Felipe Cucker
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Juan Felipe Cucker Farkas (born 1958) is an
Uruguayan Uruguayans () are people identified with the country of Uruguay, through citizenship or descent. Uruguay is home to people of different ethnic origins. As a result, many Uruguayans do not equate their nationality with ethnicity, but with citizen ...
mathematician and
theoretical computer scientist Theoretical computer science is a subfield of computer science and mathematics that focuses on the abstract and mathematical foundations of computation. It is difficult to circumscribe the theoretical areas precisely. The ACM's Special Inter ...
who has done research into the complexity theory of the Blum–Shub–Smale computational model and the
complexity Complexity characterizes the behavior of a system or model whose components interact in multiple ways and follow local rules, leading to non-linearity, randomness, collective dynamics, hierarchy, and emergence. The term is generally used to c ...
of
numerical algorithm Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods t ...
s in
linear programming Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements and objective are represented by linear function#As a polynomia ...
and
numerical algebraic geometry Numerical algebraic geometry is a field of computational mathematics, particularly computational algebraic geometry, which uses methods from numerical analysis to study and manipulate the solutions of systems of polynomial equations. Homotopy cont ...
.


Biography

Cucker was born in
Montevideo Montevideo (, ; ) is the capital city, capital and List of cities in Uruguay, largest city of Uruguay. According to the 2023 census, the city proper has a population of 1,302,954 (about 37.2% of the country's total population) in an area of . M ...
in 1958. Also: . Due to the situation in Uruguay in the 70s, he emigrated to Spain to study the
bachelor A bachelor is a man who is not and never has been married.Bachelors are, in Pitt & al.'s phrasing, "men who live independently, outside of their parents' home and other institutional settings, who are neither married nor cohabitating". (). Etymo ...
of mathematics at the
University of Barcelona The University of Barcelona (official name in ; UB), formerly also known as Central University of Barcelona (), is a public research university located in the city of Barcelona, Catalonia, Spain. It was established in 1450. With 76,000 students, ...
, which he completed in 1983. He obtained his PhD degree at the
University of Cantabria The University of Cantabria (UC) () is a public university located in Santander, Torrelavega and Comillas in Cantabria, Spain. It was founded in 1972 and comprises 15 schools and colleges. It was selected as Campus of International Ex ...
and
University of Rennes 1 The University of Rennes 1 was a public university located in Rennes, France. It was founded in 1970, after splitting of the historic University of Rennes into two universities. On January 1, 2023, the University of Rennes 1 merged with five gra ...
in 1986 under the supervision Tomás Recio and Michel Coste. His thesis was about
Nash functions In real algebraic geometry, a Nash function on an open semialgebraic subset ''U'' ⊂ R''n'' is an analytic function ''f'': ''U'' → R satisfying a nontrivial polynomial equation ''P''(''x'',''f''(''x'')) = 0 for all ''x'' in ''U'' (A semialgebra ...
on real
algebraic varieties Algebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics. Classically, an algebraic variety is defined as the set of solutions of a system of polynomial equations over the real or complex numbers. ...
. From 1987 to 1992 Cucker was professor at the
Polytechnic University of Catalonia The Polytechnic University of Catalonia (, , ; UPC), currently referred to as BarcelonaTech, is the largest polytechnic university in Catalonia, Spain. UPC's objectives are based on internationalization, as it is one of Europe's techni ...
. In 1992 Cucker became professor at the recently created
Pompeu Fabra University Pompeu Fabra University (, ; ) is a public university located in the city of Barcelona, Catalonia in Spain. Established in 1990 by the Autonomous Government of Catalonia and named after Pompeu Fabra, it is known for its competitiveness in resea ...
. In 1995 he was promoted to chair professor at this university. In 1993 he organized the workshop Continuous Algorithms and Complexity at the
Centre de Recerca Matemàtica The Centre de Recerca Matemàtica (CRM) () is a consortium, with its own legal status, integrated by the Institut d'Estudis Catalans (IEC) and the Catalan Government. It is a research institute associated with the Universitat Autònoma de Barcel ...
in Barcelona where he started his long-term collaboration with
Lenore Blum Lenore Carol Blum (née Epstein, born December 18, 1942) is an American computer scientist and mathematician who has made contributions to the theories of real number computation, cryptography, and pseudorandom number generation. She was a disti ...
,
Michael Shub Michael Ira Shub (born August 17, 1943) is an American mathematician who has done research into dynamical systems and the complexity of real number algorithms. Career 1967: Ph.D. and early career In 1967, Shub obtained his Ph.D. degree at the U ...
, and
Steve Smale Stephen Smale (born July 15, 1930) is an American mathematician, known for his research in topology, dynamical systems and mathematical economics. He was awarded the Fields Medal in 1966 and spent more than three decades on the mathematics faculty ...
. In 1996 he moved with them to the
City University of Hong Kong The City University of Hong Kong (CityUHK) is a public research university in Kowloon Tong, Kowloon, Hong Kong. It was founded in 1984 as the City Polytechnic of Hong Kong and formally established as the City University of Hong Kong in 1994 ...
to write the book
Complexity and Real Computation ''Complexity and Real Computation'' is a book on the computational complexity theory of real computation. It studies algorithms whose inputs and outputs are real numbers, using the Blum–Shub–Smale machine as its model of computation. For inst ...
. Although this was intended as a temporal position, Cucker would stay in Hong Kong and became an
associate professor Associate professor is an academic title with two principal meanings: in the North American system and that of the ''Commonwealth system''. In the ''North American system'', used in the United States and many other countries, it is a position ...
of this university in 1998,
full professor Professor (commonly abbreviated as Prof.) is an academic rank at universities and other post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin as a 'person who professes'. Professors ...
in 2003, and chair professor in 2006. Cucker was one of the founders of the nonprofit association
Foundations of Computational Mathematics Foundations of Computational Mathematics (FoCM) is an international nonprofit organization that supports and promotes research at the interface of mathematics and computation. It fosters interaction among mathematics, computer science, and other ...
, of which he has been a member of the board of directors since its creation in 1995 until 2017. Additionally, Cucker was Chair of this society from 2008 to 2011 and Editor-in-Chief of its journal from 2011 to 2017. In 2006 Cucker was named foreign member of the Royal Academy of Sciences and Arts of Barcelona. From 2017 to 2019 Cucker was Einstein Visiting Fellow of the Berlin Mathematical School and
Technische Universität Berlin (TU Berlin; also known as Berlin Institute of Technology and Technical University of Berlin, although officially the name should not be translated) is a public university, public research university located in Berlin, Germany. It was the first ...
. In 2019, the conference ''Complexity of numerical computation: A conference in honor of Felipe Cucker'' was organised at the
Technische Universität Berlin (TU Berlin; also known as Berlin Institute of Technology and Technical University of Berlin, although officially the name should not be translated) is a public university, public research university located in Berlin, Germany. It was the first ...
in Berlin celebrating his work. Since 2018 he is Head of the Mathematics Department at
City University of Hong Kong The City University of Hong Kong (CityUHK) is a public research university in Kowloon Tong, Kowloon, Hong Kong. It was founded in 1984 as the City Polytechnic of Hong Kong and formally established as the City University of Hong Kong in 1994 ...
.


