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 areas of computational science through conferences, events and publications.

Aim

FoCM aims to explore the relationship between mathematics and computation, focusing both on the search for mathematical solutions to computational problems and computational solutions to mathematical problems. Topics of central interest in the Society include but are not restricted to: *

Approximation Theory In mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby. Note that what is meant by ''best'' and ''simpler'' wil ...

Computational Algebraic Geometry Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...

*Computational Dynamics *Computational

Harmonic Analysis Harmonic analysis is a branch of mathematics concerned with the representation of functions or signals as the superposition of basic waves, and the study of and generalization of the notions of Fourier series and Fourier transforms (i.e. an ex ...

Image An image is a visual representation of something. It can be two-dimensional, three-dimensional, or somehow otherwise feed into the visual system to convey information. An image can be an artifact, such as a photograph or other two-dimensio ...

, and

Signal Processing Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing '' signals'', such as sound, images, and scientific measurements. Signal processing techniques are used to optimize transmissions, ...

Computational Number Theory In mathematics and computer science, computational number theory, also known as algorithmic number theory, is the study of computational methods for investigating and solving problems in number theory and arithmetic geometry, including algorithm ...

Computational Topology Algorithmic topology, or computational topology, is a subfield of topology with an overlap with areas of computer science, in particular, computational geometry and computational complexity theory. A primary concern of algorithmic topology, as it ...

and

Geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

Continuous Optimization Continuous optimization is a branch of optimization in applied mathematics. As opposed to discrete optimization, the variables used in the objective function are required to be continuous variables—that is, to be chosen from a set of re ...

* Foundations of Numerical PDE's * Geometric Integration and

Computational Mechanics Computational mechanics is the discipline concerned with the use of computational methods to study phenomena governed by the principles of mechanics. Before the emergence of computational science (also called scientific computing) as a "third w ...

Graph Theory In mathematics, graph theory is the study of '' graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conn ...

and

Combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many a ...

* Information-based Complexity * Learning Theory *Multiresolution and Adaptivity in Numerical PDE's *

Numerical Linear Algebra Numerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which efficiently and accurately provide approximate answers to questions in continuous mathematic ...

Random Matrices In probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all elements are random variables. Many important properties of physical systems can be represented mathemat ...

* Real-Number Complexity *

Special Functions Special functions are particular mathematical functions that have more or less established names and notations due to their importance in mathematical analysis, functional analysis, geometry, physics, or other applications. The term is defined b ...

and

Orthogonal Polynomials In mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonal to each other under some inner product. The most widely used orthogonal polynomials are the class ...

* Stochastic Computing *Symbolic Analysis

History

The Society for the Foundations of Computational Mathematics was launched in the Northern summer of 1995, following a month-long AMS–SIAM Summer Seminar in Park City, Utah, which was organized principally by

Stephen 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 ...

. That meeting hosted a number of sub-conferences on the frontier of Mathematics and Computation, focusing on many topics from numerical analysis and on the importance of a foundational theory of real number computation. The main thrust was on creating a shared intellectual space for activity bringing together computation and mathematics. During the final week at

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. Biography Shub obtained his Ph.D. degree at the University of California, Berke ...

's behest an informal lunch was arranged where Felipe Cucker,

Arieh Iserles Arieh Iserles (born 2 September 1947) is a computational mathematician, currently Professor of the Numerical Analysis of Differential Equations at the University of Cambridge and a member of the Department of Applied Mathematics and Theoretic ...

Narendra Karmarkar Narendra Krishna Karmarkar (born Circa 1956) is an Indian Mathematician. Karmarkar developed Karmarkar's algorithm. He is listed as an ISI highly cited researcher. He invented one of the first provably polynomial time algorithms for linear pro ...

, James Renegar,

and

decided to go ahead and create a permanent entity that would organize periodic conferences covering subjects in the interplay between these two areas. After a discussion, the name ''Foundations of Computational Mathematics'' was settled, and

was chosen to lead the initiative with a little team formed by himself,

and James Renegar. The first FoCM conference took place in Rio de Janeiro and was hosted by IMPA with the support of its then-director

Jacob Palis __NOTOC__ Jacob Palis Jr. (born 15 March 1940) is a Brazilian mathematician and professor. Palis' research interests are mainly dynamical systems and differential equations. Some themes are global stability and hyperbolicity, bifurcations, a ...

