University of Minnesota-Twin Cities

NSF Awards · FY 2025 · 2025-08

Despite their small size, parasites can change an animal’s behavior: what dog owner has not steered clear of long grassy fields to avoid ticks? Wild animals may not have bug spray or medication to protect them from these pesky parasites, but they have other tricks up their sleeves. This includes moving to habitats that help them recover from an infection or avoid the parasite in the first place. Yet this strategy may lead to an ‘out of the frying pan, into the fire’ situation: A dog walker who moves to a forest path may avoid grass-dwelling ticks but be faced with blood-sucking mosquitoes instead. This balance is also critical for wild migratory animals that travel between different habitats, though how this balance is achieved in nature remains unclear. This project uses mathematical equations and published data to explore how migrating animals time their movement to cope with parasites, just like dog walkers avoiding a forest walk at dusk when mosquitoes are out in full force. It will also explore what happens when migratory animals have more than one infection to deal with, like managing your dog’s infection with both ticks and tapeworms at the same time. The research findings will be communicated to other scientists through conference presentations and publications, and to elementary school and undergraduate students through teaching modules. The project also involves developing Wikipedia pages about scientists, and training graduate students. Despite recognition that parasites can shape seasonal migration of their hosts, important knowledge gaps remain: (i) existing conceptual frameworks typically focus on a single mechanism linking parasites, and (ii) most existing models start with a fully migratory or non-migratory host population in the absence of infection. Via the development of novel theoretical models supported by existing empirical evidence, this project will 1) determine the best timing of migration between two environments, given the tradeoffs of infection with different parasite species inhabiting each environment; and 2) determine how accounting for multiple parasite species changes our understanding of how parasites influence partial migration. Thus, this research generates a comprehensive understanding of the eco-evolutionary interactions between host movement and parasites, something that is essential for predicting the responses of migratory hosts and their parasites to anthropogenic change. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF Awards · FY 2025 · 2025-08

Sudden qualitative changes in the behavior of large complex systems can both be essential for their functioning and also lead to dramatic breakdown. Examples range from ecosystems with possible tipping points and extinction, to sudden changes in heart rhythm, and to self-organization in early development. Mathematical theory aims at predicting such changes, finding mechanisms that can prevent dramatic outcomes, or identifying causes of malfunction. Much of the theory developed in the mathematical sciences addresses transitions in simple dynamical systems, leading to universal qualitative predictions for qualitative changes in behavior. This project is concerned with case studies of transitions in large and complex systems, in particular with situations where such systems behave in apparently anomalous ways, challenging our understanding inferred from existing theory. Examples show how the complexity of large systems can eliminate system memory in transitions, thus facilitating easy switching between qualitatively different states with implications in systems biology. Transitions also involve intricate interplay between spatial organization and temporal evolution, with implications for the formation of ecological clusters and niches, as well as for the emergence of spiral waves in cardiac arrhythmia. The project integrates work of several graduate students on the projects and offers opportunities for mentoring by graduate students and research by undergraduate students during a summer project. This project focuses on the analysis of bifurcations in complex systems that mediate phase transitions. The project aims to identify coherent structures that organize the dynamics, as pacemakers, or as crystalline phases, and study their instabilities as well as the impact of spatial heterogeneity. Specifically, the project investigates interacting particle systems with competing attractive and repulsive forces, which exhibit a striking reversible phase transition from a perfectly mixed state to sorted states and states with clusters and vacuum regions. The anchoring of spiral waves at impurities and a geometric instability leading to bending of spiral arms will also be investigated. Lastly, the project studies striped patterns and the impact of spatial heterogeneity, with a focus on selection mechanisms, for position, wavenumbers, and orientation. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF Awards · FY 2025 · 2025-08

The project utilizes generative artificial intelligence to create high-quality synthetic data that accurately represents complex real-world information—such as medical images, financial records, and social media text—while ensuring individual privacy is protected. By providing scientists, engineers, and students with safe and realistic data sets, the project accelerates discovery, strengthens the nation’s technological workforce, and supports informed decision-making in health, commerce, and security. Additionally, the open benchmarks and instructional materials generated by the project encourage participation in data science, allowing everyone to contribute to and benefit from scientific advancements. The research develops a unified Generative Prediction and Inference framework that combines diffusion processes, normalizing flows, and transfer learning to model joint distributions of tabular and unstructured modalities. The framework samples synthetic multimodal data to improve supervised tasks such as image captioning and question answering, delivers calibrated uncertainty estimates, and tests for hallucinations in large language models. Key contributions include algorithms for domain adaptation, reliability metrics for trustworthy AI, and agent-based tools that automate analysis of complex datasets. The resulting software and evaluation suites establish new standards for multimodal data synthesis and statistical inference. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF Awards · FY 2025 · 2025-08

