Tan Lei (; 1963–2016) was a

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

specialising in

complex dynamics Complex dynamics is the study of dynamical systems defined by Iterated function, iteration of functions on complex number spaces. Complex analytic dynamics is the study of the dynamics of specifically analytic functions. Techniques *General **Mo ...

and functions of complex numbers. She is most well-known for her contributions to the study of the

Mandelbrot set The Mandelbrot set () is the set of complex numbers c for which the function f_c(z)=z^2+c does not diverge to infinity when iterated from z=0, i.e., for which the sequence f_c(0), f_c(f_c(0)), etc., remains bounded in absolute value. This ...

and

Julia set In the context of complex dynamics, a branch of mathematics, the Julia set and the Fatou set are two complementary sets (Julia "laces" and Fatou "dusts") defined from a function. Informally, the Fatou set of the function consists of values wit ...

Career

After gaining her PhD in

Mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

in 1986 at University of Paris-Sud, Orsay, Tan worked as an assistant researcher in

Geneva Geneva ( ; french: Genève ) frp, Genèva ; german: link=no, Genf ; it, Ginevra ; rm, Genevra is the List of cities in Switzerland, second-most populous city in Switzerland (after Zürich) and the most populous city of Romandy, the French-speaki ...

. She then conducted postdoctoral projects at the

Max Planck Institute for Mathematics The Max Planck Institute for Mathematics (german: Max-Planck-Institut für Mathematik, MPIM) is a prestigious research institute located in Bonn, Germany. It is named in honor of the German physicist Max Planck and forms part of the Max Planck S ...

and

University of Bremen The University of Bremen (German: ''Universität Bremen'') is a public university in Bremen, Germany, with approximately 23,500 people from 115 countries. It is one of 11 institutions which were successful in the category "Institutional Strategi ...

until 1989, when she was made a lecturer at Ecole Normale Superieure de Lyon in

France France (), officially the French Republic ( ), is a country primarily located in Western Europe. It also comprises of Overseas France, overseas regions and territories in the Americas and the Atlantic Ocean, Atlantic, Pacific Ocean, Pac ...

. Tan held a research position at

University of Warwick The University of Warwick ( ; abbreviated as ''Warw.'' in post-nominal letters) is a public research university on the outskirts of Coventry between the West Midlands (county), West Midlands and Warwickshire, England. The university was founded i ...

from 1995 to 1999, before becoming a senior lecturer at

Cergy-Pontoise University Cergy-Pontoise University (French: ''Université de Cergy-Pontoise'') was a French university, located in Cergy-Pontoise, France. On 1 January 2020, the university merged with the International School of Information Processing Sciences (EISTI) an ...

. She was made professor at

University of Angers The University of Angers (french: Université d'Angers; UA) is a public university in western France, with campuses in Angers, Cholet, and Saumur. It forms part of thAngers-Le Mans University Community History The University of Angers was init ...

in 2009.

Mathematical work

Tan obtained important results about the

Julia Julia is usually a feminine given name. It is a Latinate feminine form of the name Julio and Julius. (For further details on etymology, see the Wiktionary entry "Julius".) The given name ''Julia'' had been in use throughout Late Antiquity (e.g. ...

and

s, in particular investigating their fractality and the similarities between the two.''Local properties of The Mandelbrot set M, Similarity between M and Julia sets'', Proceedings of the seventh European Women in Mathematics (EWM) meeting, Madrid, 1995, S. 71-82. For example she showed that at the

Misiurewicz point In mathematics, a Misiurewicz point is a parameter value in the Mandelbrot set (the parameter space of complex quadratic maps) and also in real quadratic maps of the interval for which the critical point is strictly pre-periodic (i.e., it becomes ...

s these sets are asymptotically similar through scaling and rotation.''Similarity between the Mandelbrot set and Julia Sets'', Communications in Mathematical Physics 134 (1990), pp. 587-617. She constructed examples of polynomials whose Julia sets are homeomorphic to the

Sierpiński carpet The Sierpiński carpet is a plane fractal first described by Wacław Sierpiński in 1916. The carpet is a generalization of the Cantor set to two dimensions; another is Cantor dust. The technique of subdividing a shape into smaller copies of i ...

''A Sierpinski carpet as Julia set'', Appendix to: J. Milnor, ''Geometry and dynamics of quadratic rational maps'', Exp. Math., volume 2, 1993, pp. 78-81 and which are disconnected.With K. Pilgrim: ''Rational maps with disconnected Julia set'', Astérisque, volume 261, 2000, pp. 349-384 She contributed to other areas of complex dynamics.With G.-Zh. Cui: ''A characterization of hyperbolic rational maps'', Invent. math., Band 183, 2011, S. 451-516.With Xavier Buff: ''The quadratic dynatomic curves are smooth and irreducible'', in: Araceli Bonifant, Misha Lyubich, Scott Sutherland (eds.), ''Frontiers in Complex Dynamics: In Celebration of John Milnor's 80th Birthday'', Princeton University Press, 2014, S. 49-72. She also wrote some surveys and popularisation work around her research topics.With Xavier Buff and G.-Zh. Cui: ''Teichmüller spaces and holomorphic dynamics'', in: Athanase Papadopoulos (ed.), ''Handbook of Teichmüller Theory, Volume 4'', EMS 2014With Arnaud Chéritat
''Si nous faisons danser les racines? Un hommage à Bill Thurston''
, Images des mathématiques CNRS, 7 Nov. 2012

Legacy

A conference in Tan's memory was held in

Beijing } Beijing ( ; ; ), alternatively romanized as Peking ( ), is the capital of the People's Republic of China. It is the center of power and development of the country. Beijing is the world's most populous national capital city, with over 21 ...

China China, officially the People's Republic of China (PRC), is a country in East Asia. It is the world's most populous country, with a population exceeding 1.4 billion, slightly ahead of India. China spans the equivalent of five time zones and ...

, in May 2016.

Publications

Thesis

Books

Articles

References

{{DEFAULTSORT:Tan, Lei 1963 births 2016 deaths Chinese women mathematicians Chinese mathematicians 20th-century French mathematicians French women mathematicians Academic staff of the University of Angers Academic staff of Paris-Sud University Wuhan University alumni Paris-Sud University alumni People from Pingxiang 21st-century French mathematicians Mathematicians from Jiangxi Chinese emigrants to France 20th-century women mathematicians 21st-century women mathematicians Chinese science writers Writers from Jiangxi 20th-century French women 21st-century French women