diff --git a/Geometric-Analysis/Awards-Geometric-Analysis-2024.csv b/Geometric-Analysis/Awards-Geometric-Analysis-2024.csv index 4ce0ed4..f2f937c 100644 --- a/Geometric-Analysis/Awards-Geometric-Analysis-2024.csv +++ b/Geometric-Analysis/Awards-Geometric-Analysis-2024.csv @@ -1,18 +1,19 @@ "AwardNumber","Title","NSFOrganization","Program(s)","StartDate","LastAmendmentDate","PrincipalInvestigator","State","Organization","AwardInstrument","ProgramManager","EndDate","AwardedAmountToDate","Co-PIName(s)","PIEmailAddress","OrganizationStreet","OrganizationCity","OrganizationState","OrganizationZip","OrganizationPhone","NSFDirectorate","ProgramElementCode(s)","ProgramReferenceCode(s)","ARRAAmount","Abstract" -"2403557","Fundamental Gap Estimates and Geometry /Topology of Ricci Limit Spaces","DMS","GEOMETRIC ANALYSIS","07/01/2024","05/01/2024","Guofang Wei","CA","University of California-Santa Barbara","Continuing Grant","Qun Li","06/30/2027","$181,166.00","","wei@math.ucsb.edu","3227 CHEADLE HALL","SANTA BARBARA","CA","931060001","8058934188","MPS","126500","","$0.00","Various problems of mathematical physics can be modeled by the Laplacian or more general Schrodinger equations. The difference of the first two eigenvalues of the Laplacian is referred to as the fundamental gap, which represents the energy needed to excite a particle from ground level to the next level in quantum mechanics. The principal investigator will estimate the fundamental gap for various spaces. The proposed activities are related to optimal transport, information geometry and discrete geometry. The project will also support educational activities and diversity through mentoring undergraduate and graduate students as well as postdocs; recruiting women and other underrepresented groups; organizing seminars, workshops and research programs promoting young scholars.

The project is centered around Riemannian geometry and geometric analysis with three parts. The first is about the fundamental gap estimates of the Laplacian with Dirichlet boundary conditions on a horoconvex domain in the hyperbolic space and convex domain in locally symmetric spaces by comparison with some suitable 1-dim model. The second concerns geometry and topology of spaces with Ricci curvature lower bound, especially the fundamental group of noncompact manifolds with nonnegative Ricci curvature; minimal volume entropy rigidity for metric measure spaces with curvature lower bounds. The last is to study integral curvature for the critical power.

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." +"2405175","Minimal Surfaces, Groups and Geometrization","DMS","GEOMETRIC ANALYSIS","11/01/2024","05/03/2024","Antoine Song","CA","California Institute of Technology","Continuing Grant","Qun Li","10/31/2027","$121,081.00","","aysong@caltech.edu","1200 E CALIFORNIA BLVD","PASADENA","CA","911250001","6263956219","MPS","126500","","$0.00","Differential geometry is a field which studies the shape of objects. Of particular importance are shapes that are ""optimal"" under natural constraints. An important class of optimal shapes is given by ""minimal surfaces"": a soap film spanning a metal wire, which tends to minimize its energy, is an example of minimal surface. This type of surfaces appears in many places in physics, but is also of intrinsic interest. The investigator will work on deforming smooth spaces, also called ""manifolds"", into an optimal shape by using the concept of minimal surfaces. Manifolds are ubiquitous in mathematics, and hopefully this approach will give new insights on their possible shapes. This project will moreover support student training and inclusion through seminars, workshops and knowledge dissemination efforts.


The notion of ""geometric structure"" serves as a unifying concept in geometry and topology, as exemplified by the Uniformization theorem for surfaces and the Geometrization theorem for 3-manifolds. In those classical instances, geometric structures are essentially defined as homogenous spaces with a geometric discrete group action. In higher dimensions, those geometric structures are very rare, and perhaps too rigid compared to the diversity of closed manifolds. In this project, the investigator proposes to consider a more general and flexible notion: minimal surfaces in (possibly infinite dimensional) homogeneous spaces, invariant under a geometric discrete group action. With this point of view, the investigator will explore a series of questions which relates minimal surfaces to geometric group theory and representation theory. A typical problem is the following: what group can act geometrically on a connected minimal surface in a Hilbert sphere?

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." +"2404309","Rigidity Properties in Dynamics and Geometry","DMS","GEOMETRIC ANALYSIS","06/01/2024","05/01/2024","Ralf Spatzier","MI","Regents of the University of Michigan - Ann Arbor","Continuing Grant","Eriko Hironaka","05/31/2027","$204,000.00","","spatzier@umich.edu","1109 GEDDES AVE, SUITE 3300","ANN ARBOR","MI","481091079","7347636438","MPS","126500","","$0.00","Dynamical systems and ergodic theory investigate the evolution of physical, biological or mathematical systems over time, such as turbulence in a fluid flow, the motions in planetary systems or the evolution of diseases. Fundamental ideas and concepts such as information, entropy, chaos and fractals have had a profound impact on our understanding of the world. Dynamical systems and ergodic theory have developed superb tools with applications to sciences and engineering. Symbolic dynamics, for example, has been instrumental in developing efficient and safe codes for computer science. Tools and ideas from smooth dynamics are used as far afield as cell biology and meteorology. Geometry is a highly developed, ancient yet superbly active field in mathematics. It studies curves, surfaces and their higher dimensional analogs, their shapes, shortest paths, and maps between such spaces. Surveying the land for his principality, Gauss developed the fundamental notions of geodesics and curvature, laying the groundwork for modern differential geometry. It has close links with physics and applied areas like computer vision or the more current geometric and topological data analysis. Geometry and dynamics are closely connected. Indeed, important dynamical systems such as the geodesic flow come from geometry, and conversely one can use geometric tools to study dynamics. One main goal of this project is to study symmetries of dynamical systems, especially when one system is unaffected by the changes brought on by the other. The quest is to study these systems via unexpected symmetries. Important examples arise from geometry when the space contains many flat subspaces. Under additional assumptions, one can classify such spaces. Finally, group theory is introduced in both dynamics and geometry via the group of symmetries of a geometry or dynamical system. The principal investigator will continue training a new generation of researchers in mathematics, and students at all levels in their mathematical endeavors. This project includes support for research training opportunities for graduate students and summer research experiences for undergraduates.