This project aims to break the low latency performance barrier in today’s fifth generation (5G) networks that hinders progress and adoption of remote driving industry (the “vertical” application). It advances an innovative “vertical-aware” framework to optimize both 5G networks and the vertical application. Despite tremendous progress, today’s “self-driving” cars may encounter many situations where they cannot drive themselves safely. Examples include construction zones and traffic accidents on the road. By ensuring low latency needed for remote driving, the developed solutions will allow a human teleoperator to remotely steer a “connected and autonomous” vehicle (CAV) through complex situations as if sitting in the driver seat. Technological advances enabled by this project will help (re-)establish the U.S.’s leadership in next-generation (NextG) wireless telecommunications and major vertical industries such as automotive and robotic automation. This project also provides a unique educational platform to train students and expand the STEM (Science, Technology, Engineering & Mathematics) workforce. Two major hurdles in ensuring low latency over 5G networks are i) high mobility of vehicles leads to poor radio channel conditions, causing data delivery errors; ii) frequent handovers among radio base stations further prolong data delivery. The project will develop a novel Open Radio Access Network (O-RAN) enabled, vertical-driven framework with mobility-aware, proactive mechanisms to reduce impacts of high mobility and handovers on the tail latency performance of the target vertical application. This is achieved by enabling 5G networks to utilize information (e.g., vehicle trajectory and speed) provided by remote driving applications to make intelligent decisions to speed up the delivery of sensor and command-and-control data that are critical to remote driving, whereas CAVs can also take advantage of vertical-aware predictions made by 5G networks to decide when and how to transmit data. Additional innovations include incorporation of integrated 5G and cellular vehicle-to-everything (C-V2X) technologies for cooperative situation awareness to further ensure safe remote driving operations. The phased approach to developing the proposed solutions and demonstrating their capabilities will ensure a high chance of successful execution, truly moving the needle with transformative impacts on relevant industrial sectors. The project represents close collaboration across three academic institutions and two industry leaders in key relevant sectors providing an accelerated pathway to technology transition. By demonstrating the value of vertical-aware advanced 5G/NextG networks in support of remote and cooperative driving and other industrial use cases, this project will help create new opportunities and business models for both mobile network operators and network equipment vendors for sustained investments in network innovations. It will also help accelerate adoption of autonomous driving with teleoperation capabilities. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF Awards · FY 2025 · 2025-08

This research will advance the progress of science by creating a set of new statistical tools for analyzing complex networks that are fundamental to the nation's prosperity and welfare. Understanding the underlying structures of these networks is critical for making informed, data-driven decisions to promote better and higher productivity in academia. This project will analyze the complex networks of faculty hiring between U.S. universities to understand how factors such as institutional research productivity, geography, and field of study influence hiring dynamics. The outcomes will enhance the efficiency of the U.S. academic system and provide valuable insights for researchers and policymakers. A key guiding principle of this project is a commitment to broad engagement; all outreach, recruitment, and participatory activities are designed to be fully open to all Americans. The project will also create a faculty hiring dataset with open access to the public, release all new methods in a free software package, and develop training opportunities for the next generation of American data scientists. From a technical perspective, this research will create a versatile statistical toolkit for analyzing weighted, directed networks, which pose significant challenges for existing methods. The investigators will develop four novel methodologies designed for commonly seen applications in analyzing the hiring networks. First, the project will establish a network-to-covariate regression model to handle count-based network data while accounting for complex dependencies between connections. Second, the research will introduce a nonparametric testing framework using network U-statistics to rigorously test for dependence structures. Third, a new method will be developed to identify and perform inference on "core-periphery" structures, allowing researchers to distinguish informative patterns from non-informative ones. Finally, the project will introduce a conformal inference framework to formally compare entire populations of networks, even when the networks differ in size. These new statistical methods will be validated through simulation and applied to the comprehensive faculty hiring network dataset, with results disseminated through peer-reviewed publications and the project's open-source software. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF Awards · FY 2025 · 2025-08

The aim of this project is to explore the wealth of deep connections lying at the interface of three subjects: algebraic topology, quantum algebra, and statistical problems in arithmetic. A meeting point of these subjects is in the study of moduli spaces: these are spaces which parameterize mathematical objects of a given sort. Deep questions in arithmetic may be formulated in terms of properties of these spaces, and those properties may be studied through the lens of algebraic topology. Remarkably, the sort of answers that topological tools provide has a close connection to the study of quantum groups and related objects arising in quantum physics. The main goals of this proposal are two-fold; the first is to more deeply explore how algebro-topological tools can address open questions in quantum algebras, such as the conjecture posed by Andruskiewitsch-Schneider on the generation of pointed Hopf algebras, and the conjecture of Etingof-Ostrik on the cohomology of finite tensor categories. The second is to use these tools, in concert with machinery of the Weil conjectures, to enumerate points on moduli spaces over finite fields, thereby establishing statistical conjectures on the distribution of Galois groups (e.g., those of Malle and Cohen- Lenstra), or moments of L-functions (e.g., those of Conrey-Keating-Farmer-Rubinstein-Snaith). This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF Awards · FY 2025 · 2025-08

Generative Artificial Intelligence (AI) has demonstrated its ability to create novel content, such as images and text while also providing tools that are driving breakthroughs in varied scientific disciplines. However, its rapid advancement has introduced fundamental theoretical challenges that remain largely unaddressed. The primary goal of this project is to establish the mathematical foundations of two models that underpin generative AI methodologies in a number of scientific contexts: score-based generative models and transformer-based foundation models. This project will utilize and develop mathematical tools for examining the generative capabilities of score-based generative models in high dimensions and understanding the predictive capabilities and limitations of transformers in solving a broad range of scientific problems. These fundamental understandings are intended to contribute to the development of scientifically reliable AI systems. The project will also support undergraduate and graduate students through research mentorship and education in the mathematical foundations of generative AI. This project aims to study the mathematical underpinnings of score-based generative models and transformer-based foundation models. The project will study the role of fine data structures in mitigating the curse of dimensionality of score-based generative models, through quantifying the improved approximation, statistical and algorithmic complexities in learning high-dimensional distributions with two ubiquitous physical structures: symmetry and hierarchy. The project will also investigate the in-context learning capabilities of transformer-based foundation models for solving partial differential equations by characterizing their scaling laws and generalization performance under distribution shifts. Finally, the project will develop unsupervised foundational generative models for sampling from multiple distributions with provable guarantees. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF Awards · FY 2025 · 2025-08

