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Analysis/Awards-Analysis-2024.csv

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 "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"
+"2406319","Conference: C*-Algebraic Quantum Mechanics and Topological Phases of Matter","DMS","ANALYSIS PROGRAM","06/01/2024","05/14/2024","Markus Pflaum","CO","University of Colorado at Boulder","Standard Grant","Jan Cameron","05/31/2025","$42,236.00","Daniel Spiegel, Michael Hermele, Agnes Beaudry","[email protected]","3100 MARINE ST","Boulder","CO","803090001","3034926221","MPS","128100","7556","$0.00","This award supports the summer school<br/>?C*-Algebraic Quantum Mechanics and Topological Phases of Matter?,<br/>which will take place July 29-August 2, 2024, at the University of<br/>Colorado at Boulder. This workshop will be an opportunity for graduate<br/>students and postdocs from a wide variety of institutions and<br/>backgrounds to learn about the interplay between algebraic<br/>quantum mechanics, topology, and condensed matter theory. There will be<br/>problem sessions to help participants better learn the topics<br/>presented. Materials from the conference will be disseminated broadly:<br/>The talks will be filmed and posted on the Rocky Mountain Mathematical<br/>Physics Seminar YouTube Channel. Problem sets and course notes will be<br/>made available on the summer school webpage. This will create a<br/>permanent resource for all those seeking to learn the topics of the summer<br/>school. Another goal is to give some early-career researchers an opportunity to disseminate their<br/>work. This will be done through contributed talks by junior<br/>participants. The event will also create opportunities for junior<br/>participants to interact with the speakers and more established<br/>researchers. Funding from the NSF will make it possible to support<br/>participants who would not be able to attend without support and will<br/>be primarily offered to graduate students and postdocs.  More information about the summer school can be found at https://sites.google.com/colorado.edu/caqm.<br/><br/>The scientific goal of the summer school is to explore how C*-algebras<br/>are used to study topological phases of matter in the thermodynamic<br/>limit, and how methods from topology can be applied in this setting to<br/>study phases of quantum systems. Topics will cover background on<br/>C*-algebras and the topology of state spaces, lattice spin systems,<br/>Lieb-Robinson bounds, automorphic equivalence and symmetry protected<br/>phases. In the study of quantum many-body systems with infinitely many<br/>degrees of freedom, the thermodynamic limit is often of practical and<br/>conceptual importance. A precise mathematical description of such<br/>systems requires the use of a C*-algebraic formulation of quantum<br/>mechanics, a formalism that comes with deep insights and technical<br/>challenges in equal measure. C*-algebraic quantum mechanics has a long<br/>history, with notable discoveries in the seventies, including Lieb-<br/>Robinson bounds and the Doplicher-Haag-Roberts description of<br/>superselection sectors which continue to spur modern research in<br/>mathematical physics and condensed matter physics. In just the past<br/>five years, C*-algebraic quantum mechanics has provided the basis for<br/>cutting edge research on the rigorous classification of topological<br/>phases of matter. This summer school will bring some of the foremost<br/>experts in the field to teach the next generation of mathematical<br/>physics, providing students with both a strong foundation in the<br/>C*-algebraic formalism and a broad view of active frontiers of<br/>research.<br/><br/>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."
 "2420818","Conference: Travel Support for IWOTA 2024","DMS","ANALYSIS PROGRAM","08/01/2024","05/13/2024","Raul Curto","IA","University of Iowa","Standard Grant","Wing Suet Li","07/31/2025","$25,600.00","","[email protected]","105 JESSUP HALL","IOWA CITY","IA","522421316","3193352123","MPS","128100","7556, 9150","$0.00","This award will cover travel for sixteen U.S.-based early-career mathematicians to attend the International Workshop in Operator Theory and Applications (IWOTA), to be held at the University of Kent in Canterbury, United Kingdom, during August 12 - 16, 2024. The conference is not only the largest operator theory in the world, but it is also considered the premier event that connects operator theory to other disciplines that employ operator theoretic techniques and related mathematical results. IWOTA 2024 will be devoted to all aspects of operator theory and its applications and will feature top researchers from all around the world. Having such a major event organized in Canterbury will also provide a unique opportunity to reinforce research ties between some of the best experts in the field in the United States and the United Kingdom.<br/><br/>Many problems in physics, mathematics, and engineering can be best described by representing complex physical entities as large arrays of numbers and mathematical symbols called matrices. Matrices help us visualize how linear transformations act on vector spaces; determining their structure reveals important properties of the transformations. Hilbert space operators are infinite-dimensional generalizations of matrices. The generalization of a vector is often a function, so operators are frequently modeled as multiplications on spaces of functions. IWOTA 2024 will consist of ten plenary speakers, eleven semi-plenary speakers, and several special sessions. The topics of the special sessions include harmonic analysis and related areas, orthogonal polynomials and special functions, Jordan algebra structures, differential operators and mathematical physics, multivariable operator theory, hypercomplex analysis, free analysis and convexity, quantum information, noncommutative geometry and operator spaces, random matrices and free probability, finite and infinite dimensional moment problems, Herglotz functions and composite materials, linear algebra and control theory, systems theory/control theory, numerical ranges, spectral problems and computation, positive operators and their dynamics, operator semigroups and evolution equations, fractional calculus operators, operators on Banach spaces and lattices, operator theory on analytic function spaces, special matrices, and operator theory and applications. The conference website is https://blogs.kent.ac.uk/iwota2024/.<br/><br/>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."