This project will investigate rigidity phenomena in geometry and dynamics, especially actions of higher rank abelian and semi-simple Lie groups and their lattices. The latter is part of the Zimmer program. Particular emphasis will be put on hyperbolic actions of such groups. As higher-rank semisimple Lie groups and their lattices contain higher-rank abelian groups, the classification and rigidity problems for the abelian and semi-simple cases are closely related, with abundant cross-fertilization. The goal is the classification of such actions. Closely related are the study of automorphism groups of geometric structures. A further goal is to understand topological joinings of lattice actions on Furstenberg boundaries and the related problem of classifying discrete subgroups in semisimple ie groups with higher Prasad-Rapinchuk rank. Investigations in geometry will address higher-rank Riemannian manifolds and their classification, introducing novel methods. The dynamics of geodesic and frame flows will also be studied, with investigations of discrete subgroups of Lie groups for rank rigidity and measure properties. Besides establishing new results, the principal investigator also strives to find and introduce novel methods for investigating these problems which will lend themselves to applications in other areas.

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." "2405361","Variational Problems In The Theory of Minimal Surfaces","DMS","GEOMETRIC ANALYSIS","06/01/2024","05/02/2024","Giada Franz","MA","Massachusetts Institute of Technology","Standard Grant","Qun Li","05/31/2027","$194,991.00","","gfranz@mit.edu","77 MASSACHUSETTS AVE","CAMBRIDGE","MA","021394301","6172531000","MPS","126500","","$0.00","A submanifold is called minimal if it is a critical point of the area functional. Minimal submanifolds are of central importance in differential geometry and arise naturally in mathematical physics, as soap films and black hole horizons, for example. Therefore, understanding their behavior is of great interest from the mathematical point of view but also for applications. The objective of this project is to take steps towards a full description of all minimal submanifolds in a given ambient manifold, inspired by the variational nature of these objects. The investigator will also conduct educational activities and practice community building, with particular attention to students and junior researchers.

The project consists of three interwoven research lines. The first seeks new insights into the topological and analytical properties of minimal surfaces obtained via min-max constructions. The second line focuses on minimal surfaces with free boundary in the three-dimensional ball, with a focus on existence theorems and global properties. Finally, the project will investigate rigidity results for minimal submanifolds of higher codimension in ambient manifolds with positive curvature.

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." "2404992","Minimal Surfaces and Harmonic Maps in Differential Geometry","DMS","GEOMETRIC ANALYSIS","07/01/2024","05/02/2024","Daniel Stern","NY","Cornell University","Continuing Grant","Qun Li","06/30/2027","$76,032.00","","daniel.stern@cornell.edu","341 PINE TREE RD","ITHACA","NY","148502820","6072555014","MPS","126500","","$0.00","Solutions of geometric variational problems--objects which (locally) minimize natural notions of energy--play a central role in modern geometry and analysis, as well as physics, materials science, and engineering, where they characterize equilibrium states for various systems. Among the most important examples are harmonic maps, which arise in computer graphics and the study of liquid crystals, and minimal surfaces, which model soap films and the boundaries of black holes. The central goal of this project is to advance our understanding of the existence and structure of these objects, with an emphasis on connections to spectral geometry and certain geometric equations arising in particle physics. This project also involves the training of graduate students and postdocs, the organization of seminars and workshops on related topics, and dissemination of ideas to non-expert audiences through public lectures and survey articles.

This project concerns the existence and geometric structure of harmonic maps, minimal surfaces and minimal submanifolds of codimension 2 and 3, in relation to isoperimetric problems in spectral geometry and singularity formation for gauge-theoretic PDEs. With his collaborators, the PI will exploit new techniques for constructing extremal metrics for Laplacian and Steklov eigenvalues--developed in recent work of the PI with Karpukhin, Kusner, and McGrath--to produce many new minimal surfaces of prescribed topology in low-dimensional spheres and balls, and study related constructions of minimal surfaces in generic ambient spaces via mapping methods. Building on prior work with Pigati and Parise-Pigati, the PI will continue to investigate the relationship between the abelian Higgs model and minimal submanifolds of codimension two, and explore an analogous correspondence between the SU(2)-Yang-Mills-Higgs equations and minimal varieties of codimension 3. In another direction, the PI will further develop the existence and regularity theory for harmonic maps on manifolds of supercritical dimension n ? 3, combining variational methods with new analytic techniques to study the existence and compactness theory for harmonic maps with bounded Morse index into general targets.

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." -"2404309","Rigidity Properties in Dynamics and Geometry","DMS","GEOMETRIC ANALYSIS","06/01/2024","05/01/2024","Ralf Spatzier","MI","Regents of the University of Michigan - Ann Arbor","Continuing Grant","Eriko Hironaka","05/31/2027","$204,000.00","","spatzier@umich.edu","1109 GEDDES AVE, SUITE 3300","ANN ARBOR","MI","481091079","7347636438","MPS","126500","","$0.00","Dynamical systems and ergodic theory investigate the evolution of physical, biological or mathematical systems over time, such as turbulence in a fluid flow, the motions in planetary systems or the evolution of diseases. Fundamental ideas and concepts such as information, entropy, chaos and fractals have had a profound impact on our understanding of the world. Dynamical systems and ergodic theory have developed superb tools with applications to sciences and engineering. Symbolic dynamics, for example, has been instrumental in developing efficient and safe codes for computer science. Tools and ideas from smooth dynamics are used as far afield as cell biology and meteorology. Geometry is a highly developed, ancient yet superbly active field in mathematics. It studies curves, surfaces and their higher dimensional analogs, their shapes, shortest paths, and maps between such spaces. Surveying the land for his principality, Gauss developed the fundamental notions of geodesics and curvature, laying the groundwork for modern differential geometry. It has close links with physics and applied areas like computer vision or the more current geometric and topological data analysis. Geometry and dynamics are closely connected. Indeed, important dynamical systems such as the geodesic flow come from geometry, and conversely one can use geometric tools to study dynamics. One main goal of this project is to study symmetries of dynamical systems, especially when one system is unaffected by the changes brought on by the other. The quest is to study these systems via unexpected symmetries. Important examples arise from geometry when the space contains many flat subspaces. Under additional assumptions, one can classify such spaces. Finally, group theory is introduced in both dynamics and geometry via the group of symmetries of a geometry or dynamical system. The principal investigator will continue training a new generation of researchers in mathematics, and students at all levels in their mathematical endeavors. This project includes support for research training opportunities for graduate students and summer research experiences for undergraduates.

