جستجوی استاد راهنمای دانشگاهی

Nadine Großeمشاهده پروفایل

استاد

• Geometric Analysis
• Differential Geometry
• Spin Geometry
• +۴ مورد دیگر

Nadine Große is a Professor at the University of Freiburg's Department of Mathematics. She holds a PhD and habilitation in Mathematics from the University of Leipzig and has held academic positions including Interim Professor at TU Dresden and Associate Professor at the University of Freiburg. Her research focuses on geometric analysis, differential geometry, spin geometry, conformal geometry, and spectral theory, with emphasis on Yamabe-type problems, Dirac operators, and curvature on open manifolds. Education: Studied Mathematics and Physics at the University of Leipzig (2000–2005), earned a PhD in Mathematics (2008) with a thesis on spin conformal invariants, followed by a habilitation in 2014. She has held postdoctoral positions at the Universities of Regensburg and Leipzig. Research interests include geometric analysis, with a focus on boundary value problems, spectral theory of Dirac and Laplace operators, and applications to general relativity. Her work bridges differential geometry and functional analysis, addressing questions on manifolds with special geometric structures. Key publication trends include studies on Dirac operators, spectral geometry, and geometric PDEs, often collaborating with experts like Nelia Charalambous and Bernd Ammann. Her articles explore topics such as magnetic Dirac spectra, Yamabe equations on noncompact manifolds, and boundary value problems in bounded geometry contexts. Advising: Supervises PhD students including Marius Amann and Jonah Reuß. Former students include Ksenia Fedosova (now at Münster) and Simone Murro (now at Genoa). Active in organizing conferences like the ANGEL-Meeting (2025) and maintains a research group focused on geometric analysis and spectral theory. Labs/Teams: Leads the Differential Geometry Research Group at Freiburg, coordinating the Oberseminar Differentialgeometrie with Sebastian Goette. Her team contributes to both pure and applied aspects of geometric analysis, including teaching advanced courses on differential geometry and mathematical physics.

• Differential Geometry
• Riemannian Geometry
• Partial Differential Equations
• +۳ مورد دیگر

Giovanni Catino is a Full Professor at the Dipartimento di Matematica of Politecnico di Milano. His research focuses on Differential and Riemannian Geometry, Partial Differential Equations, and Geometric Analysis. He has authored numerous papers on topics such as Einstein manifolds, Ricci solitons, geometric flows, and curvature rigidity. Catino has also co-authored several textbooks, including volumes on calculus and geometric analysis. His work frequently intersects with geometric variational problems, nonlinear PDEs, and the study of canonical metrics in Riemannian geometry. Recent research trends include investigations into Liouville-type theorems in sub-Riemannian settings, rigidity phenomena in geometric structures, and closure results in globally hyperbolic spacetimes. He actively participates in academic conferences and has organized events such as the 'Perspectives in Geometric Analysis' seminar series. Catino’s contributions span both pure mathematics and applications, with a strong emphasis on geometric PDEs and their implications in differential geometry.

Renato G Bettiolمشاهده پروفایل

دانشیار

• Differential Geometry
• Geometric Analysis
• Partial Differential Equations
• +۳ مورد دیگر

Renato G. Bettiol is an Associate Professor in the Department of Mathematics at Lehman College and a doctoral faculty member at the Graduate Center of The City University of New York (CUNY). His research focuses on Differential Geometry, Geometric Analysis, and Partial Differential Equations. He is a co-organizer of the CUNY Geometric Analysis seminar and has received prestigious awards including an NSF CAREER Award (2022-2027) and a CUNY Feliks Gross Award (2023). B.Sc. and M.Sc. from University of São Paulo (2008, 2010) Ph.D. from University of Notre Dame (2015) under Karsten Grove Hans Rademacher Instructor at University of Pennsylvania (2015-2018) Postdoctoral work at Max Planck Institute for Mathematics (2016) Joined CUNY as Assistant Professor (2018), promoted to Associate Professor (2023) Bettiol's research centers on two main areas: Curvature and Topology, and Geometric Analysis. In Curvature and Topology, he investigates how curvature constraints affect global shape, working on problems like the Hopf questions and Bott conjecture. He develops innovative approaches using the curvature operator R: ∧²TM → ∧²TM, particularly employing the Finsler-Thorpe trick in dimension 4. His work connects to Convex Algebraic Geometry through spectrahedral shadows, enabling computational approaches to curvature problems. In Geometric Analysis, he applies bifurcation theory to prove existence of multiple solutions to problems like the Yamabe problem and minimal surface equations, often analyzing degenerations of symmetric solutions. His recent publications show a strong focus on minimal surfaces in symmetric spaces, curvature operators in four dimensions, bifurcation phenomena, and connections between curvature conditions and topological constraints. The work demonstrates increasing sophistication in combining geometric, topological, and computational approaches to tackle longstanding problems in Riemannian geometry. NSF CAREER Award (2022-2027) CUNY Feliks Gross Award (2023) Bettiol serves as a doctoral advisor at the CUNY Graduate Center and has mentored numerous students through his research collaborations. His current research is supported by the NSF CAREER Award DMS-2142575, following previous support from NSF Award DMS-1904342. He actively collaborates with researchers worldwide, particularly with Paolo Piccione, Marcelo Kummer, and Ricardo Mendes. As co-organizer of the CUNY Geometric Analysis seminar, he fosters a vibrant research community focused on weekly discussions of cutting-edge developments in the field. Bettiol is deeply involved in the CUNY Geometric Analysis research group, which meets weekly at the Graduate Center. His work bridges pure mathematics with computational approaches, as evidenced by his participation in workshops like the Computational Geometric Analysis workshop. He maintains active collaborations with institutions including the Max Planck Institute, University of Pennsylvania, and various international research centers, contributing to a dynamic research environment that connects theoretical insights with computational methods.

