Spherical Mean Value Operator Professors and Supervisors

Peter McGrathمشاهده پروفایل

استادیار

North Carolina State UniversityUnited States

Peter McGrath is an Assistant Professor in the Department of Mathematics at North Carolina State University (NC State), part of the College of Sciences. His research focuses on geometric analysis, minimal surfaces, and partial differential equations. He holds a PhD in Mathematics from Brown University (2017). His expertise spans Ordinary Differential Equations, Partial Differential Equations and Analysis, and Topology, Geometry, and Mathematical Physics research groups. McGrath’s work explores advanced topics such as spectral geometry, free boundary problems, and geometric flows. His recent research emphasizes minimal surface constructions, topological asymptotics, and applications of eigenvalue optimization. Notable contributions include studies on free boundary minimal surfaces in the unit ball and advancements in understanding the Canham problem in biomembrane modeling. McGrath is affiliated with NC State’s Department of Mathematics, located at 2108 SAS Hall, Raleigh, NC. His contact information includes pjmcgrat@ncsu.edu and office SAS Hall 3248.

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Rupert Frankمشاهده پروفایل

استاد

Ludwig Maximilian University of MunichGermany

Rupert Frank is a Professor of Mathematics at the University of Munich (LMU Munich) . He has held academic positions at Caltech (2013–2021) and Princeton University (2009–2013). His research spans Mathematical Physics , Spectral Theory , and Functional Inequalities , with a focus on quantum many-body systems, stability of matter, and nonlocal operators. Research Themes : Analysis of eigenvalues for Schrödinger and Pauli operators with complex potentials Semi-classical spectral asymptotics and effective theories for quantum systems Matrix inequalities and quantum information theory Calculus of variations in models like the liquid drop problem Geometric inequalities and their applications to quantum mechanics Magnetic field effects on spectral properties Recent Publications : 2025: Sharp stability for Sobolev/log-Sobolev inequalities with dimensional dependence 2025: Endpoint Schatten class properties of commutators 2024: Degenerate stability of Caffarelli-Kohn-Nirenberg inequality 2024: Hardy inequalities for large fermionic systems 2023: Review on Scott conjecture for Coulomb systems Scientific Awards : Young Scientist Prize in Mathematical Physics (2009) Grants and Collaborations : Principal Investigator in CRC TRR 352 (2023–) PI in Munich Center for Quantum Science and Technology (2019–) Multiple NSF grants (2009–2020) DFG and DAAD grants Editorial and Conference Leadership : Editorial boards: Communications in Mathematical Physics , Journal in Mathematical Physics , Journal of Spectral Theory , SIAM Journal on Mathematical Analysis , Springer Lecture Notes Organized conferences/workshops on quantum many-body systems, spectral methods, and functional inequalities (2018–2025)

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Alice Guionnetمشاهده پروفایل

پژوهشگر

Paris Sciences et Lettres UniversityFrance

Alice Guionnet is a French mathematician and Research Director at the CNRS, affiliated with the Unité de Mathématiques Pures et Appliquées (UMPA) at École Normale Supérieure de Lyon since 2005. Her research focuses on random matrix theory, probability theory, and their applications in statistical mechanics and large deviations principles. She completed her doctorate in 1995 with a thesis on spin glass dynamics, supervised by Gérard Ben Arous. Her work includes groundbreaking contributions such as the Single Ring Theorem (2009) and studies on large deviations for eigenvalues of Wigner and heavy-tailed matrices. She has been honored with the Oberwolfach Prize (1998), Loève Prize (2009), and Blaise Pascal Medal (2018), and was elected to the French Academy of Sciences in 2017. Key research interests include non-linear Wigner spiked models, spectral phase transitions, and free probability. She has authored over 80 publications, including influential papers on matrix models, eigenvector delocalization, and stochastic processes in disordered systems. Her ERC Project LDRAM (Large Deviations in Random Matrices) explores asymptotic behaviors of random matrix ensembles. Education: PhD from École Normale Supérieure (1995), MSc in Mathematics (ENS Paris, 1989). Labs/Teams: UMPA Lyon, collaborations with CNRS and international institutions. Grants/Awards: Simons Investigator (2012–2015), CNRS Silver Medal (2010).

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Albert Mas Blesaمشاهده پروفایل

دانشیار

Polytechnic University of CataloniaSpain

Albert Mas Blesa is an Associate Professor in the Department of Mathematics at Universitat Politècnica de Catalunya (Barcelona, Spain). His academic career spans positions at Universidad Autònoma de Barcelona (PhD 2011), Universitat Politècnica de Catalunya, Universitat de Barcelona, and Universitat Autònoma de Barcelona in postdoctoral roles. He specializes in Partial Differential Equations , Mathematical Physics , Harmonic Analysis , and Geometric Measure Theory . Education : PhD in Mathematics (2007-2011), Universitat Autònoma de Barcelona Master's in Advanced Mathematics (2006-2007), Universitat Autònoma de Barcelona Bachelor's in Mathematics (2001-2006), Universitat Autònoma de Barcelona His research focuses on the intersection of quantum mechanics and geometric analysis, particularly Dirac operators, MIT bag models, and nonlocal equations. Recent work explores heat kernel monotonicity, shape optimization, and spectral properties of relativistic systems. Collaborations with leading researchers like Xavier Cabré and Luis Vega highlight his contributions to theoretical and applied PDEs. His 15 most recent publications span topics from quantum dot modeling to fractional calculus, emphasizing variational methods, symmetry analysis, and spectral theory. Key themes include MIT bag models, Dirac operators, nonlocal CMC surfaces, and harmonic analysis on Lipschitz graphs. Albert Mas Blesa has no listed scientific awards in available records and no advising history is provided. His affiliations include UPC's Campus Diagonal Besòs and institutions across Spain's Catalan universities.