This project will investigate rigidity phenomena in geometry and dynamics, especially actions of higher rank abelian and semi-simple Lie groups and their lattices. The latter is part of the Zimmer program. Particular emphasis will be put on hyperbolic actions of such groups. As higher-rank semisimple Lie groups and their lattices contain higher-rank abelian groups, the classification and rigidity problems for the abelian and semi-simple cases are closely related, with abundant cross-fertilization. The goal is the classification of such actions. Closely related are the study of automorphism groups of geometric structures. A further goal is to understand topological joinings of lattice actions on Furstenberg boundaries and the related problem of classifying discrete subgroups in semisimple ie groups with higher Prasad-Rapinchuk rank. Investigations in geometry will address higher-rank Riemannian manifolds and their classification, introducing novel methods. The dynamics of geodesic and frame flows will also be studied, with investigations of discrete subgroups of Lie groups for rank rigidity and measure properties. Besides establishing new results, the principal investigator also strives to find and introduce novel methods for investigating these problems which will lend themselves to applications in other areas.

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." +"2403557","Fundamental Gap Estimates and Geometry /Topology of Ricci Limit Spaces","DMS","GEOMETRIC ANALYSIS","07/01/2024","05/01/2024","Guofang Wei","CA","University of California-Santa Barbara","Continuing Grant","Qun Li","06/30/2027","$181,166.00","","wei@math.ucsb.edu","3227 CHEADLE HALL","SANTA BARBARA","CA","931060001","8058934188","MPS","126500","","$0.00","Various problems of mathematical physics can be modeled by the Laplacian or more general Schrodinger equations. The difference of the first two eigenvalues of the Laplacian is referred to as the fundamental gap, which represents the energy needed to excite a particle from ground level to the next level in quantum mechanics. The principal investigator will estimate the fundamental gap for various spaces. The proposed activities are related to optimal transport, information geometry and discrete geometry. The project will also support educational activities and diversity through mentoring undergraduate and graduate students as well as postdocs; recruiting women and other underrepresented groups; organizing seminars, workshops and research programs promoting young scholars.

The project is centered around Riemannian geometry and geometric analysis with three parts. The first is about the fundamental gap estimates of the Laplacian with Dirichlet boundary conditions on a horoconvex domain in the hyperbolic space and convex domain in locally symmetric spaces by comparison with some suitable 1-dim model. The second concerns geometry and topology of spaces with Ricci curvature lower bound, especially the fundamental group of noncompact manifolds with nonnegative Ricci curvature; minimal volume entropy rigidity for metric measure spaces with curvature lower bounds. The last is to study integral curvature for the critical power.

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." +"2428771","RUI: Configuration Spaces of Rigid Origami","DMS","GEOMETRIC ANALYSIS","04/15/2024","04/22/2024","Thomas Hull","PA","Franklin and Marshall College","Continuing Grant","Christopher Stark","08/31/2024","$59,029.00","","thull@wne.edu","415 HARRISBURG AVE","LANCASTER","PA","176032827","7173584517","MPS","126500","9229","$0.00","Origami, the art of paper folding, has been practiced for centuries. The mathematics behind origami, however, is not yet fully understood. In particular, some origami models can be folded and unfolded in such a way that we could make the crease lines be hinges and the paper between them stiff like sheet metal. Such models are called rigidly flexible origami and have applications that span the physical and biological sciences, ranging from unfolding solar sails to collapsible heart stents. This project will add mathematical tools that allow industrial applications to employ cutting-edge research, from large-scale architectural structures to nano-scale robotics driven by origami mechanics. The tools from this project will help design self-foldable structures. Currently self-folding designs in engineering, architecture, and the biological sciences involve building physical models in a trial-and-error approach, wasting time and resources. The self-folding research provided by this project will allow designers to avoid pitfalls and tighten the design-to-realization process significantly. In addition to the research component, the PI shall organize a diverse range of educational activities including in-service teacher training and education, undergraduate mentoring and preparation for graduate school; high-school and undergraduate classes on the mathematics of folding; for the public, general-audience articles, lectures, and exhibitions. This will increase interest in STEM fields through the fun, hands-on nature of origami while simultaneously disseminating project results.

The methods of this project involve a blend of practical experimentation with theory. Programmed self-foldability of structures will be achieved by trimming away undesired paths from the configuration space of all possible rigid foldings. One approach is to transform a given rigid folding of a crease pattern into a kinematically equivalent rigid folding with fewer degrees of freedom. The PI has proposed such a transform and will develop others. Key to all of this, however, is gaining a better understanding of rigid origami configuration spaces, which are algebraically complicated and not well understood. The project seeks to understand, and exploit, local-to-global behavior that is present in many known examples of rigid origami. In these examples approximating the configuration space near the origin (the unfolded state) leads to exact equations for the global configuration space. Formulating rigid origami configuration spaces in this way will add insight into the general field of flexible polyhedral surfaces, as well as provide the data needed to prove the feasibility of origami crease pattern transforms and design reliably self-foldable origami mechanisms.

