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.

By Patrick De Leenheer SIAM Review, Volume 62, Issue 3, Page 716-726, January 2020. We present an elementary proof of a generalization of Kirchhoff's matrix tree theorem to directed, weighted graphs. The proof...

By Lek-Heng Lim SIAM Review, Volume 62, Issue 3, Page 685-715, January 2020. This is an elementary introduction to the Hodge Laplacian on a graph, a higher-order generalization of the graph Laplacian....

By Andrii Mironchenko and Christophe Prieur SIAM Review, Volume 62, Issue 3, Page 529-614, January 2020. In a pedagogical but exhaustive manner, this survey reviews the main results on input-to-state stability (ISS) for infinite-dimensional systems....

By Ernesto Estrada, Gissell Estrada-Rodriguez, and Heiko Gimperlein SIAM Review, Volume 62, Issue 3, Page 617-645, January 2020. In a complex system, the interplay between the internal structure of its entities and their interconnection may play a...

By Jed A. Duersch and Ming Gu SIAM Review, Volume 62, Issue 3, Page 661-682, January 2020. Rank-revealing matrix decompositions provide an essential tool in spectral analysis of matrices, including the Singular Value Decomposition (SVD) and...

By Vicky Chuqiao Yang, Daniel M. Abrams, Georgia Kernell, and Adilson E. Motter SIAM Review, Volume 62, Issue 3, Page 646-657, January 2020. Since the 1960s, Democrats and Republicans in the U.S. Congress have taken increasingly polarized positions, while the public's policy...

By Patrick De Leenheer SIAM Review, Volume 62, Issue 3, Page 716-726, January 2020. We present an elementary proof of a generalization of Kirchhoff's matrix tree theorem to directed, weighted graphs. The proof...

By Lek-Heng Lim SIAM Review, Volume 62, Issue 3, Page 685-715, January 2020. This is an elementary introduction to the Hodge Laplacian on a graph, a higher-order generalization of the graph Laplacian....

By Andrii Mironchenko and Christophe Prieur SIAM Review, Volume 62, Issue 3, Page 529-614, January 2020. In a pedagogical but exhaustive manner, this survey reviews the main results on input-to-state stability (ISS) for infinite-dimensional systems....

By Ernesto Estrada, Gissell Estrada-Rodriguez, and Heiko Gimperlein SIAM Review, Volume 62, Issue 3, Page 617-645, January 2020. In a complex system, the interplay between the internal structure of its entities and their interconnection may play a...

By Jed A. Duersch and Ming Gu SIAM Review, Volume 62, Issue 3, Page 661-682, January 2020. Rank-revealing matrix decompositions provide an essential tool in spectral analysis of matrices, including the Singular Value Decomposition (SVD) and...

By Vicky Chuqiao Yang, Daniel M. Abrams, Georgia Kernell, and Adilson E. Motter SIAM Review, Volume 62, Issue 3, Page 646-657, January 2020. Since the 1960s, Democrats and Republicans in the U.S. Congress have taken increasingly polarized positions, while the public's policy...

By Darinka Dentcheva SIAM Review, Volume 62, Issue 3, Page 683-683, January 2020. This issue of SIAM Review contains two papers in the Education section. The first paper, “Hodge Laplacians on Graphs,”...

By Misha E. Kilmer SIAM Review, Volume 62, Issue 3, Page 615-615, January 2020. In this issue, Research Spotlights features two exciting and topically diverse articles. The authors of the first article...

By J. M. Sanz-Serna SIAM Review, Volume 62, Issue 3, Page 527-527, January 2020. Andrii Mirochenko and Christophe Prieur are the authors of “Input-to-State Stability of Infinite-Dimensional Systems: Recent Results and Open Questions,”...

By Volker H. Schulz SIAM Review, Volume 62, Issue 3, Page 729-739, January 2020. These are difficult times, but some circumstances make the work in our Book Reviews section even more difficult. Due...

By The Editors SIAM Review, Volume 62, Issue 3, Page 659-659, January 2020. The SIGEST article in this issue, “Randomized Projection for Rank-Revealing Matrix Factorizations and Low-Rank Approximations,” by Jed A. Duersch...

By Bachir El Khadir SIAM Journal on Applied Algebra and Geometry, Volume 4, Issue 2, Page 377-400, January 2020. A convex form of degree larger than one is always nonnegative since it vanishes...

By Julian Dörfler, Christian Ikenmeyer, and Greta Panova SIAM Journal on Applied Algebra and Geometry, Volume 4, Issue 2, Page 354-376, January 2020. Geometric complexity theory is an approach towards the separation of fundamental algebraic complexity classes....