Drug development is a critical yet notoriously resource-intensive and time-consuming process, typically taking 10-15 years and costing between $1 to $1.6 billion to bring a successful drug to market. To expedite the process and enhance cost efficiency, significant research has focused on developing computational methods as alternatives/in parallel to conventional experiment-based approaches. Although promising, these methods rely heavily on trial and error within limited chemical subspaces (e.g., molecular libraries), resulting in suboptimal precision and outcomes dependent on the expertise of the researchers. This reliance also limits the scalability and automation of rapid drug design for new protein targets. To address these challenges, this project seeks to develop comprehensive generative AI methodologies and computational tools that expedite drug discovery, enhance cost efficiency, and improve success rates. By creating a holistic generative artificial intelligence (AI) framework capable of generating high-quality drug candidates with multiple desired properties, the project has the potential to transform pharmaceutical research. This initiative promotes advancements in healthcare by reducing the time and costs associated with drug development, ultimately benefiting public health. It also supports education and diversity by involving students from varied backgrounds, integrating AI into coursework, and conducting outreach to K-12 students, fostering broader societal engagement with STEM fields. Generating structured data, such as molecules, with multiple properties is technically challenging. This project will develop a conditional diffusion model for 3D molecule generation to enable both ligand-based drug design and structure-based drug design. The diffusion model employs an SE(3)-equivariant denoising component conditioned on given ligands, binding pockets, or both, and a classifier-free guidance mechanism to ensure that generated molecules closely align with specified conditions. Additionally, the project introduces the Direct Multi-Property Optimization framework, which optimizes drug-specific properties without requiring expensive model retraining. This framework leverages advanced optimization techniques, such as bi-level and multi-objective methods, to enhance the quality and adaptability of generated molecules. Research activities include three thrusts: (1) developing the conditional diffusion model for conditional 3D molecule generation, (2) creating the Direct Multi-Property Optimization framework for multi-property molecule generation, and (3) conducting rigorous evaluations and validations in silico and on other applications. These innovations aim to significantly reduce the time, cost, and resources required for drug discovery while increasing its success rates. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF Awards · FY 2025 · 2025-08

Discovering how different features interact to influence outcomes is essential for understanding complex biological systems. Traditional statistical methods often fall short when applied to large-scale biological datasets. In contrast, newer artificial intelligence models show promise. These transformer-based foundation models, with their advanced capabilities and methods to focus attention on the most important features, are better suited to capture these interactions effectively. However, a gap remains between the computer science and biology communities. Many computer scientists are not fully aware of the importance of feature interaction discovery in biological research, while biologists are increasingly interested in using computational tools but may lack access to the latest developments in foundation model infrastructure. This project aims to bridge this gap by fostering collaboration between researchers in both fields. The goal is to build a scalable foundation model infrastructure specifically designed for identifying feature interactions in biological data. The main contribution of this project is to advance data-driven discovery of feature interactions through a shared foundation model infrastructure. The project will involve: (1) engaging computer science researchers through surveys, interviews, workshops, and working groups to explore feature interactions with foundation models; (2) developing scalable infrastructure for foundation models training and inference, along with creating datasets and benchmarks, for feature interaction discovery; and (3) applying the developed foundation model infrastructure to feature interaction discovery problems in biology. Together, this project will support both computer science and biology communities and fundamentally advance research in data-driven feature interaction discovery. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF Awards · FY 2025 · 2025-08

The night sky may seem eternal and unchanging, but when viewed carefully, it is incredibly dynamic. Many stars end their lives in violent explosions that produce intense flashes of light analogous to cosmic fireworks. Studying such cosmic explosions holds enormous potential for learning about the most extreme states of matter, the origin of elements in the periodic table, and the evolution of the cosmos. In recent years, puzzling new classes of cosmic explosions are being discovered where the explosion is so energetic that the resulting blast wave expands at nearly the speed of light.. A 3-year research program led by investigators at the University of Minnesota-Twin Cities aims to develop novel and accurate theoretical models that will be used to interpret existing and upcoming observations of relativistic cosmic explosions. A primary task of this project will be to develop code that accurately calculates how light is produced and escapes such explosions. Award activities will inspire public interest, increase public participation, and train the next generation of scientists through a summer outreach program within the Minnesota state parks network, enhancing the elementary school astronomy curriculum of the Como Planetarium, and the training of undergraduate and postgraduate students. Theoretical models of cosmic explosions will incorporate a full treatment of relativistic effects, which are critical when velocities are comparable to the speed of light. This will extend existing models, which either treat these effects using simplistic approximations or neglect them altogether. After developing this code, the investigators will apply the model to a wide range of observed relativistic explosions. The predictions of this model will allow accurate and unbiased inferences of the explosion properties of fast blue optical transients, the local environments of supermassive black holes (using data from jetted tidal-disruption events), and the properties of merging neutron stars, which can shed light on the behavior of nuclear matter at the highest densities in the Universe. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF Awards · FY 2025 · 2025-08

