Welcome to FoCM!  

The computer has profoundly changed the relationship between mathematics and computation.  Besides its invaluable role in numeric, symbolic, and experimental applications, computation is an important object of mathematical study in its own right and a fundamental theoretical tool. It is a source of new and exciting problems for 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 areas of computational science through conferences, events and publications. FoCM traces its beginnings to the Park City AMS--SIAM seminar  in 1995 and its first conference has been held in Rio de Janeiro in 1997.

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The FoCM conference, held every three years, covers the entire spectrum of mathematical computation. Specialized events are held from time to time, and focus on timely research topics. Membership in FoCM is free and available through this website.



Peter Clarkson

Professor Peter Clarkson, of the University of Kent, is awarded a Senior Anne Bennett Prize in recognition of his tireless work to support gender equality in UK mathematics, and particularly for his leadership in developing good practice among departments of mathematical sciences.


Albert Cohen

The European Academy of Sciences established the Blaise Pascal Medal in 2003 to recognise an outstanding and demonstrated personal contribution to science and technology and the promotion of excellence in research and education. Up to six medals may be awarded in any one year. The award ceremony will be in October, 2020.



Danylo V. Radchenko

Danylo V. Radchenko was recognized for his outstanding contributions to Approximation Theory, in particular, to the theory of spherical designs. Together with Andriy V. Bondarenko and Maryna S. Viazovska he settled a long-standing conjecture by Korevaar and Meyers on optimal asymptotic bounds for spherical t-designs. Later, in a joint paper with H. Cohn, A. Kumar, S. D. Miller and M. S. Viazoska they proved the optimality of the Leech lattice among all 24-dimensional sphere packings. Danylo Radchenko has also contributed to the Theory of Shape Preserving Approximation and to Non-uniform Sampling Theory in relation with Fourier Analysis. Parallel to Approximation Theory, he has been working in Number Theory, in particular, on Dedekind zeta functions and on cross-ratios related to the work of Goncharov.

The Prize, which consists of a marble pyramid trophy and a cash award of 2000 euros, will be presented to Radchenko by Albert Cohen of Sorbonne Université, Chair of the Popov Prize Selection Committee. The other members of the Selection Committee were Wolfgang Dahmen, Karlheinz Grochenig, Pencho Petrushev, Peter Oswald, and Vilmos Totik. The Popov Prize awarding ceremony initially scheduled at the FoCM 2020 Conference in Vancouver has been postponed due to COVID-19.

Danylo V. Radchenko holds a Hermann-Weyl-Instructor position at the Institute for Mathematical Research of ETH Zurich. He received his PhD in July 2016 from University of Bonn, under the supervision of Don Zagier.

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Alicia Dickenstein

Alicia Dickenstein, Universidad de Buenos Aires and CONICET, is being recognized for contributions to algebraic geometry and its applications within geometric modeling and in the study of biochemical reaction networks. She was a plenary speaker at FoCM '08 in Hong Kong


Kristin E. Lauter, Microsoft Research, is being recognized for the development of practical cryptography and for leadership in the mathematical community. She is scheduled to be a plenary speaker at our next FoCM conference in Vancouver.



Alfonso Bandeira

Professor Afonso Bandeira, ETH Zurich, has been awarded the fourth Stephen Smale Prize for his pioneering work on the foundation of computational mathematics. Bandeira is an incredibly productive and versatile researcher who has successfully applied and combined concepts and tools from optimization theory, probability theory, information theory, statistics, theoretical computer science, harmonic analysis, and number theory to the design and analysis of algorithms for solving real life data science problems.

Highlights of his theoretical results include a new type of Cheeger inequality for the graph connection Laplacian (with D. Spielman and A. Singer), a remarkable theorem about an important class of Gaussian random matrices (with R. Van Handel), a variant of the “little” Grothendieck theorem for the orthogonal group (with C. Kennedy and A. Singer), guarantees for the Burer-Monteiro factorization of SDPs (with N. Boumal and V. Voroninski), lower bounds on the sample complexity of multi-reference alignment (with A. Perry, J. Weed, P. Rigollet, and A. Singer), and new understanding of computational-to-statistical gaps (with A. Perry and A. Wein).

Bandeira employed these theorems to advance our understanding of fundamental algorithms for data analysis. The applications include cryo-electron microscopy, community detection in networks, and phase retrieval. A beautiful example is his paper (with E. Abbe and G. Hall) that proves optimal bounds for exact recovery for graph clustering in the stochastic block model and derives an efficient SDP recovery algorithm that achieves the optimal bound.

