 19-22, 2015.
Minisymposium on Inverse Problems for Elliptic Systems, the 7th International Conference on Inverse Problems and Related Topics (ICIP 2014), National Taiwan University, Taiwan, Dec 15-19, 2014
Invited Talks
Colloquium, Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan. March 16, 2024.
Scientific Computing Seminar, Department of Mathematics, National University of Singapore, Singapore. October 16, 2023.
Numerical and Applied Analysis Seminar, Graduate School of Informatics, Department of Advanced Mathematical Sciences, Kyoto University, Kyoto, Japan. March 2, 2023.
Seminar Talk, Johann Radon Institute for Computational and Applied Mathematics (RICAM), Linz, Austria. February 7, 2023.
Lecture, Graduate School of Mathematical Sciences, The University of Tokyo, Tokyo, Japan. January 12, 2023.
Colloquium, Department of Mathematics, Tamkang University, Taipei, Taiwan. November 1, 2022.
Colloquium, Department of Mathematics, National Cheng Kung University, Tainan, Taiwan. October 27, 2022.
Analysis Seminar, Institute of Mathematics, Academia Sinica, Taipei, Taiwan. March 24, 2022.
International Zoom Inverse Problems Seminar, University of California, Irvine, USA. December 2, 2021.
Colloquium, Department of Applied Mathematics, National Chengchi University, Taipei, Taiwan. May 3, 2021.
Nonlinear Analysis Seminar Series. Okinawa Institute of Science and Technology (OIST), Okinawa, Japan. March 11, 2021.
Colloquium, Department of Applied Mathematics, National University of Kaohsiung, Kaohsiung, Taiwan. December 9, 2020.
Colloquium, Institute of Computational and Modeling Science, National Tsing Hua University, Hsinchu, Taiwan. November 3, 2020.
Colloquium, Department of Mathematics, National Cheng Kung University, Tainan, Taiwan. October 29, 2020.
Online Seminar, NCTS Math Division, May 6, 2020.
Colloquium, Department of Mathematics, National Cheng Kung University, Tainan, Taiwan. November 28, 2019.
Colloquium, Department of Mathematics, National Chung Cheng University, Chiayi, Taiwan. October 28, 2019.
Colloquium, Department of Applied Mathematics, National University of Kaohuiung, Kaohuiung, Taiwan. September 25, 2019.
Arbeitsgemeinschaft Angewandte Analysis Seminar, MPI for Math, Leipzig, Germany. June 28, 2019.
Colloquium, Department of Mathematics, Hong Kong Baptist University, Hong Kong. June 5, 2019.
Applied Math Seminar, School of Mathematics, University of Minnesota, Minneapolis, USA. May 6 2019.
Seminar Talk, Johann Radon Institute for Computational and Applied Mathematics (RICAM), Linz, Austria. April 25, 2019.
NCTS PDE & Analysis Seminar, National Center for Theoretical Sciences Mathematics Division, Tapei, Taiwan. December 26, 2018.
Inverse Problem Seminar, Department of Mathematics, University of Helsinki, Finland. December 3, 2018.
Analysis Seminar, Department of Mathematics and Statistics, University of Jyväskylä, Finland. Nov 28, 2018.
Computational & Applied Mathematics (CAM) seminar, Yau Mathematical Sciences Center, Tsinghua University, Beijing, China. June 20, 2018.
Colloquium, Department of Applied Mathematics, National Sun Yat-sen University, Kaohuiung, Taiwan. April 11, 2018.
Colloquium, Department of Mathematics, National Central University, Taoyuan, Taiwan. January 11, 2018.
Colloquium, Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan. January 08, 2018.
IAS program on Inverse Problems, IAS, HKUST, Hong Kong. October 11, 2017.
PDE seminar, School of Mathematics, University of Minnesota, Minneapolis, USA. Sept 27, 2017.
Inverse problem seminar, Department of Mathematics, Colorado State University, Fort Collins, USA. Sept 21, 2017.
The Hong Kong Mathematical Society Annual General Meeting 2017, HKUST, Hong Kong. May 20, 2017.
Postdoc Seminar, Institute for Mathematics and its Applications (IMA), University of Minnesota, Minneapolis, USA. March 21, 2017.
Applied Mathematics Talk, Department of Mathematics, Hong Kong University of Science and Technology (HKUST), Hong Kong. Nov 28, 2016.
PDE semniar, Department of Mathematics, National Cheng Kung University, Tainan,Taiwan. Oct 31, 2016.
Postdoc and student seminar, Department of Mathematics, National Central University, Taoyuan, Taiwan. July 28, 2015.
Sub-Department of Applied Analysis, Graduate School of Informatics, Kyoto University, Kyoto, Japan. July 9, 2015.