PART 1: NON-TECHNICAL SUMMARY Polyolefins like polyethylene found in packaging and polypropylene found in nearly all automobiles are ubiquitous and essential to modern society. The remarkable array of properties they offer has enabled numerous technologies that include lightweight transportation, food packaging, membrane materials for clean water and energy applications. However, a long-standing challenge has been the incorporation of chemical functional groups into polyolefins that would enable explosive growth in potential applications thus fostering economic growth in this class of materials. Moreover, while polyethylene has enjoyed some recycling success, such functional polyolefins would enable new recycling strategies that would bring important benefits to this immensely useful class of polymers especially in terms of promoting a self-sustaining circular polyolefin economy. This includes reuse and recycling of locally prepared and utilized plastics. The work described in this proposal will significantly advance our understanding of how to readily prepare the target functional polyolefins using the modern tools of polymer synthesis, which will in turn clear the path for implementation of new technologies. This work will emphasize new materials applications for next generation thermally, mechanically, and chemically robust polyethylenes as high performance plastics and membranes. The proposed activities will benefit society in several ways. These activities will improve the well-being of individuals given the urgent need to solve our pressing plastics predicament: society depends on these polymeric materials and continually expects increased performance but suffers consequences from the associated pollution that can result. PART 2: TECHNICAL SUMMARY The work described in this proposal will focus on how to efficiently prepare functional telechelic polyolefins with high atom economy using an approach that combines metathesis polymerization and catalytic hydrogenation using a dual function catalyst. Specifically, Project 1 will establish a wholly new strategy to create crosslinked polyethylene using an unprecedented reactive precursor approach that will lead to the material benefits of established crosslinked polyethylenes while adding chemical recyclability and highly tunable molecular features that include molar mass between crosslinks, crystallinity, and functional group concentration. A separate strategy to create high stability PEX materials by eliminating tertiary carbons that are susceptible to oxidative degradation will also be pursued. Project 2 will spearhead the generation and development of new nanostructures and mechanically robust nanoporous materials that have utility in, for example, separation membranes and in the formation of nanobubbles for water treatment and biomedical applications. Importantly, the work proposed will uncover methods that allow for the generation of mechanically robust materials through molecular engineering of the block polymer structure. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF Awards · FY 2025 · 2025-08

Gamma-ray astronomy studies the physics of powerful systems like black holes found in the centers of active galaxies and the remnants of supernova explosions, which mark the end of many massive stars’ lives. These systems produce radiation across the entire electromagnetic spectrum and can be observed using ground-based detectors. The VERITAS gamma-ray observatory, located at the F. L. Whipple Observatory in Arizona, plays a crucial role in advancing this field. It has made important discoveries that have greatly enhanced our understanding of the most energetic processes in the universe. The VERITAS team at the University of Minnesota focuses on exploring how active galaxies generate gamma rays and how this relates to the origins of ultra-high-energy cosmic rays and astrophysical neutrinos—two very significant questions in astrophysics. The teams at University of Minnesota includes students and postdocs. Ground-based very-high-energy (VHE) gamma-ray astrophysics has matured as a field in the last decade, expanding the VHE catalog from a handful to over 300 objects across a wide range of source classes that represent the most extreme phenomena in the Universe. VERITAS observations combined with a wealth of multi-wavelength data from radio to X-ray, and especially high-energy gamma rays from NASA’s Fermi-LAT satellite, has significantly increased our understanding of the most energetic processes in the Universe. The work carried out by the University of Minnesota VERITAS team under this grant is crucial to maintaining and extending the analysis packages of VERITAS to maximize the science return on data taking campaigns across the spectrum as well as with multi-messenger observatories. These efforts enable discoveries of new VHE emitting active galactic nuclei (AGN) and observations of known VHE blazars and radio galaxies to better characterize the so-called blazar sequence. The blazar sequence postulates an inverse relationship between blazar luminosity and peak synchrotron emission frequency potentially due to cosmic evolution. Results from this work are being used to elucidate the astrophysics behind gamma-ray emission in blazars and its potential links to the origin of ultra-high-energy cosmic rays and astrophysical neutrino production. The UMN team is also developing the software pipelines that are enabling the production of Legacy Data Products that are being made publicly available. These public data sets will be compatible with data formats that enable the broader scientific community, including members of the Cherenkov Telescope Array Observatory (CTAO), to analyze VERITAS datasets for long-term source variability as an example. The development of these pipelines also includes the ability to jointly analyze VERITAS data and the co-located prototype Schwarzschild-Couder telescope for both improved operations and science extraction purposes. This project advances the objectives of "Windows on the Universe: the Era of Multi-Messenger Astrophysics", one of the 10 Big Ideas for Future NSF Investments. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF Awards · FY 2025 · 2025-08

