The virtual program runs from the end of June through the beginning of August. Faculty commitment is a few hours per week, working with a group of three or four high school students. IMD can also provide undergraduate teaching assistants. Faculty will receive stipends for their participation.

Projects can be theoretical or empirical, and many involve analysis of real-life data. Some of the past projects include the study of properties of voting methods, the influence of court decisions on measures of gerrymandering, modeling proportional representation in the U.S., and analyzing the effect of alternative sizes and apportionments of House of Representatives on presidential elections. 

If you are interested in being a faculty mentor for this program or to learn more about it, please email us at contact@math-democracy.org.

We look forward to working with you to support student engagement with mathematics and democracy!

The post Seeking Faculty Mentors for 2026 High School Summer Research Program appeared first on Institute for Mathematics and Democracy.

All students and faculty also meet once a week for guest lectures given by prominent mathematicians and democracy reformers. One session is dedicated to a discussion of the college application process and the final session consists of presentations of the projects (here are some of the presentations from the 2025 program*).

If you’re a high school student interested in participating in IMD’s summer 2026 online research program, visit this page. Linked there is a form you should fill out to apply by March 6, 2026.

If you have any questions, feel free to write to us at contact@math-democracy.org. We are looking forward to reading your application!

The post Apply Now: 2026 IMD Summer High School Research Program appeared first on Institute for Mathematics and Democracy.

High school students Serena Pallan, Ananya Shah, and Zubin Rajesh met while working on gerrymandering research through IMD’s summer program, where they developed geometric proofs that create guidelines to determine what is political gerrymandering and what is a fair drawing of district lines. Now, together with fellow students Thea Vedula and Angelina Wang, they are translating their research into action.

In their recent op-ed for The Fulcrum, they share their plans to use a Carnegie Young Leaders for Civic Preparedness grant, awarded to 100 teams nationwide, to address gerrymandering by combining math with civic action. Through their work, they “hope to inspire local communities to challenge district lines that deny representation, states to establish independent redistricting commissions, and Congress to pass reforms that protect fair elections… mak[ing] change that lasts beyond news cycles and AP Government flashcards.”

Read more here: https://thefulcrum.us/governance-legislation/gerrybuster-fix-democracy

The post Op-Ed: Too Young to Vote, Not Too Young to Fix Democracy appeared first on Institute for Mathematics and Democracy.

Analyzing Swing States in Presidential Elections: The Case of Wisconsin – Michelle Zuo

This paper quantitatively analyzes county-level voting patterns in Wisconsin’s presidential elections from 2000 to 2024. As a pivotal swing state, Wisconsin has alternated between Democratic and Republican candidates since 2012. Using data from the Wisconsin Elections Commission, we examine vote totals across 72 counties and seven election cycles. Pearson correlations measure similarity in county voting trajectories, while choropleth maps visualize spatial shifts. Results show strong clustering of vote changes: Democratic and Republican gains between 2016 and 2020 were concentrated in southeastern urban and suburban counties, with rural areas showing little change. Correlations reveal a north-south divide, as southern counties exhibit similar trends and northern ones diverge. These findings highlight spatial heterogeneity in electoral dynamics and the decisive role of urban mobilization in statewide outcomes.

A Comparison of Precinct and District Voting Data Using Persistent Homology to Identify Gerrymandering in North Carolina – Ananya Shah

Gerrymandering is one of the biggest threats to American democracy. By manipulating district lines, politicians effectively choose their voters rather than the other way around. Current gerrymandering identification methods (namely the Polsby-Popper and Reock scores) focus on the compactness of congressional districts, making them extremely sensitive to physical geography. To address this gap, we extend Feng and Porter’s 2021 paper, which used the level-set method to turn geographic shapefiles into filtered simplicial complexes, in order to compare precinct level voting data to district level voting data. As precincts are regarded as too small to be gerrymandered, we are able to identify discrepancies between precinct and district level voting data to quantify gerrymandering in the United States. By comparing the persistent homologies of Democratic voting regions at the precinct and district levels, we detect when areas have been “cracked” (split across multiple districts) or “packed” (compressed into one district) for partisan gain. This analysis was conducted for North Carolina House of Representatives elections (2012-2024). North Carolina has been redistricted four times in the past ten years, unusually frequent as most states redistrict decennially, making it a valuable case study. By comparing persistence barcodes at the precinct and district levels (using the bottleneck distance), we show that precinct level voting patterns do not significantly fluctuate biannually, while district level patterns do, suggesting that shifts are likely a result of redistricting rather than voter behavior, providing strong evidence of gerrymandering. This research presents a novel application of topological data analysis in evaluating gerrymandering and shows persistent homology can be useful in discerning gerrymandered districts.

The post IMD High School Summer Researchers Release Research Papers appeared first on Institute for Mathematics and Democracy.

Photo credit: The 2025 Carnegie Young Leaders for Civic Preparedness convene, via Institute for Citizens & Scholars

The post IMD High School Program Alums Win Carnegie Young Leaders Fellowship appeared first on Institute for Mathematics and Democracy.