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." "2403981","Scalar Curvature, Optimal Transport, and Geometric Inequalities","DMS","GEOMETRIC ANALYSIS","07/01/2024","05/01/2024","Simon Brendle","NY","Columbia University","Standard Grant","Qun Li","06/30/2027","$254,266.00","","sab2280@columbia.edu","615 W 131ST ST","NEW YORK","NY","100277922","2128546851","MPS","126500","","$0.00","This project focuses on questions at the intersection of differential geometry and the theory of partial differential equations. Differential geometry uses techniques from calculus to understand the shape and curvature of surfaces. These ideas can be generalized to higher-dimensional manifolds. In particular, they provide the mathematical framework for the Einstein equations in general relativity, which link the matter density to the curvature of space-time. A major theme in differential geometry has been to study the interplay between the curvature and the large-scale properties of a manifold. To study these questions, various techniques have been developed, many of them based on partial differential equations. Examples include the minimal surface equation and the partial differential equations governing optimal mass transport. This project is aimed at understanding these partial differential equations. This is of significance within mathematics. There are also connections with general relativity. Moreover, ideas from optimal transport have found important applications in statistics and computer science. The project also includes a variety of mentoring and outreach activities.

An important topic in geometry is to understand the geometric meaning of the scalar curvature. The PI recently obtained a new rigidity theorem for metrics with nonnegative scalar curvature on polytopes. The PI plans to extend that result to the more general setting of initial data sets satisfying the dominant energy condition. In another direction, the PI plans to work on geometric inequalities and optimal mass transport. On the one hand, the PI plans to use ideas from differential geometry and partial differential equations to study the behavior of optimal maps. On the other hand, the PI hopes to use ideas from optimal transport to prove new geometric inequalities. Ideas from optimal transport can be used to give elegant proofs of many classical inequalities, including the isoperimetric inequality and the sharp version of the Sobolev inequality. Moreover, the recent proof of the sharp isoperimetric inequality for minimal surfaces is inspired by optimal transport.

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." "2403728","Singularity, Rigidity, and Extremality Phenomena in Minimal Hypersurfaces","DMS","GEOMETRIC ANALYSIS","06/01/2024","05/01/2024","Christos Mantoulidis","TX","William Marsh Rice University","Standard Grant","Qun Li","05/31/2027","$215,057.00","","christos.mantoulidis@rice.edu","6100 MAIN ST","Houston","TX","770051827","7133484820","MPS","126500","","$0.00","Riemannian geometry is a modern version of geometry that studies shapes in any number of dimensions. Other than ""lengths"" and ""angles,"" its key notions also include ""minimal surfaces,"" which generalize the concept of a straight line, and ""curvature,"" which measures how a shape is bent. The principal investigator (PI) will study problems involving minimal surfaces and their curvature that arise from physical theories including Einstein?s general theory of relativity and the van der Waals?Cahn?Hilliard theory for phase transitions in multicomponent alloy systems. In addition to the research, this project will also support the PI's continued efforts to promote student learning and training through seminar organization, conferences, expository articles, and notes.

This project will specifically examine singularity, rigidity, and extremality phenomena in the theory of minimal surfaces. First, the PI will further investigate the structure of minimal surface singularities, meaning points of curvature blow-up, in area-minimization problems as well as their dynamic counterpart in mean curvature flow. Second, the PI will study enhanced rigidity properties of critical points in the van der Waals?Cahn?Hilliard phase transition theory, which can be thought of as diffuse variants of minimal surfaces. Third, the PI will study extremal behaviors of different quasi-local mass notions in general relativity, as seen through their interactions with scalar curvature and minimal surfaces, which correspond to energy density and boundaries of black hole regions.

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." "2426238","Conference: Pacific Northwest Geometry Seminar","DMS","GEOMETRIC ANALYSIS","06/01/2024","04/26/2024","Christine Escher","OR","Oregon State University","Standard Grant","Eriko Hironaka","05/31/2027","$50,397.00","Tracy Payne, Eric Bahuaud","tine@math.orst.edu","1500 SW JEFFERSON AVE","CORVALLIS","OR","973318655","5417374933","MPS","126500","7556","$0.00","This award will support meetings of the Pacific Northwest Geometry Seminar (PNGS) to be held at the University of British Columbia (2025), Seattle University (2026) and Lewis & Clark College (2027). Active researchers in geometry are scattered throughout the various colleges and universities involved in the Pacific Northwest Geometry Seminar. The PNGS meetings will bring these researchers together for consultation, collaboration, and stimulation of new ideas, and will give graduate students an excellent opportunity to see the broader picture of research in geometry. The meetings are also valuable for the growing number of geometers working at some of the smaller universities in the region, such as Pacific University, Seattle University, and Idaho State University. Conference support will be especially targeted toward graduate students, early career researchers and members of groups underrepresented in mathematics.

The meetings will feature five to six invited research talks by leading experts in differential geometry and geometric analysis, as well as three to four shorter talks by junior researchers or graduate students. The meetings will also include discussion sessions in which the speakers and participants assess the state of various areas in geometry and highlight open problems in these areas. For the first meeting at the University of British Columbia the grant will support travel of US based participants only. More information can be found on the conference website: https://sites.google.com/view/pnwgeometryseminar/home.

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." -"2428771","RUI: Configuration Spaces of Rigid Origami","DMS","GEOMETRIC ANALYSIS","04/15/2024","04/22/2024","Thomas Hull","PA","Franklin and Marshall College","Continuing Grant","Christopher Stark","06/30/2024","$59,029.00","","thull@wne.edu","415 HARRISBURG AVE","LANCASTER","PA","176032827","7173584517","MPS","126500","9229","$0.00","Origami, the art of paper folding, has been practiced for centuries. The mathematics behind origami, however, is not yet fully understood. In particular, some origami models can be folded and unfolded in such a way that we could make the crease lines be hinges and the paper between them stiff like sheet metal. Such models are called rigidly flexible origami and have applications that span the physical and biological sciences, ranging from unfolding solar sails to collapsible heart stents. This project will add mathematical tools that allow industrial applications to employ cutting-edge research, from large-scale architectural structures to nano-scale robotics driven by origami mechanics. The tools from this project will help design self-foldable structures. Currently self-folding designs in engineering, architecture, and the biological sciences involve building physical models in a trial-and-error approach, wasting time and resources. The self-folding research provided by this project will allow designers to avoid pitfalls and tighten the design-to-realization process significantly. In addition to the research component, the PI shall organize a diverse range of educational activities including in-service teacher training and education, undergraduate mentoring and preparation for graduate school; high-school and undergraduate classes on the mathematics of folding; for the public, general-audience articles, lectures, and exhibitions. This will increase interest in STEM fields through the fun, hands-on nature of origami while simultaneously disseminating project results.

