This research area covers applied geometry, algebraic geometry, and geometric design covering mathematics and computing in related areas of diverse applications in areas like biology, coding theory, complexity theory, computer graphics, computer vision, cryptography, game theory and economics, and robotics. Applied geometry also includes mathematical and computational issues that arise in generating and processing geometric information for various engineering applications.

The Pioneer Prize is awarded every four years at the International Council for Industrial and Applied Mathematics (ICIAM) Congress to one individual for pioneering work introducing applied mathematical methods and scientific computing techniques to an industrial problem area or a new scientific field of applications. Nominations can be submitted via the ICIAM website.

By Ernest Davis
Shape: The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else. By Jordan Ellenberg. Penguin Press, New York, NY, May 2021. 480 pages, $28.00. ...

By Shane Kepley, Konstantin Mischaikow, and Lun Zhang SIAM Journal on Applied Algebra and Geometry, Volume 5, Issue 2, Page 388-416, January 2021. In this paper we consider the classical problem of computing linear extensions of a...

By Katherine E. Stange SIAM Journal on Applied Algebra and Geometry, Volume 5, Issue 2, Page 366-387, January 2021. We provide a reduction of the Ring-LWE problem to Ring-LWE problems in subrings, in...

By Carlos Améndola, Kathlén Kohn, Philipp Reichenbach, and Anna Seigal SIAM Journal on Applied Algebra and Geometry, Volume 5, Issue 2, Page 304-337, January 2021. We uncover connections between maximum likelihood estimation in statistics and norm minimization over a...

By Harm Derksen and Visu Makam SIAM Journal on Applied Algebra and Geometry, Volume 5, Issue 2, Page 338-365, January 2021. We study the log-likelihood function and maximum likelihood estimate (MLE) for the matrix normal...

By Michael DiPasquale and Nelly Villamizar SIAM Journal on Applied Algebra and Geometry, Volume 5, Issue 2, Page 250-277, January 2021. A tetrahedral complex all of whose tetrahedra meet at a common vertex is called...

By Elina Robeva and Jean-Baptiste Seby SIAM Journal on Applied Algebra and Geometry, Volume 5, Issue 2, Page 278-303, January 2021. Building on the theory of causal discovery from observational data, we study interactions between...

By Daniel C. Cohen, Michael Farber, and Shmuel Weinberger SIAM Journal on Applied Algebra and Geometry, Volume 5, Issue 2, Page 229-249, January 2021. We introduce and study a new concept of parametrized topological complexity: a topological invariant...

By Volker H. Schulz SIAM Review, Volume 63, Issue 2, Page 419-431, January 2021. The April issue of SIAM News sadly reported on the death of Bob O'Malley (https://sinews.siam.org/Details-Page/obituary-robert-e-omalley-jr). He led the Book...

By The Editors SIAM Review, Volume 63, Issue 2, Page 373-373, January 2021. The SIGEST article in this issue is “A General Framework for Fractional Order Compartment Models,” by Christopher N. Angstmann,...

By J. M. Sanz-Serna SIAM Review, Volume 63, Issue 2, Page 247-247, January 2021. ``Stochastic Control Liaisons: Richard Sinkhorn Meets Gaspard Monge on a Schrödinger Bridge,” by Yongxin Chen, Tryphon T. Georgiou, and...

By Darinka Dentcheva SIAM Review, Volume 63, Issue 2, Page 393-393, January 2021. This issue of SIAM Review presents two papers in the Education section. The first paper, “Rotations in Three Dimensions,”...

By Misha E. Kilmer SIAM Review, Volume 63, Issue 2, Page 315-315, January 2021. Under what conditions does a semilinear parabolic equation have the maximum bound principle, and do numerical approximations of it...

By Christopher N. Angstmann, Austen M. Erickson, Bruce I. Henry, Anna V. McGann, John M. Murray, and James A. Nichols SIAM Review, Volume 63, Issue 2, Page 375-392, January 2021. Compartment models are a widely used class of models that are useful when considering the flow of objects, ...

By Art B. Owen and Daniel Rudolf SIAM Review, Volume 63, Issue 2, Page 360-372, January 2021. This article provides a strong law of large numbers for integration on digital nets randomized by a nested uniform...