. Several conferences were organized later (see below), bringing together some of the world leading mathematicians and computer scientists, although the society was not formally established as a legal entity until 1999 simultaneously with the creation of the journal Foundations of Computational Mathematics. Ever since, its main activities are its triennial meetings, special semesters and the support of the FoCM journal, as well as general advocacy of the mathematical areas underlying computation.

Meetings

The main FoCM conference is held every three years. Previous meetings include: * Park City AMS—SIAM 1995 Summer Seminar (Utah, USA), considered as the founding event of the society
Announcement
* FoCM'97 (Rio de Janeiro, Brazil)

* FoCM'99 (Oxford, United Kingdom)

FoCM 2002
(Minneapolis, USA).
FoCM 2005
(Santander, Spain).
FoCM 2008
(Hong Kong, China).
FoCM 2011
(Budapest, Hungary).
FoCM 2014
(Montevideo, Uruguay). These conferences aim to cover the entire spectrum of mathematical computation. In addition to that, specialized events focusing on particular research topics are organized by the society, including: * Foundations of Computational Mathematics Half Year Program, Berkeley, 1998,

Mathematical Sciences Research Institute The Simons Laufer Mathematical Sciences Institute (SLMath), formerly the Mathematical Sciences Research Institute (MSRI), is an independent nonprofit mathematical research institution on the University of California campus in Berkeley, Calif ...

Organizing committee

Hong Kong, 1999,

City University of Hong Kong City University of Hong Kong (CityU) is a world-class public research university located in Kowloon Tong, Hong Kong. It was founded in 1984 as City Polytechnic of Hong Kong and became a fully accredited university in 1994. Currently, CityU is ...

.
Thematic Program on the Foundations of Computational Mathematics
Toronto, 2009, Fields Institute.
From Dynamics to Complexity A conference celebrating the work of
Mike Shub, Toronto, 2012 Fields Institute.

Publications

Since January 2001, FoCM supports the journa
''Foundations of Computational Mathematics''
Editors in Chief of the journal: *

(2001–2002). * Peter Olver (2002–2008). *

(2002–2011). * Michael Todd (2008–2011). * Felipe Cucker (2011–2017). * Albert Cohen (2014–2020). * Hans Munthe-Kaas (2017–present). * Teresa Krick (2020–present).

Chairs

The Chair of FoCM is elected every 3 years. This position has been held by various mathematicians worldwide. *

(1995–1997). *

(1997–2000). * Ronald DeVore (2000–2002). *

Endre Süli Endre Süli (also, Endre Suli or Endre Šili) is a mathematician. He is Professor of Numerical Analysis in the Mathematical Institute, University of Oxford, Fellow and Tutor in Mathematics at Worcester College, Oxford and Adjunct Fellow of ...

(2002–2005). * Michael Todd (2005–2008). * Felipe Cucker (2008–2011). * Teresa Krick (2011–2014). * Wolfgang Dahmen (2014-2017). * Agnes Szanto (2017-2020). * Albert Cohen (2020--present).

Stephen Smale Prize

FoCM awards the , whose objective is to recognize the work of a young mathematician in the areas at the heart of the society's interests and to help to promote his or her integration among the leaders of the scientific community. Smale Prize recipients: * Snorre H. Christiansen (2011)
Laudatio
* Carlos Beltrán and Mark Bravermann (2014)
Laudatio
*

Lek-Heng Lim Lek-Heng Lim () is a Singaporean mathematician. Lim earned a bachelor's degree at the National University of Singapore, studied for his master's at Cornell University and the University of Cambridge, and completed a doctorate at Stanford Universi ...

(2017). * Afonso Bandeira (2020).

References

External links

the FoCM websiteJournal FoCM website
{{authority control Mathematical societies