Project Grant 2506199
- This Project Grant from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) provides $193,202 to Columbia University from August 15, 2022 through July 31, 2025. The funding will support research investigating long-time behavior and large population limits of stochastic processes with random times. Specifically, the university will develop mathematical and computational tools to analyze complex interacting systems, with a focus on stochastic models involving...
- This $250,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports research in two areas: (1) regularized optimal transport theory and (2) price impact modeling in financial markets. For the first part, the project investigates the mathematical foundations and theoretical guarantees for sparsity in quadratically regularized optimal transport. This builds on prior work on entropically regularized optimal transport....
- This $239,999 federal Project Grant award from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) supports research by Brown University into probability flows and stochastic processes, with applications ranging from materials science to artificial intelligence. The project has two key research directions: 1) developing a novel dynamical formulation of multi-marginal optimal transport and related optimization problems, and 2) investigating the...
- This $293,784 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports fundamental and applied research on fluctuating systems, random environments, and stochastic algorithms. The research aims to improve understanding and exploitation of randomness across diverse settings, including materials science, fluid dynamics, and machine learning. Key areas of focus include stochastic homogenization, stochastic partial...
- This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) provides $117,090 to New York University (NYU) to advance the mathematical foundations of robust finance and decision-making under uncertainty. The project has two key focus areas: 1) Developing a systematic framework to quantify divergences between stochastic models, with the goal of uncovering the underlying geometric structure of stochastic processes to facilitate...
- This $150,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research at Carnegie Mellon University to advance the theoretical and applied frontiers at the intersection of probability, geometry, and combinatorics. The project focuses on three main research directions: 1) enabling efficient statistical inference for geometric probability distributions, 2) analyzing minimum lengths of combinatorial structures in...
- This Project Grant award of $350,000 from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) will support research to develop new mathematical frameworks and solution algorithms for large-scale stochastic models across a range of application areas. The project will investigate geometric principles and strategies for effectively incorporating randomness into model representations and algorithm design, with a focus on solving equilibrium problems in...
- This $299,057 federal Project Grant award from the National Science Foundation's (CFDA 47.049) Mathematical and Physical Sciences program supports research on optimal transport for risk management and scenario generation. The project, titled "OPTIMAL TRANSPORT FOR RISK MANAGEMENT AND SCENARIO GENERATION (OTRIMAGE)," aims to contribute to the mathematical foundations of risk management in finance and develop robust generative models. Key components include designing dynamic stochastic...
- This $180,000 Project Grant awarded by the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049) will investigate open problems at the intersection of probability theory and physics, with the goal of developing new techniques for studying the Anderson transition - a concept in condensed matter physics describing a sharp change in material properties from conducting to insulating behavior. The project aims to establish a rigorous mathematical...
- This National Science Foundation (NSF) Project Grant award for $106,291, under the Mathematical and Physical Sciences program (CFDA 47.049), will support research to extend classical extreme value theory to models with interdependent numerical values and mean-field interaction. The project aims to study the convergence of upper and intermediate order statistics of certain systems of stochastic differential equations as their size grows, with applications in finance, medicine, and other...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) provides $225,094 to investigate foundational and emerging areas of probability theory with broad applications in mathematics, physics, finance, and machine learning. The key research areas include limit theorems, entropic gradient flows, stochastic control with partial observation, and stochastic portfolio theory. The award aims to advance the theoretical foundations of probability while offering practical insights for real-world systems. It will develop a stochastic theory of portfolios that operates without equivalent martingale measures and allows for portfolio outperformance. The research also explores stochastic optimization under partial information, combining control, stopping, and filtering. Additionally, the project will characterize necessary and sufficient conditions for probabilistic limit theorems. The award was made on August 15, 2025 and is set to be completed by July 31, 2028. The Trustees of Columbia University in the City of New York is the awardee for this grant.
Mod # | Description | ReasonForModification | Federal Obligation | Date |
|---|---|---|---|---|
| Not listed | $225.1k | 8/8/25 |