By Qiang Du, Lili Ju, Xiao Li, and Zhonghua Qiao SIAM Review, Volume 63, Issue 2, Page 317-359, January 2021. The ubiquity of semilinear parabolic equations is clear from their numerous applications ranging from physics and biology to materials...

By Milton F. Maritz SIAM Review, Volume 63, Issue 2, Page 395-404, January 2021. The Rodrigues formula for the $3\times 3$ rotation matrix is hardly ever derived from first principles in a simple...

By Yongxin Chen, Tryphon T. Georgiou, and Michele Pavon SIAM Review, Volume 63, Issue 2, Page 249-313, January 2021. In 1931--1932, Erwin Schrödinger studied a hot gas Gedankenexperiment (an instance of large deviations of the empirical distribution). Schrödinger's...

By Pablo D. Brubeck, Yuji Nakatsukasa, and Lloyd N. Trefethen SIAM Review, Volume 63, Issue 2, Page 405-415, January 2021. Vandermonde matrices are exponentially ill-conditioned, rendering the familiar “polyval(polyfit)” algorithm for polynomial interpolation and least-squares fitting ineffective at higher...

By Renato G. Bettiol, Mario Kummer, and Ricardo A. E. Mendes SIAM Journal on Applied Algebra and Geometry, Volume 5, Issue 2, Page 200-228, January 2021. We study the structure of the set of algebraic curvature operators satisfying a sectional...

By Daniel Augot, Alain Couvreur, Julien Lavauzelle, and Alessandro Neri SIAM Journal on Applied Algebra and Geometry, Volume 5, Issue 2, Page 165-199, January 2021. This paper extends the study of rank-metric codes in extension fields equipped with...

By Alexander Heaton, Serkan Hoşten, and Isabelle Shankar SIAM Journal on Applied Algebra and Geometry, Volume 5, Issue 1, Page 140-164, January 2021. This paper explores the geometric structure of the spectrahedral cone, called the symmetry adapted...

By Claus Scheiderer SIAM Journal on Applied Algebra and Geometry, Volume 5, Issue 1, Page 114-139, January 2021. Semidefinite programming (SDP) is the task of optimizing a linear function over the common...

By Daniel Plaumann, Rainer Sinn, and Stephan Weis SIAM Journal on Applied Algebra and Geometry, Volume 5, Issue 1, Page 86-113, January 2021. Kippenhahn's theorem asserts that the numerical range of a matrix is the convex hull...

By Mateusz Michałek, Leonid Monin, and Jarosław A. Wiśniewski SIAM Journal on Applied Algebra and Geometry, Volume 5, Issue 1, Page 60-85, January 2021. We study the maximum likelihood (ML) degree of linear concentration models in algebraic statistics....

By Lu Lu, Xuhui Meng, Zhiping Mao, and George Em Karniadakis SIAM Review, Volume 63, Issue 1, Page 208-228, January 2021. Deep learning has achieved remarkable success in diverse applications; however, its use in solving partial differential equations (PDEs) has...

By Nicholas A. Battista SIAM Review, Volume 63, Issue 1, Page 181-207, January 2021. While students may find spline interpolation quite digestible based on their familiarity with the continuity of a function and...

By Bengt Fornberg SIAM Review, Volume 63, Issue 1, Page 167-180, January 2021. The trapezoidal rule uses function values at equispaced nodes. It is very accurate for integrals over periodic intervals, but...

By Michelle Feng and Mason A. Porter SIAM Review, Volume 63, Issue 1, Page 67-99, January 2021. A crucial step in the analysis of persistent homology is the transformation of data into an appropriate topological object...

By Juan Kuntz, Philipp Thomas, Guy-Bart Stan, and Mauricio Barahona SIAM Review, Volume 63, Issue 1, Page 3-64, January 2021. Computing the stationary distributions of a continuous-time Markov chain (CTMC) involves solving a set of linear equations. In most...

By Nour Riman, Jonathan D. Victor, Sebastian D. Boie, and Bard Ermentrout SIAM Review, Volume 63, Issue 1, Page 100-120, January 2021. Animals use stereo sampling of odor concentration to localize sources and follow odor trails. We analyze the dynamics of...

