Schernikau’s poster, “Carbodicarbenes as hydride donor catalysts in the reduction of CO₂,” highlights ongoing work exploring the catalytic potential of carbones, zerovalent carbon compounds that can drive the multi-stage conversion of carbon dioxide into useful products such as N-methylamines.

His research, which he presented at the 2026 ACS Spring Meeting, focuses on the reaction mechanisms that enable carbones, distinct from carbenes, to function as hydride donor catalysts in carbon dioxide reduction pathways. Understanding these mechanisms contributes to broader efforts to develop more efficient catalytic systems for chemical synthesis and carbon utilization.

The award was presented during the Division of Physical Chemistry poster session, where Schernikau’s project was recognized for its scientific rigor and clarity of presentation.

“For Max to be recognized for his exemplary research during the physical chemistry division poster session at the ACS Meeting is a testament to his hard work and wonderfully highlights the high caliber of undergraduate research we do here at 91̽�� Mudd,” said chemistry professor Maduka Ogba.

The ACS Spring Meeting is a national conference featuring research across chemistry disciplines and keynote sessions from leading scientists in the field.

Kavassalis and the research team focus on solving an enduring challenge: Despite decades of progress to improve air quality, ozone pollution remains a persistent health risk to Southern Californians. They are examining how volatile organic compounds (VOCs) released by native plants, particularly California coastal sage scrub species, interact with nitrogen oxide pollution from transportation and industrial sources to influence ozone formation. The Los Angeles region was once covered by coastal sage scrub, but now it exists primarily in fragmented urban and coastal patches. These native ecosystems are critical for maintaining biodiversity and strengthening climate resilience.

Some native plants can emit highly reactive compounds that may accelerate ozone formation under certain urban conditions, especially during extreme heat. The team aims to identify when natural plant emissions do not meaningfully influence air quality, helping support restoration and urban greening efforts that protect both ecosystem health and community air quality. Their work could help reshape how native vegetation is incorporated into urban landscapes and may ensure that restoration and greening efforts deliver climate, water and biodiversity benefits to support healthier air for communities across Southern California.

The research connects atmospheric chemistry, plant ecology and policy, which can offer interdisciplinary opportunities that can exist even beyond the grant’s continuance. Field measurements will be conducted at the Bernard Field Station in Claremont, which hosts the only AmeriFlux tower in Los Angeles County. This tower, referred to as US-BFS, measures carbon and water exchange over the coastal sage scrub habitat. Laboratory analysis will be paired with ecosystem-scale measurements to build a more complete picture of how plant emissions respond to heat and droughts along with other common environmental drivers.

Kavassalis and the research team aim to identify distinct emission patterns among individual plants during the project period, quantify how these emissions affect the surrounding atmosphere and develop a public archive of coastal sage scrub VOC emissions for use in regional and state air quality modeling. A project goal is to produce easily digestible, culturally valued planting guidance to help cities and decision-makers select lower-emission plant variants while maintaining biodiversity and saving water.

The project provides hands-on experience in environmental chemistry, ecology and policy-relevant science, with undergraduate training incorporated throughout. The work is designed to support decision-making agencies, such as the California Air Resources Board and the South Coast Air Quality Management District, while contributing to broader efforts to understand urban air quality in a changing climate.

Co-authors Johnson, Aaron L. Odom, Remi Beaulac, Mitch R. Smith, James K. McCusker and Chip Nataro designed the textbook to fill a longstanding gap in chemistry education: a single, cohesive resource that goes beyond introductory inorganic texts while remaining more accessible and pedagogically grounded than highly specialized graduate monographs.

“This book was designed to fill a niche where there haven’t been many options,” said Johnson, Ray and Mary Ingwersen Professor of Chemistry and chair of 91̽�� Mudd’s Department of Chemistry. “There are good introductory inorganic books, and there are good, advanced topic books, but not an advanced, comprehensive textbook that prepares students for research.”