Dr. Karen Saxe is Associate Executive Director of the American Mathematical Society and Director of their Office of Government Relations. She represents the 30,000 members of the AMS in science policy discussions at the federal level and connects the math community to decision-makers in Washington, DC. She is also Professor Emerita at Macalester College, where she taught for almost 30 years.

Rachel Hutchinson is Senior Policy Analyst at FairVote, an organization working toward better elections and a more representative democracy. Alongside her work at FairVote in ranked choice voting (RCV) and proportional representation, her areas of research include primary elections, voter behavior, and political polarization.

We would like to express our gratitude to these speakers for sharing their expertise and invaluable insights into math and policy with our high school researchers. 

The post Guest Speakers Visit IMD’s High School Summer Research Program appeared first on Institute for Mathematics and Democracy.

Siddhi Bharadwaj is a rising senior at Pleasant Valley High School in Iowa. She has always enjoyed math and social studies and is excited to explore the intersection of these fascinating subjects this summer. She is interested in public health and is currently working to raise awareness about iron-deficiency in women. She can’t wait to embark on this journey with IMD!

Boston Bulis is a rising senior at Newton South High School in Massachusetts with a passion for government, reducing political polarization, and understanding how policy and legislation impact different communities. They love all things math and are especially excited to explore its applications in real-world, democratic issues. On weekends, Boston enjoys researching and debating a range of topics with their high school’s debate team (PF). They’re particularly interested in number theory and group theory, and how abstract math connects to systems of governance. This summer, Boston is thrilled to be pursuing research at IMD, and is passionate about exploring the intersection of mathematics, politics, and democracy. In their free time, they enjoy throwing pottery and making short films.

Aditya Chiduruppa is a rising senior at Lexington High School in Massachusetts. He is drawn to mathematical and machine learning methods that tackle real-world problems, especially in areas where data-driven decisions shape society. At IMD, Adi looks forward to exploring the use of computational research methods to help strengthen democratic systems in ways that promote fairness and access.

Alexandra Cirino is a rising junior at Shorecrest Preparatory School. As someone passionate about both mathematics and social justice, Alex is excited to explore how quantitative tools can support more equitable democratic systems. She serves as the president of her school’s feminism club, where she leads discussions and initiatives focused on gender equity and civic awareness. Through the Institute for Mathematics and Democracy’s summer program, she hopes to connect her interest in advocacy with data-driven research that informs real-world change.

Truman Edell is from New York, New York. He is an American patriot and history buff, spending his summers interning at Congress in DC, where he worked on tax and educational access policy as well as taking college-level math-driven, public policy coursework. During the school year, while enrolled at The Ramaz School, his free time is spent working with those in need through UJA’s PACT program, at swim and krav maga practice or editing a novel he wrote with his best friend. Fun fact: Truman is a certified deep, open-water scuba rescue diver (like an underwater emergency medical technician).

Erik Hill is a rising freshman at Rice University where he plans to double major in computational applied mathematics and economics. He is passionate about finding ways to use rigorous mathematical methods to approach real-world problems. He aspires to pursue a career in research where he can continue to use his mathematical abilities to benefit humanity.

Jeev Hora is a rising Illinois senior interested in math, statistics and social science. He’s always been interested in these fields, and wants to explore their intersection through IMD. At IMD, he’s interested in being with a community of like-minded peers who want to use the mathematical and statistical sciences for good.

Gabby Licayan is a rising senior at Thomas Jefferson High School for Science and Technology in Alexandria, Virginia with a strong passion in politics, civic engagement, and public policy. They are excited to explore how data and mathematics can be used to strengthen democracy and drive positive change in our society, specifically in policy-making.

Rohan Licht is a rising senior at Belmont High School in Massachusetts. Rohan is excited to research the intersection of math and politics at IMD. Politics are usually seen as very subjective, and applying math to politics in order to better understand certain processes and decisions is a fascinating way to remove some of the ambiguity that comes with studying something like politics.

Serena Pallan is a junior from Baltimore, Maryland, and this is her third year with the Institute of Math and Democracy! Serena’s research at IMD is focused on exploring generalizations of Condorcet paradoxes within voting sets that follow a one-dimensional spatial structure.

Rishan Paul is a rising senior at Eastlake High School in Sammamish, Washington. He has always had a deep passion for politics and mathematics, and he is ecstatic to combine the two interests into one. He has been hooked on both since he watched a political debate and did a simple addition problem. He hopes to use what he has learned from this program to develop his understanding of how data shapes policy decisions, voter behavior, and campaign strategies. He is incredibly grateful and excited to work with the IMD program to meet new people and research more about this rising field.

Ananya Shah is a rising senior at Edgemont Junior-Senior High School in New York. Her current research focuses on using mathematics, specifically using persistent homology to compare precinct and district level voting data to quantify gerrymandering in the United States At IMD, she is excited about collaborating with other individuals who are also interested in the fascinating connection between mathematics and democracy.