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Peter Kuchmentمشاهده پروفایل

استاد

Texas A&M UniversityUnited States

Peter Kuchment is a University Distinguished Professor in the Mathematics Department at Texas A&M University. His research focuses on Partial Differential Equations, Mathematical Physics, Medical Imaging, and Geometric Analysis. He holds prestigious fellowships from the AAAS, AMS, APS, and SIAM. Kuchment has advised numerous PhD and master's students, many of whom have gone on to academic and industry roles globally. His work spans theoretical advancements in inverse problems, quantum graphs, and tomographic imaging techniques. Education: Science Doctor (1983), PhD (1973), and MS (1971) in Mathematics from institutions in Ukraine and Russia. Professional Memberships: Extensive involvement in mathematical societies including AMS, SIAM, and IEEE. Key research interests include spectral theory of periodic operators, medical imaging modalities like thermoacoustic tomography, and applied mathematics in novel materials science. Kuchment has organized major international conferences and workshops on topics such as quantum graphs and hybrid imaging methods. Scientific Awards: Multiple recognitions for student advisement and research contributions. Active in academic service, he directs outreach programs like the Summer Mathematics Research Training (SMaRT) camp and contributes to departmental initiatives in mathematics education and outreach.

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Rakeshمشاهده پروفایل

استاد

University of DelawareUnited States

Rakesh is a Professor in the Department of Mathematical Sciences at the University of Delaware (UD), part of the College of Arts & Sciences. He holds a BA(Hons) and MA from the University of Delhi, India, and a PhD from Cornell University, USA. His research focuses on inverse problems for hyperbolic partial differential equations (PDEs), including the Fixed Angle Scattering Problem, Backscattering Problem, and Inversion of the Spherical Mean Value Operator. He has also contributed to dynamical systems, geometry, probability, and economics. Education: BA(Hons) in Mathematics, University of Delhi MA in Mathematics, University of Delhi PhD in Mathematics, Cornell University His research emphasizes theoretical and applied aspects of inverse problems, such as uniqueness, stability, and inversion techniques for hyperbolic PDEs. Recent work includes contributions to formally determined inverse problems in Lorentzian and Riemannian geometries. Earlier research included studies on the spherical mean value operator and one-dimensional hyperbolic inverse problems. His publications span over 30 years, addressing topics like wave equation inverse problems, dynamic pricing models, and spectral analysis of Brownian motion. He has been on sabbatical for 2025. Rakesh collaborates internationally, with notable co-authors including Mikko Salo, Gunther Uhlmann, and Paul Sacks. His work bridges pure and applied mathematics, with applications in physics, engineering, and economics.

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Dustin Mixonمشاهده پروفایل

دانشیار

Ohio State UniversityUnited States

Dustin Mixon is Associate Professor of Mathematics at Ohio State University, specializing in applied harmonic analysis, compressed sensing, and frame theory. His research develops mathematical foundations for signal processing, including equiangular tight frames, optimal line packings, and phase retrieval guarantees. Recent work addresses max filtering injectivity, Euclidean distortion of orbit spaces, and clustering algorithms via semidefinite programming. Mixon has contributed to the theory of numerically erasure-robust frames (NERFs) and deterministic matrix constructions with the restricted isometry property. He co-authored papers on group-invariant packings and phase transitions in phase retrieval, solving open problems in combinatorial geometry. His blog 'Short, Fat Matrices' disseminates research on frame theory and compressed sensing.

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Oleg Ivriiمشاهده پروفایل

مدرس ارشد

Max Planck Institute for MathematicsGermany

Prof. Oleg Ivrii is a Senior Lecturer in the Department of Theoretical Mathematics at Tel Aviv University's Faculty of Exact Sciences. He earned a B.Sc. in Mathematics from the University of Toronto (2009) and a Ph.D. in Mathematics from Harvard University (2014). Following postdoctoral research positions at the University of Helsinki (2014-2016) and California Institute of Technology (2016-2019), he joined Tel Aviv University in 2019. Research Focus: Complex analysis, conformal geometry, thermodynamic formalism, and geometric function theory. Key Contributions: Studies on analytic mappings of the unit disk, inner functions, quasiconformal homogenization, and Makarov's principle. His work explores critical structures of inner functions, stable convergence, and applications to dynamical systems. He has advised Emanuel Sygal (Master's thesis) and collaborated with Artur Nicolau, Mariusz Urbański, and Vladimir Marković. Ivrii's publications appear in journals like Inventiones Mathematicae , Journal of Differential Geometry , and Analysis & PDE .

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