A Decade-Long Collaboration Rooted in the Chemistry Community

The origins of the book trace back to an American Chemical Society (ACS) national meeting in San Diego 10 years ago, when Johnson was first approached by co-author and former graduate school colleague Aaron Odom about joining the project.
Johnson said, “We felt that having authors from both R1 and primarily undergraduate institutions would be a strong selling point for the text.”

Over time, the author list expanded to include leaders across multiple subdisciplines of inorganic chemistry. Johnson’s longtime collaborator Chip Nataro joined the project as well, building on nearly two decades of shared work on the teaching resource website ionicviper.org.

Research-driven, Current and Pedagogically Grounded

Johnson began researching his chapters shortly after that initial ACS meeting, with the bulk of the writing completed during the COVID-19 pandemic. He authored the chapters on organometallic chemistry, his primary research area, as well as bioinorganic chemistry, a field he worked in during his postdoctoral training at UC Berkeley.

“Relearning bioinorganic chemistry at a deeper level allowed me to see the similarities between the two fields,” Johnson said. “It really highlighted the importance of the local structure around a metal atom in dictating its reactivity. We have a lot to learn from biology, and these naturally evolved proteins improve our own ability to have such strong control over reactivity in a laboratory-synthesized metal complex.”

Across all chapters, the authors prioritized currency and connection to the primary literature. Johnson’s chapters include references through 2024—“as current as a textbook can be,” he noted. “We wanted students to see what inorganic chemistry actually looks like today.”

Bridging Coursework and Research

The book emphasizes the development of bonding theories that go beyond introductory chemistry, including ligand field theory and symmetry concepts taught alongside group theory and projection operators.

“This level of theory is important to explain chemical reactivity, structure and spectroscopy of metal complexes, which is what the majority of inorganic chemists study,” Johnson said. “But we also outline current research efforts across the discipline, from making new materials for gas separations, to catalysts to make pharmaceuticals, to understanding how platinum anticancer drugs work.”

Johnson particularly enjoyed writing about one of his favorite topics: molecular orbital theory. “This textbook has several chapters that build on knowledge from first-year chemistry to develop molecular orbital theory such that it can be applied to more complex systems. Then, the book uses this theory extensively to explain observed reactivity and spectroscopy.”

To support both instructors and students, the textbook includes advanced optional topics, extensive worked examples, end-of-chapter problems tied to the primary literature and a full answer key.

A Teaching Perspective Informed by PUI and R1 Faculty

Johnson believes the mix of perspectives among the authors is one of the book’s greatest strengths.

“Faculty at primarily undergraduate institutions tend to think deeply about teaching and pedagogy—how material is presented and received by students,” he said. “R1 faculty often focus more on research opportunities and pushing the frontiers of science. Having both perspectives in one book allows more breadth of how the material will be presented.”

Cottrell Scholars are chosen through a rigorous peer-review process of applications from public and private research universities and primarily undergraduate institutions in the United States and Canada. Their award proposals incorporate both research and science education.

“It’s exciting to become a part of and interact with a remarkable group of scholars across many different fields and interests, particularly at a time when federal funding for science is so uncertain,” Tamayo said. “This grant will allow us to integrate some of our group’s recent theoretical developments into our open-source numerical packages and probe the chaotic early phases of planetary systems’ lives. This will help elucidate the dominant physical processes shaping the orbital configurations that planetary systems settle into, which we can test against the large and rapidly expanding demographics of planetary systems discovered around other stars.

Planetary Systems Research

Each planetary system that is discovered orbiting another star is the product of a sequence of violent rearrangements through interplanetary collisions and ejections, which presumably has reached a long-term stable configuration. Yet, understanding whether a given orbital configuration of planets will lead to collisions or be long-term stable, remains a major unsolved problem.

Through this Cottrell Scholars Award, Tamayo will combine recent theoretical developments in the dynamics driving such instabilities with machine learning methods to develop an interpretable stability classifier and apply these tools to better understand the planet formation process. Researchers will leverage the rapidly growing ecosystem of open-source astrophysics codes to develop numerical demonstrations and homework exercises for an upper-level introduction to astrophysics survey course. These educational materials will be publicly hosted and will provide students around the world with hands-on learning activities and a practical on-ramp into the numerical tools used in cutting-edge astronomical research.