Bandeira’s work spans a wide range of applications and delivers essential insights in multiple fields. It signals a very productive and talented individual with a breadth of vision that Stephen Smale exemplified.

The winner will receive a "如何将手机改成国外的ip地址" as the prize insignia.

Mark Braverman - 2019 NSF Waterman Awardee

Mark Baverman

Mark Braverman, Princeton University Professor of Computer Science, has been named a recipient of the Alan T. Waterman Award for his work "devoted to developing algorithms and designs that can withstand the effects of ubiquitous noise present in all learning and computational tasks." Professor Braverman is also a recipient of FoCM's 2014 Stephen Smale Prize.

Wolfgang Dahmen is honored as 2019 SIAM Fellow

Wofgang Dahmen

Wolfgang Dahmen is SmartState Endowed Chair in Data Analysis, Simulation, Imaging, and Visualization; Williams-Hedberg-Hedberg Chair in Mathematics at the University of South Carolina. He was the Chair of the FoCM Society between 2014-17.

FoCM 2020 Conference Location: Vancouver, Canada



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Lek-Heng Lim from University of Chicago and Volker Mehrmann from TU Berlin
are 2019 Hans Schneider prize recipients.

Lek-Heng Lim and Volker Mehrmann

The Hans Schneider Prize in Linear Algebra is awarded every three years by The International Linear Algebra Society for research, contributions, and achievements at the highest level of Linear Algebra. The Prize may be awarded for an outstanding scientific achievement or for lifetime contribution.

Jiawang Nie wins the 2018 SIAM Activity Group on Linear Algebra Best Paper Prize


for his paper, Generating Polynomials and Symmetric Tensor Decompositions, Foundations of Computational Mathematics 17(2): 423-465 (2017)

Jiawang Nie graduated in UC Berkeley under the supervision of Bernd Sturmfels and James Demmel in 2006. He is now on the faculty at UCSD (如何将手机改成国外的ip地址)

For more information, see


The Le Monde published the best scientific pictures from the year 2017: Link


Among these, the computational realization of the Nash C^1 embedding theorem by Borrelli et al. published in the Journal of FoCM, July 10, 2017: Link

Le Monde also published a longer article about this result earlier in 2017 (in French): Link


The Catalan Math Society has set up a prize for papers on Dynamical Systems,
sponsored by Carles Simó:


The last edition of the prize was given to the authors of a paper published at the FoCM Journal:
Jordi-Lluís Figueras, Àlex Haro and Alejandro Luque, "Rigorous Computer Assisted Application of KAM Theory: A Modern Approach", Found Comput Math (2016).



Mireille Bousquet Melou Photo

The European Mathematical Society Newsletter published an interview with Mireille Bousquet-Mélou, written by Juanjo Rué. The interview took place at the FoCM 2017 Conference at the Universitat de Barcelona.

Link to interview  


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Bernd Sturmfels

Bernd Sturmfels, University of California, Berkeley, will receive the 2018 George David Birkhoff Prize in Applied Mathematics for his instrumental role in creating the field of applied algebraic geometry.

Bernd Sturmfels has made foundational contributions to combinatorics, algebraic geometry, and symbolic computation, and has introduced algebraic techniques to numerous areas of applied mathematics including bioinformatics, computer vision, optimization, and statistics. Like Birkhoff, the intellectual range of his work stretches from pure mathematics to the very applied, and demonstrates the unity of mathematics. In addition, he is an exceptional expositor, a wonderful teacher, and a dedicated mentor to young mathematicians.

Bernd is a founding member of the SIAM Activity Group on Algebraic Geometry, the editor in chief of the SIAM Journal on Applied Algebra and Geometry, and an active member of the FoCM Society.



Lek-Heng Lim wins SIAM'S Wilkinson Prize in Numerical Analysis and Scientific Computing


The Prize was awarded at the 2017 SIAM Annual Meeting.
Lek-Heng Lim is also the recipient of the 2017 Smale Prize.




Pierre Lairez wins the SIAM Activity Group on Algebraic Geometry Early Career Prize


Pierre Lairez wins the SIAM Activity Group on Algebraic Geometry Early Career Prize, in recognition of his paper A Deterministic Algorithm to Compute Approximate Roots of Polynomial Systems in Polynomial Average Time, which represents the final step in the resolution of Smale’s 17th problem.