A common strategy employed in mathematics when one wishes to understand an intricate structure is to split it into smaller pieces, study these more manageable pieces first, and then reassemble this piecewise information into data about the original structure. The research area of K-theory was precisely engineered to achieve this, and for this reason it permeates a wide range of mathematical fields, encoding meaningful information about any setting where there is a reasonable notion of “splitting”. A K-theory machinery stores this data in a topological space, which is able to record which objects break up into smaller pieces, as well as how these splittings occur. Unpacking the data present in a K-theory space and reinterpreting it in terms of the original structures of interest, is both the main goal and the main challenge of the field of K-theory. In this project, the PI will carry out two independent research lines in this direction that aim to make strides in our understanding of the K-theory spaces of manifolds (smooth shapes with no sharp edges or corners, central to geometry and physics) and of Lawvere theories (a main character in universal algebra and logic), using the newly-introduced framework of combinatorial K-theory. A third research line, and an underlying theme throughout this project, pushes the state of the art of combinatorial K-theory, developing tools and paving the way for new examples and applications to come. Integrated into this project is the mentoring and training of students, as well as the organization of a collaborative workshop, the creation of a new professional development class for graduate students on mathematical communication skills, and the development of new active learning materials for undergraduate education that will be made broadly available to the mathematical community. The emerging subfield of combinatorial K-theory introduces new techniques to study structures whose splittings have a combinatorial flavor; for instance, by placing a focus on complements, instead of quotients or cofibers. Exciting new developments in the field, such as the introduction of new simplicial models and of robust comparison theorems reminiscent of the best features of classical algebraic and homotopical settings, place combinatorial K-theory in an advantageous spot and make this an ideal time for ambitious explorations. In this project, the PI will exploit these recent developments in order to explore three applications of vastly different mathematical flavors. The PI plans to: (a) Give a first computation of K1 of cut-and-paste K-theory for manifolds; (b) Introduce a K-theory of endomorphisms and a version of the Fundamental theorem of K-theory in the combinatorial setting, with a particular focus on finite sets; and (c) Explore connections between K-theory and logic by constructing localizations for the K-theory of Lawvere theories. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF Awards · FY 2025 · 2025-08

This project explores exciting new interactions between two central areas of mathematics - algebra and geometry - and their unexpected connections through physics. Algebra and geometry are foundational tools in mathematics, widely used in numerous scientific and engineering applications, such as computer science, data analysis, robotics, and theoretical physics. Historically, the interplay between algebraic equations and geometric shapes has led to powerful methods and profound insights, shaping much of modern mathematics and technology. In recent decades, researchers discovered surprising connections linking algebraic geometry, which studies shapes defined by polynomial equations, to symplectic geometry, an area crucial to physics and engineering. This project leverages these emerging connections to develop new mathematical tools that bridge algebra and geometry. Broader impacts of this research include significant training and mentoring activities. The project supports early-career researchers and graduate students, providing extensive professional development through workshops, virtual seminars, public lectures, and the creation of publicly available computational tools. On the technical side, the project aims to advance understanding in multigraded commutative algebra, toric geometry, and symplectic geometry. It addresses long-standing gaps and open questions in commutative algebra and toric geometry by introducing methods inspired by recent advances in homological mirror symmetry into purely algebraic contexts. The P.I.’s will explore new approaches to studying multigraded polynomial rings, aiming to uncover deeper structural properties that parallel classical results for standard graded polynomial rings. The project will develop algebraic analogues of effective symplectic geometry techniques, such as "stop manipulation," adapting these symplectic methods to algebraic settings. The project will also extend foundational results, including Orlov’s Theorem, to multigraded and toric settings, construct novel categorical structures that unify algebraic and geometric perspectives, explore applications to virtual resolutions and other questions involving shortest resolutions, and investigate extensions to broader classes of geometric objects through toric degenerations and natural generalizations from toric varieties. Furthermore, by establishing explicit links between algebraic constructions and Fukaya categories, the project will introduce new computational tools and theoretical approaches in symplectic geometry. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF Awards · FY 2025 · 2025-07

Scientific progress is vital for advancing technology, fostering social development, and tackling global issues. Research indicates that innovative activity in science is slowing. The causes behind this decline are unknown. Addressing this issue is hindered by our limited ability to empirically test how individual scientists make breakthrough discoveries. The researchers draw on the interdisciplinary expertise of a team with deep knowledge in sociology, agent-based modeling, and philosophy of science. By combining both theoretical and empirical studies, this award helps science to further understand the causes of, and solutions to, our declining rate of innovation. By providing a deeper understanding of the factors that drive or hinder innovation, the award informs policies aimed at fostering a more conducive environment for scientific breakthroughs. The supported research uses a novel mixed-method approach, where empirically informed agent-based simulation models are combined with empirical analysis of the scientific record. This allows for a comparison of both internal factors---those related to the structure and dynamics of scientific content---and external factors that operate outside and influence the body of scientific knowledge. Internal factors involve the proliferation of scientific knowledge, while external factors encompass funding incentives, pressure to publish, and the challenges of remote collaboration. To increase innovation, it is essential to implement actionable policies that mitigate these factors and guide scientists in their contributions to scientific knowledge. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF Awards · FY 2025 · 2025-07

This project uses algebra to enhance famous counting formulas by (insightfully) throwing in an extra variable "q". These q-counts have connections to quantum theory and to the theory of error-correcting codes, which help reduce errors in noisy transmissions from objects in space. A beautiful feature of these "q-counts" is that they respect the symmetries present in the objects being counted. The project will involve undergraduate and graduate students in the research. The PI proposes a suite of problems, conjectures and questions concerning the "point orbit method" for producing q-analogues in various counting problems. These include q-analogues of Ehrhart's theory of lattice point counting in dilated polytopes, and the Crapo-Rota "finite field" method for analyzing hyperplane arrangements. The point orbit method originated in the invariant theory of polynomial rings, and a second thread of the project concerns cases where deformations of these invariant rings turn out to be Koszul algebras. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF Awards · FY 2025 · 2025-07