“This is an exceptional cohort of teacher‑scholars whose innovative work fuels discovery across the physical sciences,” said Eric Isaacs, president and CEO of RCSA. “Their insights and energy will strengthen a 600‑member network of researchers, leaders and mentors dedicated to pushing the boundaries of knowledge while shaping the future of science and science teaching in the United States and Canada.”

Located at Robert J. Bernard Field Station in Claremont, California, the continuously tracks the daily exchange of carbon dioxide, water vapor and energy between the Field Station’s native coastal sage scrub ecosystem and the surrounding Los Angeles atmosphere. The tower offers rare, year-round insights into how a drought-adapted, urban ecosystem “breathes” across seasons, including heat waves and dry spells.

The tower is part of AmeriFlux, a network of sites that measure ecosystem CO₂, water, energy fluxes and other climate-related data in North, Central and South America. The network connects research on field sites, all of which represent major climate and ecological biomes. Prior to the US-BFS’s establishment, there were no active monitoring sites of this kind in all of Los Angeles County. This gap meant scientists lacked continuous, reliable data on whether native coastal sage scrub in an urban setting function as a carbon sink or if it can transform to becoming a carbon source under extreme heat and drought. Researchers say determining the answer is critical for improving climate models and understanding how much carbon the Earth’s surface can realistically remove from the atmosphere. 

The tower measures three main categories of data: ecosystem fluxes, which capture how much carbon dioxide, water vapor and heat move between plants, soil and air; basic meteorology, including wind, temperature, humidity, sunlight and soil moisture; and local air-quality indicators such as particulate matter and gases like ozone. Together, these measurements allow students and collaborators to link ecosystem behavior directly to changing environmental conditions.

US-BFS is distinctive as it is the only of its kind in Los Angeles County as well as for the leading role students played in building and maintaining it.

“This is all a story of student accomplishments,” said Professor of Climate and Chemistry Sarah Kavassalis. “They turned instruments into a community resource.”

During the 2023–2024 academic year, Helen Chen ’24 designed the entire site as part of her undergraduate chemistry thesis, where she determined where the tower should be placed and how the instruments should be arranged. Before heading into the field, Chen and Sorin Jayaweera ’27 tested and validated the full system in the lab to ensure it could collect reliable data.

In summer 2024, Chen led a team of students (Mia Mirabelli ’26, Anna Figge ’27 and Matthew Simpson ’27), which installed the tower at the Field Station and connected the tower online. 

After Chen graduated, Simpson took over as the project’s lead and wrote the site’s data-processing code from scratch, producing the first publishable US-BFS dataset. This dataset was a milestone that made the measurements accessible to the wider scientific community.

“Most of my research involves processing the data from the flux tower,” said Simpson. “Understanding whether our local ecosystem is a carbon source or sink could better inform scientific modelers and policymakers when they calculate our carbon budget. Having accurate, ground-based measurements is important to verify climate models and satellite data products.”

In summer 2025, Simpson led another student team, including Figge, Stephanie Fulcar ’25, Kennetta Roebuck ’26 and Tzaara Jauhar ’27, to relocate the tower within the Field Station to an even more optimal location. The team adapted their processing tools to make them more user-friendly for outside researchers.

“I have learned so much about atmospheric chemistry, especially the eddy covariance method, which is the technique we use to measure fluxes and surface-level atmospheric dynamics,” said Simpson. “There has also been a lot that’s gone wrong along the way. The tower’s generator was stolen one winter, and we had to move the tower during the summer of 2025 to get better measurements. This taught me that scientific research is a very nonlinear process. It is reassuring to see that research can still produce interesting and impactful results despite the difficulties that researchers often face.”

The result is a site that functions as both a research platform and a community resource for researchers. Because the data is archived and shared through the AmeriFlux network, the US-BFS’s data is now part of a global system of ecosystem monitoring stations that supports climate and environmental science worldwide.