By Nicolás Botbol, Laurent Busé, Marc Chardin, and Fatmanur Yildirim SIAM Journal on Applied Algebra and Geometry, Volume 4, Issue 2, Page 322-353, January 2020. We contribute a new algebraic method for computing the orthogonal projections of a point...

By Max Lieblich and Lucas Van Meter SIAM Journal on Applied Algebra and Geometry, Volume 4, Issue 2, Page 297-321, January 2020. We study multiview moduli problems that arise in computer vision. We show that these...

By Ling Guo, Akil Narayan, and Tao Zhou SIAM Review, Volume 62, Issue 2, Page 483-508, January 2020. Polynomial approximations constructed using a least-squares approach form a ubiquitous technique in numerical computation. One of the simplest ways...

By Lloyd N. Trefethen SIAM Review, Volume 62, Issue 2, Page 439-462, January 2020. Boundary-value problems involving the linear differential equation $\varepsilon y'' - x y' + y = 0$ have surprising properties...

By Yair Carmon and John C. Duchi SIAM Review, Volume 62, Issue 2, Page 395-436, January 2020. We consider minimization of indefinite quadratics with either trust-region (norm) constraints or cubic regularization. Despite the nonconvexity of these...

By Anne Greenbaum, Ren-Cang Li, and Michael L. Overton SIAM Review, Volume 62, Issue 2, Page 463-482, January 2020. We present first-order perturbation analysis of a simple eigenvalue and the corresponding right and left eigenvectors of a general...

By Philipp Grohs, Sarah Koppensteiner, and Martin Rathmair SIAM Review, Volume 62, Issue 2, Page 301-350, January 2020. The problem of phase retrieval, i.e., the problem of recovering a function from the magnitudes of its Fourier...

By Michael T. Schaub, Austin R. Benson, Paul Horn, Gabor Lippner, and Ali Jadbabaie SIAM Review, Volume 62, Issue 2, Page 353-391, January 2020. Using graphs to model pairwise relationships between entities is a ubiquitous framework for studying complex systems and data. Simplicial...

By Volker H. Schulz SIAM Review, Volume 62, Issue 2, Page 511-526, January 2020. I am writing these lines in April 2020 while science is in lockdown mode globally. They will be published...

By The Editors SIAM Review, Volume 62, Issue 2, Page 393-393, January 2020. The SIGEST article in this issue, “First-Order Methods for Nonconvex Quadratic Minimization,” by Yair Carmon and John C. Duchi,...

By Misha E. Kilmer SIAM Review, Volume 62, Issue 2, Page 351-351, January 2020. The current issue of SIAM Review features the Research Spotlights article “Random Walks on Simplicial Complexes and the Normalized...

By Darinka Dentcheva SIAM Review, Volume 62, Issue 2, Page 437-438, January 2020. The Education section of SIAM Review presents three papers in this issue. In the first paper Lloyd N. Trefethen...

By J. M. Sanz-Serna SIAM Review, Volume 62, Issue 2, Page 299-299, January 2020. In a previous issue of SIAM Review, I started my introduction to the Survey and Review section by saying...

By Andreas Bluhm and Ion Nechita SIAM Journal on Applied Algebra and Geometry, Volume 4, Issue 2, Page 255-296, January 2020. In this work, we establish the connection between the study of free spectrahedra and...

By Sandra Di Rocco, David Eklund, and Madeleine Weinstein SIAM Journal on Applied Algebra and Geometry, Volume 4, Issue 1, Page 227-253, January 2020. A bottleneck of a smooth algebraic variety $X \subset \mathbb{C}^n$ is a pair $(x,y)$...

By Irina A. Kogan, Michael Ruddy, and Cynthia Vinzant SIAM Journal on Applied Algebra and Geometry, Volume 4, Issue 1, Page 185-226, January 2020. In this paper, we adapt the differential signature construction to the equivalence problem for...

By Michael Lesnick, Raúl Rabadán, and Daniel I. S. Rosenbloom SIAM Journal on Applied Algebra and Geometry, Volume 4, Issue 1, Page 141-184, January 2020. A topological approach to the study of genetic recombination, based on persistent homology, was...

By Volker H. Schulz SIAM Review, Volume 62, Issue 1, Page 283-297, January 2020. The frame for the Book Reviews section this time is formed by the books of two very well known...

By The Editors SIAM Review, Volume 62, Issue 1, Page 197-197, January 2020. The SIGEST article in this issue, “Asymptotically Compatible Schemes for Robust Discretization of Parametrized Problems with Applications to Nonlocal...

By Misha E. Kilmer SIAM Review, Volume 62, Issue 1, Page 131-131, January 2020. Tensors, or multiway arrays, are often used for storage of high-dimensional data. In order to have compression, completion,...