Many processes of industrial and technological importance involve the impact of drops on a surface. Drop impact is a key step in applying coatings to solid surfaces and in various printing processes. Controlling the dynamics of drop impact is essential in achieving uniform coatings and in realizing high-resolution printing. One way to regulate drop impact is to tailor the properties of the substrate – the surface upon which drops impact. Prior research demonstrated that soft substrates could inhibit splashing and avoid the formation of small extraneous drops. However, the underlying physics and the role of substrate properties on drop impact are poorly understood. This project will systematically study how variations in substrate properties influence drop impact behaviors. Conducted in collaboration with industrial engineers, the research will focus on substrates most relevant to industrial coating processes. Thus, the proposed research will enrich the fundamental understanding of drop impact dynamics and potentially revolutionize existing industrial coating practices, particularly the processes of multi-layer coating and coating on compliant surfaces. The central hypothesis of this research is that precise tuning of substrate mechanical properties offers a powerful route to control drop impact outcomes with high specificity. This research will systematically investigate how compliant, heterogeneous, and non-Newtonian substrates influence drop impact dynamics. By modulating substrate elasticity to control drop impact, the research aims to reveal the missing link between the onset of splashing and the distribution of impact pressure, addressing a long-standing question in the study of drop impact. The project will unfold in three stages, examining how (1) thin elastic substrates, (2) mechanically heterogeneous substrates, and (3) rheologically complex substrates alter the underlying fluid dynamics of drop impact. Motivated by pressing engineering challenges such as multi-layer coatings and coatings on compliant surfaces, this research will decompose complex impact scenarios into simple model processes, enabling the development of predictive understanding applicable to more complex industrial settings. A strong partnership with industrial researchers ensures that the project remains aligned with the most relevant and urgent engineering needs. In addition to industrial impact, the project will contribute to STEM education through student exchange programs and outreach initiatives. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF Awards · FY 2025 · 2025-07

The research will provide a more detailed understanding of the ways that interplanetary (IP) shocks, a common space weather event, can impact Earth’s magnetic environment (magnetosphere). Past studies have focused on a limited range of shock properties that do not reflect the possible breadth of parameters. This research study will expand the range of shock properties investigated by comparing observations from multiple space missions with detailed computer simulations. These detailed, multi-platform studies will be the first to fully exploit existing data sets to address fundamental problems that are vital for achieving NSF’s strategic goals. Such events may affect technological systems, astronauts and spacecraft, electrical power grids, and other important technologies that modern society has come to depend on. The long-term impact of the study will be to significantly benefit society by allowing us to eventually predict the geoeffectiveness of potential IP shock impacts and take steps to mitigate their damage. The results of our study may also be relevant to understanding the behavior of other planetary magnetospheres to IP shock impacts. Numerous satellites orbit the Earth within its magnetosphere, often taking measurements simultaneously after the occurrence of space weather events such as interplanetary shocks. The research will investigate a large database of such simultaneous observations, showing how different regions of near-Earth space react to shocks with different properties. This analysis will be complemented by computer simulations that investigate variations in one shock property at a time, which will reveal the most important properties or combinations and their possible consequences. Specifically, we will determine how the response, typically an electromagnetic wave pulse, propagates through the magnetosphere (radially, azimuthally, or a combination thereof); what wave mode and Poynting flux are associated with this response; and how the wave mode evolves. We will also characterize particle energization, scattering, and loss associated with the passage of the pulse through the dayside magnetosphere. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF Awards · FY 2025 · 2025-07

The Polar Geospatial Center (PGC) at the University of Minnesota supports scientific research in the polar regions. PGC distributes high-resolution optical imagery, made available via the National Geospatial-Intelligence Agency, to U.S. Government-funded polar scientists. Its wide array of services includes satellite imagery, topographic maps and educational content. PGC’s activities provide essential support for field operational activities, such as expedition, route and facility planning. The data provided by PGC also aid expansive studies documenting the evolution of the Earth’s cryosphere, supporting research in glaciology, geology, geophysics, and Earth System science. Examples of innovative imagery techniques and products that are made possible by PGC include: Digital Elevation Models for both polar regions, mapping seasonal changes of sea ice coverage and dynamics of continental ice sheets, quantifying meltwater on the ice sheet surface in Greenland and Antarctica, preparing detailed topography maps and permafrost changes, identifying actual coastlines masked by ice or meltwater, impacts of extreme weather events for polar atmospheric and ocean studies, watching polar flora seasonal changes and climate-driven ecosystem shifts, and even counting vertebrate (e.g., polar bears, penguins, etc.) populations. PGC facilitates scientists' access to geospatial resources and respective domain knowledge by providing the following products and services to the polar community: (1) Access to sub-meter resolution satellite imagery of all locations poleward of 60° latitude in each hemisphere, and the ability to request new imagery targets for commercial satellite cameras; (2) Access to high-resolution topographic models generated as part of ArcticDEM and the Reference Elevation Model of Antarctica (REMA), which document the morphology of the Earth’s surface as a function of time; (3) Discipline knowledge of geospatial and computational techniques to help solve challenging problems at high-resolution over continental scales; and (4) Educational content via online materials that provide researchers with tools needed to advance science and promote modern best practices of geospatial data processing. PGC is also a source of public geospatial data that empowers researchers, educators, and others from outside the National Science Foundation polar community to investigate the current understanding of Earth surface processes. By developing rapid data access interfaces, PGC has made substantial advances in more directly and efficiently connecting its users to the data they need. Continued advances in rapid data delivery will make PGC services more responsive to the dynamic work done by its vast user community. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF Awards · FY 2025 · 2025-07