US-BFS was designed to serve as a long-term monitoring site. The team is building a multiyear record capable of capturing climate variability and extreme conditions, while actively maintaining and continuously updating the public dataset. New multiyear research funding from a grant by the Seaver Foundation will also support the expansion of complementary measurements at the site.

Interest in the data is already growing. Researchers at The Claremont Colleges are developing projects that build on the tower’s footprint, including studies of plant water stress and soil greenhouse-gas fluxes. US-BFS was also selected as a participating site in a soil hydrology project led by Indiana University, Bloomington, and faculty from other higher education institutions have reached out about potential collaborations.

The project’s hands-on research of interdisciplinary learning and societal impact of science and engineering was a key focus. Students involved in US-BFS bring together chemistry, atmospheric science, ecology, engineering and data science, designing field instrumentation, writing and validating code and interpreting how carbon, water, and energy move through a vulnerable native ecosystem. AmeriFlux’s sharing and archiving system also allows students to learn best practices in open data science while contributing a community resource used well beyond campus. 

The experience is already shaping students’ academic paths. Two project alumni took paths in graduate studies involving atmospheric chemistry, carrying their field and data-science training into the next stage of their research careers. For Simpson, the project is preparing him for his pursuit of a career as a university professor, which he anticipates will include substantial scientific research.

“It’s been exciting to be positioned in an understudied environment so I can investigate the instrumental and data processing mechanisms that are often less emphasized in other research groups,” said Simpson. “I was part of the team that first set up the tower in the summer of 2024, so it has been satisfying to see how far we have come with the project since then.”

The establishment of the US-BFS tower also opens doors to future grants and partnerships through the AmeriFlux network. The network provides shared tools and scientific visibility that connect researchers working across climate, ecology, biology and Earth systems science.

The tower functions as a major contribution to scientific research. The US-BFS transformed a patch of native landscape into a living, “breathing” laboratory, resulting in a worldwide effort to understand a changing planet.

The Bridge Award is a prestigious follow-on grant designed to catalyze the continued research and leadership of outstanding teacher-scholars. This first-time emergency initiative by the RCSA is intended to help stabilize strong research programs that have experienced disruptions due to abrupt changes to their federal funding. Shuve is one of only 11 Cottrell Scholars nationwide to receive this recognition, marking a significant milestone in a trajectory that began when he was first named a Cottrell Scholar in 2021. 91̽��, a recent recipient of the Carnegie Classification for “Research Colleges and Universities,” is the only undergraduate-only institution and one of two non-R1 institutions to receive this grant ( institutions are those with the highest level of research [at least $50 million each year]).

Advancing the Search for Dark Matter

The 2021 Cottrell Scholar Award supported Shuve’s foundational project, “Matter-Antimatter Asymmetry from Dark Matter Freeze-In,” which addresses dark matter and matter-antimatter asymmetry. The project is based on in which the production and scattering of dark matter shortly after the Big Bang has a back-reaction effect that can generate an excess of matter over antimatter and hence explains why humans are made of particles and not anti-particles. Shuve identified a number of new theoretical and experimental studies that will provide a more complete picture of how scientists can test theories of dark matter and the matter-antimatter asymmetry.

The new RCSA Bridge Award will allow Shuve and his students to expand this research, further investigating new ways in which current and future experiments can test the mechanisms of dark matter and other theoretical models. Shuve’s work is highly collaborative, integrating undergraduate researchers into high-level computational modeling and theoretical analysis.

“This award will support my group’s ongoing work to uncover possible signatures of dark matter or other particles that may be hiding in the debris of high-energy atom smashers,” said Shuve, a faculty member since 2016. “In one case, we are studying ways in which the Higgs boson, the most recently discovered but one of the least understood elementary particles, could be hiding interesting new particles amongst its decays. This research will be done by HMC students, including summer students who will be supported by the award. The award will also allow us to deepen collaborations with experimentalists working at CERN or other labs, and provide travel funding for students to present their work at conferences and connect with members of our broader research community.”