Work

During the 90s, he worked in the complexity classes that appear when dealing with the
Blum–Shub–Smale machine In computation theory, the Blum–Shub–Smale machine, or BSS machine, is a model of computation introduced by Lenore Blum, Michael Shub and Stephen Smale, intended to describe computations over the real numbers. Essentially, a BSS machine is a Ra ...
. In 1998, he co-authored one of the fundamental books in this topic, ''
Complexity and Real Computation ''Complexity and Real Computation'' is a book on the computational complexity theory of real computation. It studies algorithms whose inputs and outputs are real numbers, using the Blum–Shub–Smale machine as its model of computation. For inst ...
'', together with
Lenore Blum Lenore Carol Blum (née Epstein, born December 18, 1942) is an American computer scientist and mathematician who has made contributions to the theories of real number computation, cryptography, and pseudorandom number generation. She was a disti ...
,
Michael Shub Michael Ira Shub (born August 17, 1943) is an American mathematician who has done research into dynamical systems and the complexity of real number algorithms. Career 1967: Ph.D. and early career In 1967, Shub obtained his Ph.D. degree at the U ...
, and
Steve Smale Stephen Smale (born July 15, 1930) is an American mathematician, known for his research in topology, dynamical systems and mathematical economics. He was awarded the Fields Medal in 1966 and spent more than three decades on the mathematics faculty ...
. In the 2000s he focused on the analysis of numerical algorithms in linear programming. Together with Dennis Cheung he introduced the notions of the GCC condition number in linear programming. In 2007 together with
Steve Smale Stephen Smale (born July 15, 1930) is an American mathematician, known for his research in topology, dynamical systems and mathematical economics. He was awarded the Fields Medal in 1966 and spent more than three decades on the mathematics faculty ...
he proposed the so-called Cucker-Smale flocking model. This model, which has received extensive attention in mathematics and other fields, plays an important role in the mathematical study of flocking dynamics. In 2011 together with
Peter Bürgisser Peter Bürgisser (born 1962) is a Swiss mathematician and theoretical computer scientist who deals with algorithmic algebra and algebraic complexity theory. Education and career Bürgisser received in 1990 his doctorate from the University of Ko ...
he contributed to the solution of Smale's 17th problem. In 2013 Cucker won an Honorable Mention in the Category of Mathematics of the
PROSE Awards The PROSE Awards (where ''PROSE'' is an abbreviation for "professional and scholarly excellence") are presented by the Association of American Publishers' (AAP) Professional and Scholarly Publishing (PSP) Division. Presented since 1976, the awar ...
for his book ''Manifold Mirrors: The Crossing Paths of the Arts and Mathematics'', which dealt with
mathematics and art Mathematics and art are related in a variety of ways. Mathematics has itself been described as an art mathematical beauty, motivated by beauty. Mathematics can be discerned in arts such as Music and mathematics, music, dance, painting, Mathema ...
.


Selected publications

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References


External links


Personal website
at the City University of Hong Kong. * * {{DEFAULTSORT:Cucker, Felipe Living people 1958 births 20th-century American mathematicians 21st-century American mathematicians University of Barcelona alumni University of Cantabria alumni Academic staff of Pompeu Fabra University