Kinetic theory has transformed our understanding of interacting particle systems in both nature and engineering. Despite their importance, kinetic equations remain challenging to solve. This difficulty arises from their high dimensionality, the presence of multiple scales, and the need to preserve key structures such as conservation, positivity, and entropy dissipation. Additionally, the multi-query task of parameter identification places a higher demand on solver's efficiency. This project intends to address these challenges by developing efficient and scalable variational computational methods. These methods will integrate ideas from optimal transport, scientific machine learning, and stochastic methods, along with the unique structure of kinetic equations. The project also includes the training of graduate students, contributing to the development of the next generation of computational mathematicians. The project has two main objectives. The first is to develop and analyze learning-enhanced, structure-preserving particle methods for nonlinear partial differential equations, with a particular focus on plasma models. The methods will preserve both the Hamiltonian structure of the field terms and the dissipative nature of the collision. They are intended to complement existing particle-in-cell approaches for collisionless plasmas and to offer improvements in scalability and stability for collisional plasma simulations. The second objective is to design reduced-order methods for optimization problems constrained by kinetic equations. This will involve leveraging the multiscale nature of the equations or employing intelligent use of randomness. The proposed methods aim to meet the pressing need for efficient inverse solvers, particularly given the growing applications of kinetic theory to real-world problems. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF Awards · FY 2025 · 2025-06

This project aims to revolutionize how scientists discover new materials, which are essential for advancing technologies like solar cells, batteries, medicine, and catalysts. Materials discovery is often driven by complex and expensive simulation methods, typically accurate but time-intensive. The emerging machine and deep learning (MDL) models, trained on the massive simulated data collected over the past decades, offer a faster alternative. Unfortunately, these mdoels often fail to predict critical material properties, such as material stability, that the current project shall focus on. This project addresses these shortcomings of MDL models by integrating fundamental physical principles into the training of MDL models. By doing so, the models will better capture the intricate relationships between materials, leading to more reliable predictions. The project will benefit science and our society in a multitude of ways. Faster and more accurate materials discovery will accelerate innovation in clean energy, electronics, healthcare, national security, and more. The project also contributes to the advancement of artificial intelligence by introducing new techniques for constrained learning, which will impact fields beyond materials science. Additionally, the project emphasizes education and engagement by providing interdisciplinary training for graduate students, equipping them with skills at the intersection of computer science, materials science, and engineering. The goal of this project is to boost the capability of deep learning models to accelerate the discovery of solid-state inorganic materials, based on the massive publicly available simulated data from the gold-standard density functional theory computation based on quantum mechanics. The central hypothesis is that the current Deep learning models suffer in stability prediction because materials are presumed independent during training, against the physical fact that stability is intrinsically a property defined by material groups. To test this hypothesis and remedy this deficiency, this project will introduce a new approach to training models for materials discovery by incorporating explicit and implicit physics-informed constraints to encode the thermodynamic stability of materials with respect to phase transition and phase separation . The effect of these constraints will be assessed using existing benchmark problems and by generating additional data based on quantum mechanics to assess tailored problems in the spaces of random structure searching and fine-tuning universal machine learning interatomic potentials. The proposed work can lead to new developments not only for materials discovery but also for constrained stochastic optimization in numerical optimization and structured-output modeling in deep learning. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF Awards · FY 2025 · 2025-06

This award will provide support for US participants, especially graduate students, postdocs, and junior faculty, to attend the thirty-seventh and thirty-eighth international conferences in Formal Power Series and Algebraic Combinatorics (FPSAC), held at Hokkaido University, Sapporo (Japan) from July 21-25, 2025 and the University of Washington, Seattle (USA) from July 13-17, 2026. The most important annual conference series in algebraic combinatorics in the world, FPSAC offers junior American researchers a unique opportunity to interact closely with top mathematicians from many countries. Each conference, which includes nine one-hour plenary lectures, thirty half-hour contributed talks, and sixty posters, will attract over 200 participants from all over the world. A distinguishing characteristic of FPSAC conferences is the concerted effort to recognize and encourage outstanding junior scientists. At least one plenary speaker is an "emerging star," and talented junior researchers are well represented among the speakers selected for contributed talks. Attendance at this conference will be exceptionally valuable for graduate students and junior researchers. Somewhat interdisciplinary, the conferences link research in combinatorics to other topics in pure mathematics such as algebraic geometry, commutative algebra, representation theory, K-theory and symplectic geometry, and to topics in other sciences such as computer science, physics, and biology. More information can be found at https://www.math.sci.hokudai.ac.jp/sympo/fpsac2025/ and https://fpsac.org/confs/fpsac-2026/. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF Awards · FY 2025 · 2025-06

The 2025 Conference on Statistics in Genomics and Genetics (STATGEN 2025) will be held at the University of Minnesota in Minneapolis, MN from May 21 to May 23, 2025. The conference will bring together researchers, including students, postdoctoral researchers, and early career scientists, to share ideas and collaborate in the rapidly evolving fields of genetics and data science. This event is an invaluable opportunity for early-career researchers to connect with experts, build professional networks, and gain insight from cutting-edge scientific work. By supporting the participation of students and early career researchers, the conference will help cultivate the next generation of scientists who will contribute to advancing knowledge and innovations in this important area of research. Building on the success of the inaugural meeting, the conference will expose attendees to cutting-edge research and methods in genomics, statistics, and data science. This event will contribute to ongoing dialogue and innovation in genetics and genomics and the integration of statistical methods into genomic research, supporting the development of future breakthroughs in areas such as personalized medicine and disease prevention. Special emphasis will be placed on fostering the collaboration and participation of early-career researchers, with travel assistance provided by the NSF grant. By facilitating broad participation, the conference will help shape the next generation of researchers and leaders in the field of genomics and data science. The conference will feature a variety of presentations, including keynotes, panels, invited, contributed, speed, and poster sessions, offering attendees the platform to explore the latest research and discoveries. Attendees will discuss and promote the latest advancements in statistical theory, methods, and tools, particularly in genetics and genomics, aimed at making evidence-based statistical inferences from complex, noisy, and high dimensional data sources. More information may be found athttps://www.sph.umn.edu/events-calendar/statgen-2025. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF Awards · FY 2025 · 2025-05