Beyond his theoretical research, Shuve’s 2021 grant supported an educational initiative to bridge the gap between introductory concepts and high-level abstraction in the course Theoretical Mechanics. By developing interactive digital applets, Shuve provided students with a way to visualize and manipulate the complex mathematical objects used to solve advanced problems in gravity and mechanics. These tools allow students to connect abstract theoretical methods with familiar physical concepts like force and acceleration, creating a vital resource for advanced physics pedagogy both at 91̽�� Mudd and peer institutions.

STEM for a Better World

The receipt of this award comes at a pivotal moment as the College implements its strategic plan, STEM for a Better World—HMC Strategy 2025-2035. The Bridge Award directly supports the College’s commitment to being a “distinguished institution that enforces a creative interplay of STEM and the liberal arts to graduate problem solvers for some of the world’s most pressing challenges.”

By pushing the boundaries of fundamental science, Shuve’s lab embodies the strategic goal of “impactful research and discovery.” His work instills curiosity about the universe while training students in high-performance computing, critical thinking, communication and complex problem-solving—all necessary to help tackle the “global challenges” outlined in the College’s strategic plan.

Continuing a Legacy of Excellence

Since 1994, RCSA has honored teacher-scholars who demonstrate excellence in both original research and institutional leadership. Shuve’s 2021 award included both a research component and an educational initiative to improve physics pedagogy. The 2026 Bridge Award ensures that this dual commitment to discovery and education continues to thrive at 91̽�� Mudd, contributing to the “climate of innovation” that is a hallmark of the 91̽�� Mudd community.

The team—Bryce Tu Chi ’25, Stephanie Fulcar ’25, Jonathan Ipe ’25, Olivia Schleifer ’25, Rohan Subramanian ’25 and Claire Vlases CMC ’25—was advised by adjunct Professor of Computer Science Naim Matasci. Their work supports a Department of Energy (DOE) and National Cancer Institute initiative aimed at understanding how RAS–RAF protein interactions drive nearly 30% of human cancers.

The project focused on expanding access to MuMMI (multiscale machine-learned modeling infrastructure), a powerful simulation framework originally designed for DOE supercomputers, such as LLNL’s El Capitan—the most powerful supercomputer in the world. The Clinic team reengineered key components of the software to make it usable by a broader community of researchers and incorporated advanced AI algorithms to improve performance and accuracy.

Student Researchers Motivated

Olivia Schleifer says seeing the work published has been “incredibly rewarding,” marking the culmination of close collaboration between the Clinic team and LLNL scientists. “For many of us, this was our first experience taking a research project from idea to publication,” she says. “It’s given us a deeper appreciation for both the scientific process and the teamwork behind impactful research.” She hopes the machine-learning methods they developed will “help accelerate the design of new therapeutics” by potentially improving the speed and precision of computational drug-discovery pipelines.

Claire Vlases enjoyed the opportunity to use one of the world’s most powerful supercomputers and contribute to meaningful cancer research, “something most students only dream about.” The publication, she says, “shows us that we can do it. It’s motivating in a really deep way.” She says the team’s approach has the potential to lower computational barriers for researchers exploring mechanisms behind RAS-driven cancers, ultimately supporting new discoveries and potential treatments.

Project Goals Met

Matasci explains that the Clinic project filled a critical need in the national ADMIRRAL initiative (AI-Driven Multiscale Investigation of the RAS/RAF Activation Lifecycle). “Not everyone has access to DOE supercomputing resources and the expertise of the computational scientists who designed these tools,” he says. “The goal of the project, and the focus of this publication, was to make MUMMI accessible to the broader community of computational cancer researchers. The software is now available for download for everyone.”

He adds that publication was a stretch goal, one the students achieved through exceptional dedication and the mentorship of their LLNL partners. “The article’s inclusion in a special ACS collection highlighting undergraduate research ‘as the stimulus for scientific progress in the USA’ is incredibly fitting.”

The team’s accomplishment showcases the strength of 91̽�� Mudd’s Clinic Program which provides students with opportunities to contribute to high-impact scientific projects that advance both research and society.