By Xavier Allamigeon, Pascal Benchimol, Stéphane Gaubert, and Michael Joswig SIAM Review, Volume 63, Issue 1, Page 123-164, January 2021. Tropical geometry has been recently used to obtain new complexity results in convex optimization and game theory. In this...

By Misha E. Kilmer SIAM Review, Volume 63, Issue 1, Page 65-65, January 2021. We have two Research Spotlights papers in the lineup this issue. The first of these, “Persistent Homology of...

By Darinka Dentcheva SIAM Review, Volume 63, Issue 1, Page 165-166, January 2021. This issue of SIAM Review presents three papers in the Education section. The first paper, “Improving the Accuracy of...

By J. M. Sanz-Serna SIAM Review, Volume 63, Issue 1, Page 1-1, January 2021. The use of probabilistic ideas by applied mathematicians has seen a continued increase in recent decades. Probability now...

By The Editors SIAM Review, Volume 63, Issue 1, Page 121-121, January 2021. The SIGEST article in this issue is “What Tropical Geometry Tells Us about the Complexity of Linear Programming,” by...

By Volker H. Schulz SIAM Review, Volume 63, Issue 1, Page 231-245, January 2021. The section opens with a review well written by a giant in the field of numerical solution of partial...

By Avinash Kulkarni and Antonio Lerario SIAM Journal on Applied Algebra and Geometry, Volume 5, Issue 1, Page 28-59, January 2021. We prove a $p$-adic version of the integral geometry formula for averaging the intersection...

By Neriman Tokcan, Jonathan Gryak, Kayvan Najarian, and Harm Derksen SIAM Journal on Applied Algebra and Geometry, Volume 5, Issue 1, Page 1-27, January 2021. We develop algebraic methods for computations with tensor data. We give three applications: extracting...

By Ernest Davis
Shape: The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else. By Jordan Ellenberg. Penguin Press, New York, NY, May 2021. 480 pages, $28.00. ...

Mathematics and statistics play a vital part in everyday life. Mathematical and statistical techniques are used to help solve real-world problems, focusing on topics such as disease spread, ...

By Meghan Rhodes , Vaughn Gzenda , and Vakhtang Putkaradze
Figure skating is a popular athletic endeavor, even taking the prime-time slot during televised broadcasts of major sporting ...

The Pioneer Prize is awarded every four years at the International Council for Industrial and Applied Mathematics (ICIAM) Congress to one individual for pioneering work introducing applied mathematical methods and scientific computing techniques to an industrial problem area or a new scientific field of applications. Nominations can be submitted via the ICIAM website.

The George Pólya Prize in Mathematics was established in 1992 as an extension into other fields of the George Pólya Prize in Combinatorics. It is awarded in areas of interest to George Pólya not covered by SIAM’s other Pólya Prizes.

The prize was established in 1986 in memory of Richard C. DiPrima, who served SIAM for many years and in 1979–1980 as SIAM President. It aims to recognize an early career researcher in applied mathematics and is based on the doctoral dissertation.

This joint prize was established in 2002 to honor Sonia Kovalevsky and her work on the theory of differential equations. It is awarded to anyone in the scientific or engineering community whose work highlights the achievements of women in applied and computational mathematics. Nominations can be submitted via the AWM website.

The SIAM Student Paper Prize is awarded annually to the student author(s) of the most outstanding paper(s) accepted by SIAM journals within the three years preceding the nomination deadline. Starting with the 2018 award, the focus of the prize is to recognize outstanding scholarship by students in SIAM journals.

This prize was created in 2013 to emphasize George Pólya’s legacy of communicating mathematics effectively. It joins two long-standing Pólya prizes SIAM has awarded in combinatorics and other fields beginning in 1969.

Established in 1998 in memory of Ralph E. Kleinman, the prize recognizes contributions that bridge the gap between high-level mathematics and engineering problems. The award is based on the quality and impact of the mathematics.

Established in 2016, the prize is awarded to an individual in their early career for research contributions to the field of algebraic geometry and its applications.

Established in 2018, the prize is awarded to an early career researcher for recent research contributions in the field of geometric design and processing.

Established in 1967, the prize honors George David Birkhoff (1884-1944), who served as the American Mathematical Society (AMS) President during 1925-1926. The prize is awarded every three years by SIAM and AMS for an outstanding contribution to applied mathematics. Nominations can be submitted via the AMS website.