Postdoc and student seminar, Department of Mathematics, National Central University, Taoyuan, Taiwan. June 30, 2015.
RCTS analysis seminar, Department of Mathematics, National Cheng Kung University, Tainan, Taiwan. May 07, 2015.
Institute of Mathematics, Academic Sinica, Taipei, Taiwan. April 20, 2015.
Conferences/Workshop Organization
Co-organizer (with Prof. Daisuke Kawagoe) of "Some approaches on ill-posed problems -theory and practice-", Research Institute for
Mathematical Sciences (RIMS), Kyoto University, Kyoto, Japan. January 10-12, 2024.
Co-organizer (with Dr. Jesse Railo and Prof. Mikko Salo) of Minisymposium: Inverse Problems for Fractional and Nonlocal Equations, AIP 2023, Gottigen, Germany. September 4-8, 2023.
Co-organizer of 10th TWSIAM annal meeting, National Yang Ming Chiao Tung University, July 23-24, 2022.
Co-organizer (with Prof. Mikko Salo) of Minisymposium: Inverse Problems of Fractional and Nonlocal Equations, AIP 2019, Grenoble, France, July 8-12, 2019.
Co-organizer of the 5th East Asia IPIA Young Scholar Symposium. Chinese Academy of Sciences, Beijing, China, June 7-8, 2019.
Research Visits
Department of Mathematics, National University of Singapore, Singapore, October 16 - 20, 2023, (working with Prof. Hui Yu)
Department of Mathematics, University of Duisburg-Essen, Germany, September 11-15, 2023, (working with Prof. Irwin Yousept)
Department of Mathematics and Statistics, University of Helsinki, Finland, July 27 - August 10, 2023, (working with Prof. Matti Lassas)
Department of Mathematics, Eidgenössische Technische Hochschule (ETH) Zürich, Zürich, Switzerland. July 14- 26, 2023. (working with Prof. Habib Ammari)
Department of Advanced Mathematical Sciences, Kyoto University, Kyoto, Japan. February 24 - March 3, 2023. (working with Prof. Yuusuke Iso)
Johann Radon Institute for Computational and Applied Mathematics (RICAM), Linz, Austria. January 25 - February 11, 2023. (working with Prof. Mourad Sini)
Graduate School of Mathematical Sciences, The University of Tokyo, Tokyo, Japan. January 4-18, 2023. (working with Prof. Masahiro Yamamoto)
Tokyo University of Science, Tokyo, Japan. August 28-31, 2019. (working with Prof. Hiromichi Itou)
Max Planck Institute, Leipzig, Germany, June 23-27, 2019. (working with Prof. Angkana Rüland)
Department of Mathematics, Hong Kong Baptist University, Hong Kong, June 3-7, 2019. (working with Prof. Hongyu Liu)
Institute of Mathematics, Goethe University Frankfurt, Germany, May 13-18, 2019. (working with Prof. Bastian von Harrach)
School of Mathematics, University of Minnesota, USA, May 3-10, 2019. (working with Prof. Ru-Yu Lai)
Johann Radon Institute for Computational and Applied Mathematics (RICAM), April 22-27, 2019. Linz, Austria. (working with Prof. Mourad Sini)
Department of Mathematics and Statistics, University of Helsinki, Finland, February 1-7, 2019. (working with Prof. Matti Lassas)
Department of Mathematics, Rice University, USA, January 26-31, 2019. (working with Prof. Maarten de Hoop)
Department of Mathematics and Statistics, University of Helsinki, Finland, December 3-10, 2018. (working with Prof. Matti Lassas)
Department of Mathematics and Statistics, University of Jyväskylä, Finland, August 24-31, 2018. (working with Prof. Mikko Salo)
Department of Mathematics, Hokkaido University, Sapporo Japan, July 8-15, 2018 (working with Prof. Gen Nakamura)
Yau Mathematical Science Center, Tsinghua University, Beijing, China, June 17-24, 2018. (working with Prof. Wenjia Jing)
School of Mathematics, University of Minnesota, USA, September 24-30, 2017. (working with Prof. Ru-Yu Lai)
Department of Mathematics, Colorado State University, USA, September 20-23, 2017. (working with Prof. Jennifer Mueller)
Department of Mathematics, The Hong Kong University of Science and Technology, Hong Kong, May 15-28, 2017. (working with Prof. Hai Zhang)
Institute for Mathematics and its Applications (IMA), University of Minnesota, USA, March 12-22, 2017. (Sponsor: IMA)
Department of Mathematics, National Cheng Kung University, October 31 - November 4, 2016. Tainan, Taiwan. (working with Prof. Ching-Lung Lin)
Department of Mathematics, Hokkaido University, August 29 - September 3, 2016. Sapporo, Japan. (working with Prof: Gen Nakamura)
Department of Mathematics, Chinese University of Hong Kong, April 25-29, 2016, Hong Kong. (working with Prof. Jun Zou)
Sub-Department of Applied Analysis, Graduate School of Informations, Kyoto University, July 5-11, 2015, Kyoto, Japan. (working with Prof. Yuusuke Iso)
Center for Partial Differential Equations, East China Normal University, June 18-22, 2015, Shanghai, China. (working with Prof. Wei-Ming Ni)
Johann Radon Institute for Computational and Applied Mathematics (RICAM), January 28- March 1, 2014, Linz, Austria. (working with Prof. Mourad Sini)
Hosting International Scholars
Prof. Hiroshi Takase (Kyushu University, Japan). Dates of visit: June 24-28, 2024.