The methods of this project involve a blend of practical experimentation with theory. Programmed self-foldability of structures will be achieved by trimming away undesired paths from the configuration space of all possible rigid foldings. One approach is to transform a given rigid folding of a crease pattern into a kinematically equivalent rigid folding with fewer degrees of freedom. The PI has proposed such a transform and will develop others. Key to all of this, however, is gaining a better understanding of rigid origami configuration spaces, which are algebraically complicated and not well understood. The project seeks to understand, and exploit, local-to-global behavior that is present in many known examples of rigid origami. In these examples approximating the configuration space near the origin (the unfolded state) leads to exact equations for the global configuration space. Formulating rigid origami configuration spaces in this way will add insight into the general field of flexible polyhedral surfaces, as well as provide the data needed to prove the feasibility of origami crease pattern transforms and design reliably self-foldable origami mechanisms.

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." -"2422900","Spectral Asymptotics of Laplace Eigenfunctions","DMS","GEOMETRIC ANALYSIS","03/01/2024","03/11/2024","Emmett Wyman","NY","SUNY at Binghamton","Standard Grant","Joanna Kania-Bartoszynska","07/31/2025","$61,364.00","","emmett.wyman@rochester.edu","4400 VESTAL PKWY E","BINGHAMTON","NY","139024400","6077776136","MPS","126500","","$0.00","The research project falls within the field of spectral asymptotics, which studies the behavior of high-frequency Laplace eigenfunctions on manifolds (surfaces and spaces with curvature). The physical analogues of eigenfunctions are standing waves, and the eigenvalues may be thought of as their corresponding frequencies. The interdependence between high-frequency eigenfunctions and the geometry of the manifold on which they live is central to a broad range of fields from quantum physics to number theory. Indeed, eigenfunctions are steady-state solutions to the Schrödinger equation, and their eigenvalues are the corresponding energies. To illustrate the connection to number theory, the task of accurately counting the number of eigenfunctions of a given frequency on the flat torus is equivalent to counting the number of ways an integer can be expressed as the sum of, say, two squares. This project aims to develop new tools to advance understanding in spectral asymptotics, whose interconnectedness to seemingly disparate areas of mathematics and science make its study particularly valuable.

As part of the research project, the PI intends to develop and use tools from microlocal analysis and the theory of Fourier integral operators to refine a variety of formulas describing the behavior of high-frequency eigenfunctions, and in particular describing what effect the underlying geometry has on these formulas. The PI intends to make advancements towards a conjecture on the remainder term of the Weyl law for products of manifolds, to develop a general multilinear theory of Fourier integral operators for use in both spectral asymptotics and geometric measure theory, and to further explore the connection between spectral quantities and the presence of corresponding geometric configurations in the manifold.

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." -"2350423","Conference: Moving to higher rank: from hyperbolic to Anosov","DMS","GEOMETRIC ANALYSIS","07/01/2024","01/30/2024","Ilesanmi Adeboye","CT","Wesleyan University","Standard Grant","Eriko Hironaka","06/30/2025","$40,000.00","Sara Maloni","iadeboye@wesleyan.edu","237 HIGH ST","MIDDLETOWN","CT","064593208","8606853683","MPS","126500","7556","$0.00","This award supports participation of US based mathematicians in the conference entitled ""Moving to higher rank: from hyperbolic to Anosov,"" which will take place in Centraro, Italy, from July 15- 19, 2024. The conference will bring together researchers and students from the classical field of hyperbolic geometry and the more recent area of higher Teichmuller theory to explore and further develop the rich connection between them. The conference will facilitate the exchange of ideas, and promote collaboration between experts in both fields, while reinforcing cooperation between the US and European mathematical communities. The organizing committee will encourage and support broad and diverse participation, and the training of the new generation of researchers.

In recent decades, the areas of hyperbolic geometry and Higher Teichmuller theory have undergone a dynamic convergence of concepts, attracting numerous scholars from hyperbolic geometry who have shifted their focus toward higher rank phenomena. Concurrently, a new generation of researchers has emerged, working at the juncture of these two domains. The conference will focus on how phenomena from hyperbolic geometry generalize to higher Teichmuller theory. Past success along these lines includes generalizations of Fenchel-Nielssen coordinates, Weil- Petersson geometry, Collar Lemmas, Length rigidity, and Patterson-Sullivan Theory. The conference will feature 18 research talks, and two lightening talk sessions for junior researchers. The URL for the conference website is https://tinyurl.com/hyp2anosov.

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." -"2350508","Conference: Noncommutative Geometry and Analysis","DMS","GEOMETRIC ANALYSIS","03/01/2024","01/05/2024","Antoine Song","CA","California Institute of Technology","Standard Grant","Swatee Naik","02/28/2025","$30,000.00","Zhongshan An, Zhizhang Xie, Simone Cecchini","aysong@caltech.edu","1200 E CALIFORNIA BLVD","PASADENA","CA","911250001","6263956219","MPS","126500","7556","$0.00","This award provides support for the 2024 Workshop in Noncommutative Geometry and Analysis that will be held at the California Institute of Technology, March 11 - 13, 2024. This is the next iteration of the annual workshop series, which began in 2022. The main goal of the workshop is to foster scientific and social interaction among early career mathematicians in various branches of mathematics, ranging from noncommutative geometry to geometric analysis. Recent advances in and interactions between these fields have given rise to a growing need for such a meeting specifically dedicated to these topics. This event is designed to have a relatively small number of participants, and it will provide a valuable platform for graduate students and postdocs to engage with current research frontiers in these areas.