By J. M. Sanz-Serna SIAM Review, Volume 62, Issue 1, Page 1-1, January 2020. Bernard Brogliato and Aneel Tanwani are the authors of “Dynamical Systems Coupled with Monotone Set-Valued Operators: Formalisms, Applications, Well-Posedness,...

By Darinka Dentcheva SIAM Review, Volume 62, Issue 1, Page 229-230, January 2020. The Education section of SIAM Review presents three papers in this issue. In the first paper Robert M. Corless...

By Xiaochuan Tian and Qiang Du SIAM Review, Volume 62, Issue 1, Page 199-227, January 2020. Many problems in nature, being characterized by a parameter, are of interest both with a fixed parameter value...

By Bernard Brogliato and Aneel Tanwani SIAM Review, Volume 62, Issue 1, Page 3-129, January 2020. This survey article addresses the class of continuous-time systems where a system modeled by ordinary differential equations is...

By David Hong, Tamara G. Kolda, and Jed A. Duersch SIAM Review, Volume 62, Issue 1, Page 133-163, January 2020. Tensor decomposition is a fundamental unsupervised machine learning method in data science, with applications including network analysis and sensor...

By Tracy L. Stepien, Eric J. Kostelich, and Yang Kuang SIAM Review, Volume 62, Issue 1, Page 244-263, January 2020. Most undergraduates have limited experience with mathematical modeling. In an effort to respond to various initiatives, such as the...

By Antônio Francisco Neto SIAM Review, Volume 62, Issue 1, Page 264-280, January 2020. In this work we introduce a new operator based approach to matrix analysis. Our main technical tool comprises an...

By Nawaf Bou-Rabee and Miranda C. Holmes-Cerfon SIAM Review, Volume 62, Issue 1, Page 164-195, January 2020. Sticky Brownian motion is the simplest example of a diffusion process that can spend finite time both in the...

By Robert M. Corless and Leili Rafiee Sevyeri SIAM Review, Volume 62, Issue 1, Page 231-243, January 2020. We look at two classical examples in the theory of numerical analysis, namely, the Runge example for interpolation and...

By Mireille Boutin and Gregor Kemper SIAM Journal on Applied Algebra and Geometry, Volume 4, Issue 1, Page 123-140, January 2020. We show that one can reconstruct the shape of a room with planar walls...

By Hans Z. Munthe-Kaas, Ari Stern, and Olivier Verdier SIAM Journal on Applied Algebra and Geometry, Volume 4, Issue 1, Page 49-68, January 2020. Motivated by numerical integration on manifolds, we relate the algebraic properties of invariant connections...

By Wojciech Chachólski and Henri Riihimäki SIAM Journal on Applied Algebra and Geometry, Volume 4, Issue 1, Page 69-98, January 2020. We propose the use of persistent homology in a supervised way. We believe homological...

By R. Amzi Jeffs SIAM Journal on Applied Algebra and Geometry, Volume 4, Issue 1, Page 99-122, January 2020. We define a notion of morphism between combinatorial codes, making the class of all...

By Laurentiu G. Maxim, Jose I. Rodriguez, and Botong Wang SIAM Journal on Applied Algebra and Geometry, Volume 4, Issue 1, Page 28-48, January 2020. The Euclidean distance degree of an algebraic variety is a well-studied topic in applied...

By Alexandros Grosdos Koutsoumpelias and Markus Wageringel SIAM Journal on Applied Algebra and Geometry, Volume 4, Issue 1, Page 1-27, January 2020. In this paper we study ideals arising from moments of local Dirac measures and...

By Kirk Gardner , Kirk E. Jordan , Alex Harrison , James L. McDonagh , Breanndán Ó Conchúir , Thomas J. Peters , and Donald R. Sheehy
While computational topology enjoys considerable ...

Update 7/14/20: Today, the Trump Administration rescinded these proposed rules on foreign students studying online, returning to the previous status quo. Thank you to all of the SIAM members who ...

We may not be able to meet in Toronto for this year’s Joint SIAM/CAIMS Annual Meeting (AN20) , but that doesn’t mean we can’t hold the meeting! SIAM and CAIMS are pivoting to virtual with a ...

By Vishal Patil and Jörn Dunkel
One can trace knot theory in mathematics and theoretical physics back to Lord Kelvin’s 19th century description of atoms as knotted vortices in the ether. ...

It's National Volunteer Week! This occasion is an opportunity to celebrate the dedicated individuals who offer their time in exchange for nothing more than making SIAM (and the world) a better ...

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.

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 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.

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 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.

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.

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.

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 Prizes bring attention to papers published in SIAM journals. Three awards are 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.

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 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.