Prof. Lauri Oksanen (University of Helsinki, Finland). Dates of visit: June 18-23, 2024.
Prof. Hyundae Lee (Inha University, Korea). Dates of visit: March 20-24, 2024.
Prof. Sanghyeon Yu (Korea University, Korea). Dates of visit: March 20-24, 2024.
Prof. Gen Nakamura (Hokkaido University, Japan). Dates of visit: January 14-21, 2024.
Prof. Tony Liimatainen (University of Helsinki, Finland). Dates of visit: November 20 - December 8, 2023.
Prof. Bastian von Harrach (Goethe University Frankfurt, Germany). Dates of visit: May 10-19, 2023.
Prof. Kenji Nakanishi (Kyoto University, Japan). Dates of visit: March 6-13, 2023.
Prof. Gen Nakamura (Hokkaido University, Japan). Dates of visit: November 15- December 1, 2022.
International Conferences Attendence
Inverse Problems, Imaging and Partial Differential Equations, IAS, HKUST, March 12-16, 2018.
Frontier of Theory and Applications of Nonlinear Partial Differential Equations, IAS, HKUST, Dec. 11-15, 2017.
Novel and Optics, IMA, University of Minnesota, March 13-17, 2017.
Inverse Problems, Imaging and Partial Differential Equations, IAS, HKUST, Dec 5-9, 2016.
LIASFMA on Control and Inverse Problems for PDEs, Oct 24-28, 2016, Zhejiang University, Hangzhou, China.
Inverse Problems, Imaging and Partial Differential Equations, IAS, HKUST, Sep 28 - Oct 2, 2015, Hong Kong.
The Tenth East China Partial Differential Equations Conference, East China Normal University, June 15-18, 2015, Shanghai, China.
The Global Young Scientists Summit @ one north (GYSS 2014), Nanyang Technological University, Jan 19-24, 2014, Singapore.
Summer Schools
EMS Summer School: Partial Differential Equations from Theory to Applications. University of Milan, Italy. July 1-5, 2019.
Summer School: Inverse and Spectral Problems for (Non)-Local Operators, Max Planck Institute (MPI) for Mathematics in the Sciences, Sept 10-14, 2018.
Summer School: Unique Continuation and Inverse Problems, Wolffhotel in Kopp, Bonn. Sept 2-7, 2018.
Summer School: Applied Inverse Problems (AIP 2015), University of Helsinki, Finland. May 18-22, 2015.
Academic Services
Referee for "Journal Differential Geometry", "Rev. Mat. Iberoam.", "SIAM J. Math Anal.", "Journal of Differential Equations", "Cal. Var. PDE", "Inverse Problems", "Inverse Problems and Imaging", "Nonlinearity", "Nonlinear Analysis", "Applicable Analysis", "Mathematics in Engineering", "Taiwanese Journal of Mathematics"...etc.
Executive Committee Member of East Asia Section of Inverse Problems International Association (EAIPIA).
Teaching assistant, Partial Differential Equations (graduate level), September 2015 - June 2016, National Taiwan University.
Teaching assistant, Real Analysis (graduate level), September 2015- June 2016, National Taiwan University.
Teaching assistant, Advanced Calculus (undergraduate level), September 2012 - June 2014, National Taiwan University.
Research Assistant, July 2011 - June 2012, Institute of Mathematics, Academic Sinica, Taiwan.
Military service, July 2010 - June 2011 (one-year obligation for men by the Taiwan Constitution).
Teaching assistant, Partial Differential Equations (graduate level), September 2009 - June 2010, National Taiwan University.
Teaching assistant, Calculus I & II (undergraduate level), September 2008 - June 2009, National Taiwan University.
Non-Mathematical Experiences
Before being a mathematician, I was a pseudo-musician. Besides, I won the ERHU (二胡/南胡) championship in Taiwan several times and I have practiced it for more than 15 years since I was 11 years old. I also gave many concerts in Taiwan, New Zealand and USA (solo in those concerts). I also played the piano but not good enough.