Through the generosity and inspiration of Gerald and Judith Porter, the Mathematical Association of America (MAA), American Mathematical Society (AMS), and SIAM offer this annual lecture at the Joint Mathematics Meetings. The lecture, first awarded in 2010, is given on a mathematical topic accessible to the broader community.

Named in honor of I. E. Block, a co-founder and the first managing director of SIAM, this lecture is open to the public at the SIAM Annual Meeting. It is intended to encourage public appreciation of applied mathematics and computational science by reaching out to the local community.

Established in 1959, the prize honors John von Neumann, a founder of modern computing. The prize is awarded annually for distinguished contributions to applied mathematics and for the effective communication of these ideas to the community.

The JPBM Communications Award is given annually to reward and encourage communicators who, on a sustained basis, bring mathematical ideas and information to non-mathematical audiences. The prize may be awarded in two categories: For Public Outreach and For Expository and Popular Books. Nominations can be submitted via the AMS website.

Established in 1967, the prize honors Norbert Wiener, a founder of the field of cybernetics. The prize is awarded every three years by SIAM and the American Mathematical Society (AMS) for an outstanding contribution to applied mathematics. Nominations can be submitted via the AMS website.

The prize recognizes students for outstanding solutions to real world math problems. It is awarded to two of the teams judged "Outstanding" in the Mathematical Contest in Modeling (MCM) administered annually by the Consortium for Mathematics and Its Applications (COMAP). Registration is accepted via the COMAP website.

The SIAM Outstanding Paper Prize is not currently active. For the 20 years before it was discontinued in 2019, the SIAM Outstanding Paper Prizes brought attention to papers published in SIAM journals. Three awards were made each year to the authors of papers deemed by SIAM journal editors-in-chief worthy of particular attention.

The prize, established in 1985 and originally intended to be awarded periodically, is now awarded annually for contributions to the advancement of applied mathematics on the national or international level.

This group is concerned with the mathematical and computational issues that arise in generating and processing geometric information for various engineering applications, such as mechanical design, process planning, and manufacturing. The scope of the group's activities encompasses a wide spectrum of scientific, technological, and other skills, ranging from rigorous mathematics to the subjective aesthetics of shape.

The purpose of this activity group is to bring together researchers who use algebraic geometry in industrial and applied mathematics. "Algebraic geometry" is interpreted broadly to include at least: algebraic geometry, commutative algebra, noncommutative algebra, symbolic and numeric computation, algebraic and geometric combinatorics, representation theory, and algebraic topology.

SIAM Journal on Applied Algebra and Geometry (SIAGA) journal publishes research articles of exceptional quality on the development of algebraic, geometric, and topological methods with a strong connection to applications. Mathematical areas covered include algebraic geometry, algebraic and topological combinatorics, algebraic topology, commutative and noncommutative algebra, convex and discrete geometry, differential geometry, multilinear and tensor algebra, number theory, representation theory, symbolic and numerical computation.

Multiscale Modeling & Simulation
SIAM J. on Applied Algebra and Geometry
SIAM J. on Applied Dynamical Systems
SIAM J. on Applied Mathematics
SIAM J. on Computing
SIAM J. on Control and Optimization
SIAM J. on Discrete Mathematics
SIAM J. on Financial Mathematics
SIAM J. on Imaging Sciences
SIAM J. on Mathematical Analysis
SIAM J. on Matrix Analysis and Applications
SIAM J. on Numerical Analysis
SIAM J. on Optimization
SIAM J. on Scientific Computing
SIAM/ASA J. on Uncertainty Quantification
SIAM Review
Theory of Probability & Its Applications

General Opportunities

We know it can be overwhelming to keep track of career opportunities that may be relevant to you as a member of the SIAM community. So, we’ve compiled lists of some of our favorite fellowship, internship, and research opportunities. Check ‘em out!

Fellowships

Looking for financial support to further your research? Fellowships often provide funding plus experiential learning opportunities to young researchers. Learn more about fellowship opportunities.

Internships allow you to network and forge connections for future job possibilities, while also exploring possible areas of interest. Look at this list of companies who offer valuable opportunities.

Our community is founded on igniting groundbreaking developments in applied math and computational science. Take a deeper dive into your area of study with one of these opportunities.