Many of the recent developments in noncommutative geometry, index theory, geometric analysis and mathematical physics have focused on problems related to scalar curvature, minimal surfaces, and mathematical general relativity. The main goal of this workshop is to promote a better understanding of those latest developments and their interrelationships. A recent program concerning scalar curvature has given rise to new perspectives and inspired a wave of recent activity in this area. The theory of minimal surfaces has made significant strides on old questions pertaining to regularity or existence questions, while uncovering new problems related to adjacent fields. In the field of general relativity, results using harmonic maps have improved our understanding of the classical Positive Mass Theorem. This workshop aims to facilitate communication among participants from those diverse fields, fostering opportunities for potential collaboration. More information is available at the workshop webpage, https://sites.google.com/view/ymncga-2024/home

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." "2401549","Conference: CRM Thematic Program in Geometric Analysis","DMS","GEOMETRIC ANALYSIS","04/01/2024","12/04/2023","Natasa Sesum","NJ","Rutgers University New Brunswick","Standard Grant","Qun Li","03/31/2025","$48,960.00","Valentino Tosatti","natasa.sesum@gmail.com","3 RUTGERS PLZ","NEW BRUNSWICK","NJ","089018559","8489320150","MPS","126500","7556","$0.00","The Centre de Recherches Mathematiques (CRM) in Montreal will host a large, semester-long ""Thematic Program in Geometric Analysis"" from April 15 to June 29, 2024. The scientific activities of this Program will consist of 6 week-long Thematic Workshops, a two-week long Summer School (Seminaire de Mathematiques Superieures SMS), and two Aisenstadt Chairs Lectures. The Program's main theme is Geometric Analysis. This is an important field of mathematics with great impact and applications to many other parts of mathematics and physics, which uses and discovers tools in analysis and partial differential equations to address problems which originate in geometry and physics. This Program will bring together a large number of experts in different facets of geometric analysis, and will attract a large and diverse spectrum of participants from North America and beyond. A major goal of this Program is to expose graduate students and early career mathematicians to the recent developments in this important field of mathematics. This grant will provide financial support for junior US-based mathematicians (graduate students and postdocs), particularly women and members of other under-represented groups, to participate in the Program, by helping cover their travel and lodging expenses.

The last few years have seen spectacular progress on a variety of very difficult geometric problems, including the spectacular solution of the Poincare conjecture using Ricci Flow, and the solution of the Kahler-Einstein problem for Fano manifolds. The interplay between nonlinear analysis and geometry has long proved to be extremely fruitful. Generally speaking, problems involving the curvature tensor of a Riemannian or Kahler metric usually translate to nonlinear PDEs, which may present a formidable challenge from the analytic viewpoint, but which often can be attacked using the underlying geometric structure. The broad themes of the 6 Thematic Workshops will be: geometric flows; complex and Kahler geometry; special geometries in dimension 6,7,8; moduli spaces and singularities of geometric objects. The SMS summer school will be on ""Flows and Variational Methods in Riemannian and Complex Geometry: Classical and Modern Methods"", and will feature 10 mini-courses by well-known experts in the field. The Aisenstadt Chairs will be Simon Brendle and Panagiota Daskalopoulos.The Thematic Program webpage can be found here: https://www.crmath.ca/en/activities/#/type/activity/id/3880

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." +"2422900","Spectral Asymptotics of Laplace Eigenfunctions","DMS","GEOMETRIC ANALYSIS","03/01/2024","03/11/2024","Emmett Wyman","NY","SUNY at Binghamton","Standard Grant","Joanna Kania-Bartoszynska","07/31/2025","$61,364.00","","emmett.wyman@rochester.edu","4400 VESTAL PKWY E","BINGHAMTON","NY","139024400","6077776136","MPS","126500","","$0.00","The research project falls within the field of spectral asymptotics, which studies the behavior of high-frequency Laplace eigenfunctions on manifolds (surfaces and spaces with curvature). The physical analogues of eigenfunctions are standing waves, and the eigenvalues may be thought of as their corresponding frequencies. The interdependence between high-frequency eigenfunctions and the geometry of the manifold on which they live is central to a broad range of fields from quantum physics to number theory. Indeed, eigenfunctions are steady-state solutions to the Schrödinger equation, and their eigenvalues are the corresponding energies. To illustrate the connection to number theory, the task of accurately counting the number of eigenfunctions of a given frequency on the flat torus is equivalent to counting the number of ways an integer can be expressed as the sum of, say, two squares. This project aims to develop new tools to advance understanding in spectral asymptotics, whose interconnectedness to seemingly disparate areas of mathematics and science make its study particularly valuable.

As part of the research project, the PI intends to develop and use tools from microlocal analysis and the theory of Fourier integral operators to refine a variety of formulas describing the behavior of high-frequency eigenfunctions, and in particular describing what effect the underlying geometry has on these formulas. The PI intends to make advancements towards a conjecture on the remainder term of the Weyl law for products of manifolds, to develop a general multilinear theory of Fourier integral operators for use in both spectral asymptotics and geometric measure theory, and to further explore the connection between spectral quantities and the presence of corresponding geometric configurations in the manifold.

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." "2350239","Conference: Symmetry and Geometry in South Florida","DMS","GEOMETRIC ANALYSIS","02/15/2024","11/30/2023","Anna Fino","FL","Florida International University","Standard Grant","Qun Li","01/31/2025","$26,366.00","Gueo Grantcharov, Michael Jablonski, Samuel Lin","afino@fiu.edu","11200 SW 8TH ST","MIAMI","FL","331992516","3053482494","MPS","126500","7556","$0.00","The conference ?Symmetry and Geometry in South Florida? will take place at Florida International University, Miami, from February 16 to 18, 2024. This conference will serve the region of the southeastern United States, especially South Florida, and it will expose participants to cutting-edge research in Riemannian Geometry. Being organized around the principle of inclusiveness, the organizers will promote the conference to women and under-represented groups so as to increase their participation in the meeting. The meeting will feature a diverse array of speakers, including graduate students, postdocs, and established researchers.

