SIAM-Simons Undergraduate Summer Research Program

Summer Research Program

SIAM-Simons Undergraduate Summer Research Program

The SIAM-Simons Undergraduate Summer Research Program establishes five sites across the United States each year for a summer program of research and learning in applied mathematics and computational science.

About the Program


Each year, the SIAM-Simons Undergraduate Summer Research Program establishes five sites across the United States for a program of research and learning in applied mathematics and computational science. One faculty mentor and two students at each site will work together as participants learn how to conduct scientific research, effectively communicate mathematics and computational science principles, and gain an improved understanding of how they can pursue a career in applied mathematics and computational science. Students and mentors from the five sites will come together via video conference to present their work, participate in professional development activities, and engage in community-building initiatives to bring all participants together and foster a strong sense of belonging.

Students accepted to the program will:

  • Receive a weekly stipend, and expenses for lodging, meals, and travel will also be covered
  • Visit the Flatiron Institute in Manhattan
  • Attend the SIAM Annual Meeting the following year to present their research project

This program targets U.S. students from groups underrepresented in applied mathematics and computational mathematics in the U.S., specifically ethnic minorities (African American/Black, Hispanic, Native American/Indigenous Peoples, Native Alaskan, Native Hawaiian/Other Pacific Islander). The program is intended to broaden participation in mathematics by students who are underrepresented and historically marginalized in our discipline.

Apply to be a Participant

Applications to participate in summer 2024 are closed. Applications for summer 2025 will open in December of 2024.

Eligibility Criteria

You are eligible to apply if you meet the following criteria:

  • you will be an undergraduate in September 2024 (that is, you have not yet earned a bachelor’s degree)
  • you are enrolled in a college/university in the U.S.
  • you are a U.S. citizen or permanent resident

Required Materials

Applicants will be asked to submit:

  • a written statement regarding their interest in the program,
  • college transcripts, and
  • two (2) letters of recommendation.

Research Projects in 2024

Central Washington University

Interest Rate Modeling and Asset Pricing in Incomplete Markets
The modern approach to quantitative finance is as deeply connected to the mathematical tools utilized as it is to the financial economic theory it is based upon. In this project, we will apply basic linear algebra, optimization, and statistical tools to the areas of research and practice in the financial, banking and insurance sectors. Our approach is two-fold: In the area of fixed-income securities, we will utilize a time series econometrics-based framework to the modeling, analysis and forecasting of interest rate dynamics. In the area of behavioral finance, we will apply option-theoretic approach to explore the issues in pricing and optimization in incomplete markets.

Sooie-Hoe Loke

Mentor: Sooie-Hoe Loke

Purdue University

Characterizing Biological Patterns Using Optimal Transport and Topological Data Analysis
Patterns are present all around us in nature: examples include butterfly wings, stripes and spots in fish skin, venation on leaves, and fur on cats. Across these examples, determining whether two patterns are similar or different is often a qualitative process. But how similar is “similar”, and in what ways are two images of biological patterns different? Addressing this question can help provide insight into when genetic mutations and evolution give rise to different patterns and tissue. To do so, we need quantitative approaches that allow us to summarize many patterns in detail. In this project, we will distinguish and characterize images of biological patterns using computational methods from optimal transport and topological data analysis. For example, we may use persistent homology to quantify the “shape of data” or apply optimal-transport approaches to “morph” one image of a biological pattern into another and measure the difference between them.

Alexandria Volkening

Mentor: Alexandria Volkening

San Francisco State University

Fun at the Intersection of Linear Algebra and Probability
Our project will focus on strengthening our foundation in linear algebra. We will study randomized methods for efficiently representing the column space (range) of matrices in order to build robust and effective algorithms for facial recognition, music recommendation and cancer detection.

Henry Boateng

Mentor: Henry Boateng

Simpson College

Data Augmentation Applied to Tabular Data
Classification methods have become valuable tools in multiple sectors of society. Examples of classification applications include self-driving cars, ad targeting, fraud detection, face recognition, protein function prediction, and medical diagnosis. Due to its extensive use, scientists have developed powerful machine-learning techniques for data classification. One of the issues with current state-of-the-art classification approaches, such as deep learning, is that these require lots of data. However, collecting sufficient data to create reliable models is not always possible. For example, data collected from patients can be time-consuming and costly or even impossible if they no longer want to participate in the data collection. In Computer Vision, researchers get around the lack of data by applying data augmentation approaches. Data augmentation refers to creating new data points without collecting any further data. For example, in Computer Vision, new images are created by rotating, scaling, flipping, or recoloring the original image set. This process is applied so that machine learning techniques have large enough data sets to classify data accurately. We will develop and test our data augmentation methods with real tabular data, or data organized by rows and columns, to see how well our techniques keep the intrinsic patterns and if accuracy is improved.

Dr. Vazquez Landrove

Mentor: Dr. Vazquez Landrove

University of Delaware

Biomimetic Design Criteria for Self-Assembly and Self-Folding Viral Capsid Models
Many complex biological structures are formed by random processes (entropy-driven), and we seek to understand how complex, beautiful structures self-organize. In our lab, we are particularly focused on viral capsids such as the now familiar COVID structure that has recently received so much attention. We will focus on three avenues: (1) self-folding origami: developing new measurable variables associated with symmetry properties of planar nets of icosahedra and testing them with an origami simulator to see which nets fold quickly, completely, and without imperfections; (2) self-assembling physical models: developing quasicrystalline models (e.g., using tiles such as the recently discovered uni-tiles as well as Penrose kites and darts) of viral capsids and seeing if we can get them to self-assemble; and, (3) conducting form finding analyses of tensegrity expandohedra models of viral capsids: build models that expand from an icosahedron to an icosadodecahedron. Geometrically, viral capsids are of two different types: icosahedra (and higher level versions with 60, 120, 180, etc. individual subunits) and helices. Some icosahedra-type viral capsids do not fit a classic Goldberg polyhedral model, but are quasicrystals instead. We have successfully produced 4D printed (both self-assembled and self-folded) meso-models of viral capsids with up to 60 subunits. We have a database of Dürer nets and Schlegel diagrams of all 43, 380 configurations of dodecahedra and icosahedra. Besides building physical models that self-fold by placing them in warm water, we analyze their self-follding by using an origami simulator. While we have analyzed many configurations for their foldability and found that the number of vertex connections on a Dürer net is well correlated to self-foldability, there is considerable variation within vertex connections subgroups. If you enjoy three dimensional puzzles and visualization, learning about 3D printing and laser cutting, and mathematical problem solving, please consider coming to our lab at the Delaware Biotechnology Institute at the University of Delaware.

John R. Jungck

Mentor: John R. Jungck

Apply to be a Mentor

Mentors are selected from SIAM’s experienced and highly qualified member base to work closely with the student participants and SIAM. While mentors do oversee the research activities of the participants, they also serve as a primary connection between the participants and the applied math community broadly, helping them feel connected and welcomed.

Applications to be a mentor for summer 2024 are closed. Applications for summer 2025 will open in summer 2024.

About the Simons Foundation

The Simons Foundation, co-founded in 1994 by Jim and Marilyn Simons, works to advance the frontiers of research in basic science and mathematics. The foundation provides grants to individual investigators and their projects through academic institutions and conducts in-house scientific research supporting teams of top computational scientists through its Flatiron Institute. Jim and Marilyn Simons co-chair the foundation’s board.

SIAM is incredibly grateful to the Simons Foundation for funding this important program (award number 1036702) that will provide support and career advancement opportunities for undergraduate students who are historically underrepresented in the mathematical and computational sciences.

Program History

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