Ryan Singh is a rising senior at Thomas Jefferson High School for Science and Technology in Alexandria, Virginia. He has always taken an interest in numbers and math, and aspires to understand their relationship with behavioral phenomena and influences on public policy. He is excited to work under IMD to “use experiences in research and mathematics to work towards solving nationwide, real-world problems, starting from the root sources of human hope: government, politics, and democracy.”

Tanya Verma is a rising senior at Riverdale Country School. She has always been interested in applied math and statistics, as well as history, politics, and current events, and believes that there is a need for more statistics-based policy in today’s government. She is ecstatic to join IMD and use math to create real-world changes.

Brandon Wu is a rising senior at St. John’s School in Houston, Texas. He is interested in the intersection of applied mathematics and government, particularly in areas such as democratic representation, legislation, and animal welfare. He looks forward to collaborating on research that applies math to public policy issues at IMD this summer.

Yuegelica Yeong is a rising senior from Austin, Texas. She is incredibly passionate about both mathematics and politics and is eager to explore their intersection this summer. At IMD, she is looking forward to applying mathematical techniques to solve real-world policy problems, utilizing real-data to research aspects of the government, and analyzing challenges that our democracy faces today.

Michelle Zuo is a rising senior at Thomas Jefferson High School for Science and Technology in Alexandria, Virginia. She has always been interested in math and in using math to solve real-world public policy issues. At IMD, she hopes to conduct research that uses applied math and complex models to help make impactful decisions in the field of democracy.

IMD is excited to host these students and supervise their research this summer. Stay tuned for more updates about the program!

The post Introducing the 2025 High School Summer Research Cohort appeared first on Institute for Mathematics and Democracy.

Dr. Wilson plans to involve her new high school summer research team in the project this year, looking at multi-winner voting methods from both theoretical and quantitative perspectives. We are excited to see how their work evolves this summer!

The post IMD Affiliate and High School Researchers Studying Bloc Voting appeared first on Institute for Mathematics and Democracy.

IMD co-founder Stanley Chang is a professor of mathematics at Wellesley College. Jing Russell, a student at Amherst College and former IMD high school researcher, will work alongside Prof. Chang as a teaching assistant. Below is their project description.

“Our goal is to study weakly increasing ranked voting and perhaps to find ways to use poset and Moebius inversion theory to study them. Also we wish to examine stability and noise reduction in voting methods, i.e. votes that are counted incorrectly, using orthonormal systems and Fourier filtering. The hope is to use linear algebra and combinatorics heavily to arrive at some theorems.”

Natasa Dragovic (University of Saint Thomas) is interested in the intersection of probability and dynamical systems. Her research involves using mathematical models of opinion dynamics to make sense of political phenomena. See her project description below.

“We will study how voter opinions influence political candidates’ optimal positions. More specifically, we will look into three candidate elections. How often do we have the same winner whether the election is conducted under plurality voting or ranked choice? How are the candidates behaving under ranked choice when we consider different scenarios of voter opinions?”

Keaton Quinn (Wellesley College) is interested in the geometry of districting. His group will look into gerrymandering and the efficacy of redistricting in reducing it. This is his project description:

“We will study the isoperimetric inequality and its uses in attempting to detect gerrymandering (i.e., the Polsby Popper score of a district). We will then focus on explicitly computing these scores for maps before/after redistricting has been performed, as a potential way of determining if intentional redistrictings are effective at reducing gerrymandering.”

IMD co-founder Ismar Volić is a professor of mathematics at Wellesley College. This summer, his group will study proportional representation and multi-winner elections. The following outlines his project goals. 

“This project will be about proportional representation and modeling multi-member districts in the United States. The main question is whether a generalization of ranked choice voting to multi-winner elections, called single transferable vote, would yield more representative outcomes. We will also model party list systems used in most of the world’s democracies and see whether their implementation in the U.S. is feasible.”

Jennifer Wilson, Associate Professor of Mathematics at the New School, has research interests spanning various applications of mathematics to politics and voting systems. Leo Powers, a student at Oberlin College studying mathematics and politics, will be her teaching assistant. They plan to “study Bloc Voting and other multi winner voting methods using a one-dimensional spatial model to represent political opinions” and to “look at the methods from both a theoretical (fairness) perspective and a quantitative perspective.”

Thank you to all of the mentors and teaching assistants for their integral roles in the program. We look forward to seeing the work their teams will do this summer. Stay tuned for more research updates!

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If you’re a high school student interested in participating in IMD’s summer 2025 online research program, visit this page. Linked there is a form you should fill out to apply by March 7, 2025.

If you have any questions, feel free to write to us at contact@math-democracy.org. We are looking forward to reading your application!

Support for the 2025 IMD High School Summer Research Program is provided by the Mathematical Association of America and the Mary P. Dolciani Halloran Foundation.

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