Symmetry has been an essential tool in the development of differential geometry; it has been used to create crucial examples and to test special cases of general conjectures. Although symmetry is a widely used tool, the techniques involved can look substantially different across sub-fields. Given its exceptional nature, the organizers will host a conference centered around the theme of symmetry. The meeting aims to disseminate cutting-edge techniques and applications of group actions from across a broad spectrum of sub-disciplines inside differential geometry, including spectral geometry, curvature bounds, homogeneous spaces, and geometric flows. The conference also includes shorter talks by graduate students and younger researchers to showcase their work.
The link to the webpage to the conference is

https://sites.google.com/view/sgsf-2024/home-page?pli=1

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." "2348273","Conference: Geometric Flows and Relativity","DMS","GEOMETRIC ANALYSIS","02/01/2024","12/04/2023","Theodora Bourni","TN","University of Tennessee Knoxville","Standard Grant","Qun Li","01/31/2025","$34,995.00","","tbourni@utk.edu","201 ANDY HOLT TOWER","KNOXVILLE","TN","379960001","8659743466","MPS","126500","7556","$0.00","The ``Geometric Flows and Relativity? summer school and workshop will take place during March 11?March 20, 2024 in Uruguay; the summer school will be held in Montevideo and the workshop in Punta del Este. The first part of the meeting, the summer school, will consist of three lecture series whose topics will be on mean curvature flow, Ricci flow and applications of geometric flows to mathematical relativity, respectively. The second part of the meeting, a 3-day workshop, will consist of several talks aiming to discuss recent exciting progress in geometric flows and related fields. The goals of this meeting are: (1) Introduce graduate students and early career researchers from the USA, South America and other regions of the world to the field of geometric flows and applications, allowing them to learn about new exciting developments and to have direct contact with more senior researchers; (2) Promote research, by bringing together active leading specialists; and (3) Support the international environment and network by strengthening the collaborations within different institutions, particularly from the USA and South America.

Geometric analysis is one of the most active and exciting areas in pure mathematics today and geometric flows, in particular, have proven to be a powerful tool in the analysis of a large number of important problems in differential geometry, image processing and mathematical physics, leading to a profound impact on each of these fields. They also arise naturally in various physical contexts such as thermomechanics, annealing metals, crystal growth, flame propagation, wearing processes and conformal field theory. Geometric flows are therefore of interest to a diverse group of scientists outside of pure mathematical fields, including applied mathematicians, materials scientists and theoretical physicists. For all these reasons, the area has gained a large international interest to an extent that by now a large network of specialists are present all over the world. This meeting will be an international gathering on this active topic in an area where such events are sparse.

Meeting?s webpage: http://www.cmat.edu.uy/~mreiris/ssw/SSW.html

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." +"2350423","Conference: Moving to higher rank: from hyperbolic to Anosov","DMS","GEOMETRIC ANALYSIS","07/01/2024","01/30/2024","Ilesanmi Adeboye","CT","Wesleyan University","Standard Grant","Eriko Hironaka","06/30/2025","$40,000.00","Sara Maloni","iadeboye@wesleyan.edu","237 HIGH ST","MIDDLETOWN","CT","064593208","8606853683","MPS","126500","7556","$0.00","This award supports participation of US based mathematicians in the conference entitled ""Moving to higher rank: from hyperbolic to Anosov,"" which will take place in Centraro, Italy, from July 15- 19, 2024. The conference will bring together researchers and students from the classical field of hyperbolic geometry and the more recent area of higher Teichmuller theory to explore and further develop the rich connection between them. The conference will facilitate the exchange of ideas, and promote collaboration between experts in both fields, while reinforcing cooperation between the US and European mathematical communities. The organizing committee will encourage and support broad and diverse participation, and the training of the new generation of researchers.

In recent decades, the areas of hyperbolic geometry and Higher Teichmuller theory have undergone a dynamic convergence of concepts, attracting numerous scholars from hyperbolic geometry who have shifted their focus toward higher rank phenomena. Concurrently, a new generation of researchers has emerged, working at the juncture of these two domains. The conference will focus on how phenomena from hyperbolic geometry generalize to higher Teichmuller theory. Past success along these lines includes generalizations of Fenchel-Nielssen coordinates, Weil- Petersson geometry, Collar Lemmas, Length rigidity, and Patterson-Sullivan Theory. The conference will feature 18 research talks, and two lightening talk sessions for junior researchers. The URL for the conference website is https://tinyurl.com/hyp2anosov.

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." +"2350508","Conference: Noncommutative Geometry and Analysis","DMS","GEOMETRIC ANALYSIS","03/01/2024","01/05/2024","Antoine Song","CA","California Institute of Technology","Standard Grant","Swatee Naik","02/28/2025","$30,000.00","Zhongshan An, Zhizhang Xie, Simone Cecchini","aysong@caltech.edu","1200 E CALIFORNIA BLVD","PASADENA","CA","911250001","6263956219","MPS","126500","7556","$0.00","This award provides support for the 2024 Workshop in Noncommutative Geometry and Analysis that will be held at the California Institute of Technology, March 11 - 13, 2024. This is the next iteration of the annual workshop series, which began in 2022. The main goal of the workshop is to foster scientific and social interaction among early career mathematicians in various branches of mathematics, ranging from noncommutative geometry to geometric analysis. Recent advances in and interactions between these fields have given rise to a growing need for such a meeting specifically dedicated to these topics. This event is designed to have a relatively small number of participants, and it will provide a valuable platform for graduate students and postdocs to engage with current research frontiers in these areas.