 "2348748","Exploring Large-Scale Geometry via Local and Nonlocal Potential Theory","DMS","ANALYSIS PROGRAM","09/01/2024","04/02/2024","Nageswari Shanmugalingam","OH","University of Cincinnati Main Campus","Standard Grant","Jan Cameron","08/31/2027","$343,850.00","","[email protected]","2600 CLIFTON AVE","CINCINNATI","OH","452202872","5135564358","MPS","128100","","$0.00","This project will develop new mathematical tools for the analysis of metric measure spaces ? that is, spaces equipped (like Euclidean space) with notions of distance and volume ? with a focus on metric measure spaces that (unlike Euclidean space) lack smooth structure.  The analysis of non-smooth spaces is a vital area of research with diverse applications across the mathematical and physical sciences, including fluid mechanics, neurophysiology, and fractal geometry.  The PI will investigate the large-scale geometric behavior of objects in these spaces using the mathematical tools of local and nonlocal energies.   Given a function measuring a physical phenomenon, such as temperature or momentum, local energies measure the function?s nearby or small-scale oscillations, while nonlocal energies measure its variations over long distances.  A primary goal of this work is to develop much-needed mathematical tools for analyzing nonlocal energies.  The project will also enhance the professional training of graduate students and postdoctoral scholars, through collaborative research projects, instruction in effective mathematical communication, and opportunities for research interactions with undergraduate students.  <br/><br/><br/>The primary objects of study in this project are represented as metric measure spaces that lack smooth structure. The finite dimensionality of the ambient space is represented by the property of supporting a doubling Radon measure. In such a setting, nearby or asymptotic oscillation of a function is measured using upper gradients, which are viable substitutes for the derivative of a function, and the local energy is associated with the collection of functions on the object, called Sobolev functions. The large-scale variation energy is associated with the collection called Besov space of functions. Recent research has uncovered a connection between local energies on a region in a metric measure space and nonlocal energies on the boundary of the region. The project will leverage this connection to explore the large-scale geometry of nonlocal energies on the boundary of the region by linking them with small-scale behavior of local energies on the region itself. In particular, connections between Dirichlet-type boundary value problems and Neumann-type boundary value problems will be investigated.<br/><br/>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."
 "2400113","Collaborative Research: Conference: Brazos Analysis Seminar","DMS","ANALYSIS PROGRAM","04/01/2024","03/25/2024","Tao Mei","TX","Baylor University","Standard Grant","Wing Suet Li","03/31/2027","$16,000.00","Sheng Yin","[email protected]","700 S UNIVERSITY PARKS DR","WACO","TX","767061003","2547103817","MPS","128100","7556","$0.00","This award provides three years of funding to help defray the expenses of participants in the semi-annual conference series ""Brazos Analysis Seminar"" 2024-2026, the first meeting of which will be held in Spring 2024 at Texas Christian University. Subsequent meetings will rotate among the University of Texas at Austin, University of Houston, Texas A&M University, and Baylor University. The Brazos Analysis Seminar will bring together analysts at academic institutions within the South-Central region of the United States on a regular basis to communicate their research, with a particular emphasis on providing an opportunity for young researchers and graduate students to meet, collaborate and disseminate their work on a regular basis during the academic year. The format for the seminar provides ample opportunity for graduate students, postdocs, and junior investigators to present their work, start new collaborations, learn about the latest developments in modern analysis, and to advance their careers. <br/><br/>The scientific topics of this conference series will focus on the analytic theory of operator algebras and operator space theories and their connections to harmonic analysis, ergodic theory, dynamic systems, and the quantum information theory. These include free probability method in the study of quantum groups, Fourier multipliers theory on noncommutative Lp spaces, dynamical system, and K-theory of C*-algebras and von Neumann algebras. In each meeting, there will be 3 plenary talks given by prominent experts and 6 contributed talks presented by 3 experts from the region, and 3 postdoctoral or upper level PhD students. The goal is to keep both junior and senior researchers in the south-central institutions exposed and informed of the latest major mathematical developments in noncommutative Analysis, and to enhance and advance the research on the related topics. Additional information is available on the seminar website https://sites.google.com/site/brazosanalysisseminar.<br/><br/>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."