This Faculty Early Career Development (CAREER) project will fund research that leverages individual trajectory data to study traffic flow dynamics using a multiscale formulation, so that one can learn from microscopic driving behavior to infer macroscopic traffic flow dynamics. The research intends to support the creation of new traffic models by integrating high-fidelity trajectory data and machine learning techniques and will create novel traffic control strategies under both current and future transportation infrastructure settings. Properties of highway traffic flow, such as the relationship between flow (e.g., vehicles per hour) and density (number of vehicles per mile), depend on highly complex nonlinear interactions between individual drivers on the roadway. Traditionally, traffic control has been conducted using an aggregate approximation of the flow dynamics based on average observed driver behavior. However, recent advances in artificial intelligence allow for development of more nuanced and complex physics-informed models that can readily and quickly predict traffic behavior after observing driving behavior of individual vehicles in the flow. The development of such artificial-intelligence-guided traffic models will allow researchers and practitioners to leverage new data streams and integrate these into a framework for traffic control that is customized for specific observed traffic. Developed novel traffic control techniques intend to result in more efficient traffic control without the need for a major overhaul of our transportation infrastructure, saving investments and costs for infrastructure managers while improving traffic efficiency and reducing traffic congestion and travel time. The research, education and outreach plans are tightly integrated to further disseminate impacts through active and interactive learning opportunities that broaden participation in STEM. To enable next generation traffic control that considers the dynamics of individual vehicles and their impact on the aggregate traffic flow, this research intends to (i) develop methods that rely on low-rank characterizations of time-series driving data to rapidly and reliably identify an individual vehicle driving signature, (ii) develop an artificial intelligence-guided modeling framework that relies on physics-informed learning to quickly predict the resulting aggregate traffic flow dynamics of a particular collection of vehicles with distinct driving signatures and a specified local interaction network topology, and (iii) design a suite of next-generation traffic control options including both control at fixed locations in the infrastructure, as well as control distributed throughout the flow that leverage more precise knowledge of the macroscopic dynamics to adjust control strategies based on the driving signature of individual vehicles and the anticipated resulting aggregate flow dynamics. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF Awards · FY 2025 · 2025-05

This project, in collaboration with researchers at the University of Cambridge, aims to investigate a highly sensitive, low-cost sensor platform to detect circulating tumor DNA (ctDNA), a key biomarker for early cancer diagnosis, particularly in non-small cell lung cancer (NSCLC). By combining microwave photonics (MWP) with polymer-based micro-ring resonator technology, the platform addresses current limitations in cancer diagnostics, such as high costs, slow processing times, and the bulky nature of existing systems. This innovation promises to make cancer screening more accessible, offering a portable and affordable solution for point-of-care testing. Beyond healthcare, the sensor's versatility enables applications in environmental monitoring, agriculture, and other fields, delivering significant societal and economic benefits through improved efficiency and global resilience to emerging challenges. This project leverages microwave photonics (MWP) and polymer-based micro-ring resonator technology to create a precise, low-cost sensor platform for detecting ctDNA in human blood. The system is designed to address the limitations of current diagnostic tools by replacing expensive tunable lasers with a microwave frequency sweep modulated on an optical carrier. This approach dramatically reduces costs while enhancing precision and scalability. Polymer micro-ring resonators are ideal for this application due to their low manufacturing cost, compatibility with biomolecule functionalization, and ability to integrate seamlessly with microfluidics for lab-on-a-chip applications. These features make the technology suitable for multiplexed analyses of biological samples. However, achieving the high optical quality factor (Q-factor) required for high sensitivity poses significant challenges due to material imperfections, such as surface roughness and optical losses in the polymer resonators. To address these issues, advanced nano-imprint fabrication techniques are employed to minimize surface roughness, improve light confinement, and enhance light-analyte interactions. Additionally, the project employs co-design methodologies that integrate the MWP readout system with the polymer resonator design, ensuring optimal sensitivity and noise performance. Functionalized resonators with DNA-specific probes will enable selective and accurate detection of ctDNA, while integrated microfluidic channels allow for multiplexed analysis of biological samples. This design can achieve detection limits as low as tens of nanograms per milliliter, enabling reliable identification of ctDNA even in trace amounts. Validation of the platform will be conducted through rigorous testing against commercial ctDNA reference materials to ensure reliability and reproducibility. Collaboration among experts in photonics, polymer manufacturing, and oncology ensures a multidisciplinary approach to addressing both technical and clinical challenges. Beyond healthcare, the versatile platform’s modularity allows for adaptation to other fields, including environmental monitoring of pollutants and detection of pathogens in agriculture. This project advances interdisciplinary research in photonics, nanofabrication, and microfluidics while providing a scalable and cost-effective solution for global challenges. By addressing critical technological barriers, such as optimizing Q-factors and employing innovative nano-imprint methods, this project not only enhances the capabilities of polymer resonator technology but also establishes a robust framework for next-generation sensing platforms. This collaborative U.S.-U.K. project is supported by the U.S. National Science Foundation (NSF) and the Engineering and Physical Sciences Research Council (EPSRC) of United Kingdom Research and Innovation, where NSF funds the U.S. investigator and EPSRC funds the partners in the United Kingdom. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.