Find the ACS Omega published paper here:

The relationship between BTO particle size, filler-matrix interactions and the properties of BTO-PDMS nanocomposites haven’t historically been completely understood. The multi-disciplinary research team, led by advisor Albert Dato, professor of engineering and associate director of the Engineering Clinic Program, discovered that the phenomenon could be due to a decline in the dielectric constant of BTO at smaller particle sizes and filler—matrix interactions that deform the structure of BTO. Experiments and computer simulations suggest this happens because the smallest BTO particles lose some of their natural ability to hold electric charge, and because of how they interact with and change shape inside the surrounding silicone material.

The impetus for the team’s research was a Clinic project, “Permittivity of Ferroelectric Nanoparticles in a Silicone Composite,” initiated by Sandia National Laboratories. The national lab sponsored the Clinic team’s research into barium titanate, widely used in electronics and energy storage due to its ferroelectric properties. The team of Brigitte Lynch Johnson ’25 (physics), Vanessa Bartling ’26 (engineering), Kayla Long ’26 (engineering), Miranda Brandt ’26 (engineering), Ian Smith ’26 (engineering), Luis Lorenzana ’26 (engineering), Natalie Smith ’26 (engineering), Ian Osborne ’26 (engineering) and Warren Pham ’26 (engineering) fabricated the nanocomposites to measure how the properties change with nanoparticle size and performed density functional theory simulations to understand how the silicone molecules bind to the surface of a barium titanate particle.

“They sought to uncover the fundamental science behind these materials,” says Dato. “Our initial vision was that this knowledge would eventually guide the design of advanced capacitors for Department of Energy applications, such as grid storage and electric buses. However, writing and publishing our recent paper helped us realize that the potential of silicone-matrix nanocomposites containing barium titanate extends far beyond those original goals.”

Silicone filled with barium titanate is an active area of research in the scientific community. These flexible, durable materials can store electrical energy, generate electricity from mechanical motion and even sense changes in pressure, vibration or movement, making them promising candidates for next-generation clean energy and smart-material technologies. They can enable lightweight, flexible power sources and sensors for aerospace systems, wearable and self-powered medical devices and soft robotic components. Because they combine the elasticity of silicone with the remarkable dielectric, piezoelectric and sensing properties of barium titanate, they can be engineered into stretchable, shape-conforming devices that harvest, store and detect energy wherever it is needed.

“The team’s research represents an intersection of materials science, physics and engineering design and highlights how undergraduate research can drive innovation with real-world impact on the future of sustainable technology,” says Dato. “By combining creative experimental approaches with advanced modeling, the students uncovered new insights that could guide the design of next-generation energy storage, sensing and energy harvesting devices.”

In addition to the published study, the students presented their findings at the following national scientific conferences:

• April 7–11, Materials Research Society Spring 2025 Meeting, Seattle, Washington. “Examining Surface Interactions at the Filler-Matrix Interface in Silicone-Matrix Nanocomposites Containing Barium Titanate Nanoparticles for Energy Devices.”
• March 23–27, American Chemical Society Spring 2025 Meeting, San Diego, California. “Investigating Structure-Properties Relationships in Polymer-Matrix Nanocomposites Containing Barium Titanate Nanoparticles” and “Simulating Surface Interactions at the Filler–Matrix Interface in Silicone–Matrix Nanocomposites Containing Barium Titanate Nanoparticles.”
• March 16–21, 2025 American Physical Society Global Physics Summit, Anaheim, California. “Exploring Structure-Properties Relationships in Polymer-Matrix Nanocomposites Containing Barium Titanate Nanoparticles” and “Simulating Surface Interactions at the Filler-Matrix Interface in Silicone-Matrix Nanocomposites Containing Barium Titanate Nanoparticles.”

LEAPS-MPS (Launching of Early-Career Academic Pathways in the Mathematical and Physical Sciences) supports the launch of the careers of pre-tenure faculty whose research is in MPS fields. A critical goal of the program is to develop a 21st-century STEM workforce representative of society’s full spectrum of talent. The two-year grant will provide Ogba and his team with $223,656 in funding.