Many of the recent developments in noncommutative geometry, index theory, geometric analysis and mathematical physics have focused on problems related to scalar curvature, minimal surfaces, and mathematical general relativity. The main goal of this workshop is to promote a better understanding of those latest developments and their interrelationships. A recent program concerning scalar curvature has given rise to new perspectives and inspired a wave of recent activity in this area. The theory of minimal surfaces has made significant strides on old questions pertaining to regularity or existence questions, while uncovering new problems related to adjacent fields. In the field of general relativity, results using harmonic maps have improved our understanding of the classical Positive Mass Theorem. This workshop aims to facilitate communication among participants from those diverse fields, fostering opportunities for potential collaboration. More information is available at the workshop webpage, https://sites.google.com/view/ymncga-2024/home

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." "2348566","Conference: Asymptotics in Complex Geometry: A Conference in Memory of Steve Zelditch","DMS","GEOMETRIC ANALYSIS","03/01/2024","01/10/2024","Gabor Szekelyhidi","IL","Northwestern University","Standard Grant","Eriko Hironaka","02/28/2025","$35,000.00","Yuchen Liu, Benjamin Weinkove","gaborsz@northwestern.edu","633 CLARK ST","EVANSTON","IL","602080001","3125037955","MPS","126500","7556","$0.00","This award will fund a conference on Asymptotics in Complex Geometry to be held at Northwestern University, March 7-10, 2024. The purpose of this conference is to gather experts in the field of complex geometry, to report and understand the recent exciting discoveries and techniques. A common theme will be asymptotic techniques, in complex and algebraic geometry. The conference will facilitate collaboration across diverse areas within this subject and will introduce the rapid developments in this area to a new generation of mathematicians. The conference will be widely advertised to attract broad participation.

In recent years, there has been much progress, including several major breakthroughs, in complex geometry. Much of this work lies at the intersection of two seemingly disparate fields: nonlinear geometric PDE and algebraic geometry. The existence of solutions to nonlinear PDEs in complex geometry, such as Kahler-Einstein metrics or constant scalar curvature Kahler metrics, is inextricably tied to algebro-geometric conditions involving subvarieties and algebraic degenerations. At the heart of these deep correspondences are questions of asymptotics. This conference will bring together experts on a wide range of related topics: PDEs in complex geometry; Non-Archimedean geometry; K-stability of singularities; Pluripotential theory.
The conference website is: https://sites.google.com/view/asymptotics/

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." "2337630","CAREER: Isoperimetric and Minkowski Problems in Convex Geometric Analysis","DMS","GEOMETRIC ANALYSIS, ANALYSIS PROGRAM","06/01/2024","12/28/2023","Yiming Zhao","NY","Syracuse University","Continuing Grant","Eriko Hironaka","05/31/2029","$69,246.00","","yzhao197@syr.edu","900 S CROUSE AVE","SYRACUSE","NY","132444407","3154432807","MPS","126500, 128100","1045","$0.00","Isoperimetric problems and Minkowski problems are two central ingredients in Convex Geometric Analysis. The former compares geometric measurements (such as volume and surface area) while the latter recovers the shape of geometric figures using local versions of these measurements. The two types of problems are inherently connected. This project will exploit this connection to seek answers to either isoperimetric problems or Minkowski problems in various settings when answers to one exist while answers to the other remain elusive. Although these problems originate from a geometric background, their applications extend beyond mathematics into engineering and design, including areas like antenna reflector design and urban planning. The principal investigator will organize a series of events and workshops at local science museums, community centers, and schools, involving high school teachers and students as well as undergraduate and graduate students. These events and workshops aim to expose the fun and exploratory side of the principal investigator?s research and mathematics in general to students early in their educational careers, raise society's awareness and interest in mathematics, and promote mathematics among historically underrepresented populations.

The existence of solutions to the dual Minkowski problem (that characterizes dual curvature measures) in the original symmetric case has been largely settled (by the principal investigator and his collaborators) through techniques from geometry and analysis. This naturally leads to conjectures involving isoperimetric problems connected to the dual Minkowski problem. Such conjectured isoperimetric inequalities are also connected to an intriguing question behind many other conjectures in convexity: how does certain symmetry improve estimates? The principal investigator will also study Minkowski problems and isoperimetric inequalities coming from affine geometry. Special cases of these isoperimetric inequalities are connected to an affine version of the sharp fractional Sobolev inequalities of Almgren-Lieb. The techniques involved in studying these questions are from Convex Geometric Analysis and PDE. In the last few decades (particularly the last two), there has been a community-wide effort to extend results in the theory of convex bodies to their counterparts in the space of log-concave functions. In this project, the principal investigator will also continue his past work to extend dual curvature measures, their Minkowski problems, and associated isoperimetric inequality to the space of log-concave functions.

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." "2410632","Conference: A Meeting on Poisson Geometry","DMS","ALGEBRA,NUMBER THEORY,AND COM, GEOMETRIC ANALYSIS","05/01/2024","04/12/2024","Gus Schrader","IL","Northwestern University","Standard Grant","James Matthew Douglass","04/30/2025","$33,000.00","Boris Tsygan","guskschrader@gmail.com","633 CLARK ST","EVANSTON","IL","602080001","3125037955","MPS","126400, 126500","7556","$0.00","This award provides support for a conference on Poisson geometry and representation theory to be held at Northwestern University on April 11-14, 2024. This conference series consists of regular meetings in North America of mathematicians interested in Poisson geometry and its applications, attracting leading experts and young researchers alike. The aim of the series is to promote interaction between mathematicians inspired by problems arising in physics, and physicists searching for new mathematical tools. The meetings also serve as a unique forum for junior mathematicians from all over the United States to learn about cutting edge developments in Poisson geometry and to disseminate their own research results in the field.

Poisson geometry originated as the mathematical formulation of classical mechanics as the semiclassical limit of quantum mechanics. Its history began with classical work by Poisson, Hamilton, Jacobi, and Lie, developing into a separate field in its own right around 1980 via the work of Lichnerowicz and Weinstein. Today, Poisson geometry influences and is influenced by many adjacent areas of mathematics, including symplectic geometry, generalized complex geometry, Lie algebroids and Lie groupoids, geometric mechanics, cluster algebras, integrable systems, quantization, non-commutative geometry, stratification theory, and the geometry of singular symplectic and Poisson structures. The theme of the 2024 conference is the immensely rich connection between Poisson geometry and representation theory, which dates back to the original works of Sophus Lie on the realization of continuous symmetry groups by canonical transformations. The conference talks will make exciting recent developments in this area more accessible to Poisson geometers and representation theorists in the United States. The conference website is https://sites.northwestern.edu/gonefishing24/.

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."