Xiaodong Wangمشاهده پروفایل

استاد

• Geometric Analysis
• Partial Differential Equations (PDE)
• Differential Geometry
• +۴ مورد دیگر

Xiaodong Wang is a Professor in the Department of Mathematics at Michigan State University (MSU), located in D202 Wells Hall. His research focuses on Geometric Analysis and Partial Differential Equations (PDE), with particular interests in differential geometry, CR geometry, Ricci curvature, and geometric inequalities. He collaborates widely, with notable co-authors including Fengbo Hang, Zhixin Wang, and Pengzi Miao. His work addresses foundational questions in geometric PDEs, such as uniqueness theorems, sharp inequalities, and boundary effects on manifolds. Recent research has explored Yamabe invariants on Poincaré-Einstein manifolds, Liouville-type theorems on manifolds with curvature constraints, and geometric flows. Wang also contributes to mathematical physics through studies of static manifolds and geometric inequalities in relativistic contexts. Teaching responsibilities include advanced courses like MTH 890 (Readings in Mathematics) and MTH 931 (Riemannian Geometry II). His articles often bridge geometric analysis with analytic techniques, yielding results with implications for global geometry and geometric rigidity. No scientific awards are explicitly listed, though his prolific and impactful publications suggest recognition in the field. His advising and grants are not detailed in the provided texts, but his research portfolio indicates sustained institutional support. No specific lab or team affiliations are mentioned, though collaborative projects with international colleagues are evident.

• Geometric Analysis
• Calculus of Variations
• Partial Differential Equations
• +۲ مورد دیگر

Cheikh Birahim Ndiaye is an Associate Professor in the Department of Mathematics at Howard University's College of Arts & Sciences. He joined Howard's faculty in 2017 after an extensive academic journey that included positions in Senegal, Italy, Germany, France, Switzerland, and Japan. Dr. Ndiaye specializes in geometric analysis with a focus on non-compact geometric variational problems. His research spans Geometric Analysis, Calculus of Variations, Partial Differential Equations, Differential Geometry, and Nonlinear Analysis. His current fellowship research explores a Min-Max version of the Algebraic Topological argument of Bahri-Coron and Lojasiewicz's inequalities at infinity for Yamabe type problems, aiming to develop problem-solving methods applicable across diverse disciplines. His scholarly achievements have been recognized with prestigious awards including the Claytor-Gilmer Fellowship from the American Mathematical Society, the NSF Excellence in Research Award, and Howard University's College of Arts and Sciences Outstanding Research Award. Claytor-Gilmer Fellow by American Mathematical Society (2025-2026) National Science Foundation 2020 Excellence in Research Award Howard University College of Arts and Sciences 2023-2024 Outstanding Research Award Research membership at the Simons Laufer Mathematical Sciences Institute (2024) Dr. Ndiaye earned his PhD from SISSA in 2007 and continues to make significant contributions to mathematical research with international recognition.

Jeffrey Caseمشاهده پروفایل

استاد

• Geometric Analysis
• Conformal and CR Geometry
• Einstein and Poincaré-Einstein metrics
• +۳ مورد دیگر

Jeffrey Case is a Professor of Mathematics at The Pennsylvania State University, affiliated with the Department of Mathematics and the Institute for Gravitation and the Cosmos. He holds a Ph.D. from the University of California, Santa Barbara, awarded in 2010. His research focuses on geometric analysis, conformal and CR geometry, smooth metric measure spaces, and global Riemannian and Lorentzian geometry. His work often explores the interplay between differential geometry, partial differential equations, and mathematical physics. Key research interests include the study of Einstein and Poincaré-Einstein metrics, renormalized curvature integrals, and the properties of geometric operators such as the GJMS operators and CR Paneitz operator. His recent publications address topics like the Gauss-Bonnet formula for minimal submanifolds, formal self-adjointness of bidifferential operators, and sharp inequalities in trace-free matrix spaces. Dr. Case’s contributions extend to the development of geometric invariants and the exploration of conformally variational Riemannian invariants. He has investigated boundary value problems, such as the Neumann problem on the Clifford torus, and nonuniqueness results in Yamabe-type problems. His work on the weighted ambient metric and smooth metric measure spaces has advanced understanding of quasi-Einstein metrics and their applications in geometric analysis. His research also engages with CR geometry, including the study of Q-prime curvature in three dimensions and the CR Paneitz operator’s role in stability questions. He frequently employs techniques from global analysis, spectral geometry, and geometric measure theory in his investigations.