In addition to advancing the study of carbon-based organocatalysts, Ogba’s project will provide research training to six students in computational catalysis, cheminformatics, and machine learning.

“My research students are being mentored to become budding experts in several disciplines across chemistry and computer science,” says Ogba. “This focus on a multidisciplinary approach will help build their skill set such that they are highly competitive in the ever-changing STEM landscape.”

The broader impacts of the grant will also bolster 91̽��’s educational mission by providing 20 first-year HMC students, particularly first-generation students, with the opportunity to engage in STEM research rotations within faculty labs across campus during their first semester. The initiative combines structured experiential learning and enrichment activities to encourage early research involvement among the cohort, enhance their scientific identity and develop resilience in STEM from the beginning of their college journey.

The anticipated project results will inform future studies on the catalytic potential of other zerovalent species. Making the machine learning program publicly accessible encourages collaborative research and significant advancements in catalyst development. “We will be uniquely set up to collaborate with experimental groups wishing to utilize the family of reactive carbon species we are investigating in chemical reactions beyond the scope of the proposal,” says Ogba.

Earlier this year, Ogba and his research students celebrated two published papers and a $70,000 grant from the American Chemical Society Petroleum Research Fund for an interdisciplinary project that combined a similar suite of computational chemistry techniques to address the urgent need for carbon recycling. Ogba credits his students with the success of his lab. “HMC students play a significant role in advancing research in my program,” he says. “Every student in my group has inspired my research efforts.”

The grant will fund his research through December 2027 and will provide funding for four undergraduates per summer for two summers to explore the world of geometric combinatorics, a field in which geometry, combinatorics, and algebra come together to uncover the underlying structure of complex shapes and patterns.

For the next two summers, Vindas Meléndez will mentor students over 10 weeks. Participants will collaborate on original problems, many drawn from Ehrhart theory, which studies the properties of polytopes (multi-dimensional generalizations of polygons) by counting lattice points, grid-like dots with whole-number coordinates inside or on the edges of shapes.

“I want to take combinatorial objects—graphs, posets, polytopes—and associate them with geometric objects,” says Vindas Meléndez. “By studying these objects’ structures, we hope to understand something deeper about the original mathematical ideas behind them.”

Students won’t be working from pre-made datasets or repeat experiments. “They’ll write their own code, build their own data and search for patterns in the geometry,” he says.

Combinatorics is often called “fancy counting,” Vindas Meléndez says, but it’s more accurately about how objects are classified, arranged, and enumerated. “Geometric combinatorics adds a spatial dimension to that,” he says.

Combinatorics is about distilling complex structures into simpler, manageable parts. While humans may not be able to visualize a six-dimensional shape, for example, computers can. Students will use code to define, manipulate and analyze these mathematical objects, blending abstract theory with hands-on computation.

There are real-world implications. Polytopes appear in natural sciences, data science and optimization problems. They show up in crystal structures, biological cell shapes and even tiling patterns used in architecture and manufacturing.

One exciting aspect of the program is its focus on younger undergraduates, those who may just be finishing their first year and haven’t yet had much exposure to upper-level mathematics.

“It’s really powerful to show students early on that they can do math research,” Vindas Meléndez says. “They don’t need to wait until junior or senior year to start exploring.”

Vindas Meléndez emphasizes inclusion, aligning with federal regulations that require opportunities be open to all. He has consistently mentored a diverse range of students, including women, first-generation college students and students from underrepresented backgrounds in STEM. “This past summer, half of my research team were women,” he says. “I want students from all walks of life to feel they belong in mathematics.”

While geometric combinatorics has roots stretching back to the ancient Greeks and Euler’s famous polyhedral formula, the field has exploded in new directions over the past few decades.

“The growth of interdisciplinary approaches—combining algebra, number theory, geometry, combinatorics, and many other areas—has really moved this field forward,” Vindas Meléndez says.