Yannick Sireمشاهده پروفایل

استاد

• Partial Differential Equations
• Harmonic Analysis
• Geometric Analysis
• +۴ مورد دیگر

Dr. Yannick Sire is a Professor of Mathematics and Director of Graduate Studies at the Department of Mathematics, Johns Hopkins University, affiliated with the Krieger School of Arts & Sciences. He holds a PhD from Institut National des Sciences Appliquees de Toulouse (France), with postdoctoral training at the University of Texas at Austin. His research focuses on partial differential equations, harmonic analysis, geometric analysis, and dynamical systems. Notable contributions include work on conformal geometry, fractional Laplacian operators, and nonlocal equations. Education: PhD, Institut National des Sciences Appliquees de Toulouse (France), 2005 Master's degree, Université Paul Sabatier (France), early 2000s Joint engineering degree (applied mathematics) and pure mathematics degree from Toulouse institutions Research Interests: Nonlinear elliptic and parabolic PDEs Geometric flows and conformal invariants Fractional operators and their applications Free boundary problems and variational methods Singular solutions and regularity theory Recent work emphasizes the interplay between geometric analysis and nonlocal equations, including studies on spinorial Yamabe problems, fractional Schrödinger operators, and critical phenomena in nonlinear heat equations. His research has implications for mathematical physics, geometric measure theory, and materials science. Grants & Academic Roles: Director of Graduate Studies at JHU Former faculty at Aix-Marseille University (2007–2020) Recipient of grants supporting research in geometric analysis and PDEs Labs/Teams: Active in JHU's Mathematics Department research groups focused on analysis and geometry, collaborating internationally on projects involving geometric PDEs and nonlocal operators.

• Differential Geometry
• Riemannian Geometry
• Partial Differential Equations
• +۳ مورد دیگر

Giovanni Catino is a Professor of Mathematics at Politecnico di Milano, specializing in Differential Geometry and Partial Differential Equations. His research focuses on geometric analysis, Ricci solitons, Einstein manifolds, and curvature functionals. He has authored multiple influential papers and books, including the award-winning monograph 'A Perspective on Canonical Riemannian Metrics' (2020). Catino is actively involved in academic activities, organizing conferences like the 'Differential Geometry, Analysis and Epistemology in Milan' (2025) and 'Perspectives in Geometric Analysis' (2025). His work bridges geometric structures with analytical techniques, addressing rigidity phenomena, curvature inequalities, and geometric flows. Key contributions include studies on critical metrics for quadratic curvature functionals, Liouville theorems in sub-Riemannian geometries, and rigidity of Einstein manifolds. He has co-authored over 50 peer-reviewed publications and edited volumes on calculus and geometric analysis. Catino's research also extends to pedagogical contributions, such as textbooks on calculus and problem-solving for undergraduate students. His awards include the prestigious 2020 Ferran Sunyer i Balaguer Prize recognizing his monograph's impact on the field. Catino collaborates internationally, with publications in top journals like Journal of Differential Geometry and Advances in Mathematics , and frequently participates in seminars and workshops on geometric analysis.

Sagun Chanilloمشاهده پروفایل

استاد

• Nonlinear Analysis
• Partial Differential Equations
• Geometric Analysis
• +۲ مورد دیگر

Sagun Chanillo is a Professor in the Department of Mathematics at Rutgers, The State University of New Jersey . His research focuses on Nonlinear Analysis , Partial Differential Equations , and related areas in Geometric Analysis and Harmonic Analysis . Research Monographs : "Geometric Analysis of PDE and Several Complex Variables" (AMS), "Harmonic Analysis, Partial Differential Equations and Applications" (Springer), and "Optimal Weak type Inequalities for the Partial Cesaro Sum operator" Research Themes : Dr. Chanillo investigates problems in CR Geometry (e.g., embeddability of CR manifolds, Paneitz operator properties), Fluid Mechanics (e.g., Navier-Stokes with divergence-free data), and Geometric PDE (e.g., Yamabe-type problems, symmetry breaking in eigenvalue optimization). He also explores connections to Number Theory (e.g., Riemann Zeta function in scattering theory) and Mathematical Physics (e.g., Ginzburg-Landau vortices, rotating stars). Recent Publications highlight collaborations with researchers like Paul C. Yang , Jean Van Schaftingen , and Po-lam Yung . Key contributions include sharp bounds for geometric PDEs , nonlinear eigenvalue studies , and probabilistic methods in wave equations .

• Nonlinear Analysis
• Partial Differential Equations
• Differential Geometry
• +۳ مورد دیگر

Zheng-Chao Han is a Professor of Mathematics at Rutgers, The State University of New Jersey, affiliated with the Department of Mathematics. His research focuses on Nonlinear Analysis and Partial Differential Equations (PDE), with a particular emphasis on geometric PDEs, conformal geometry, and the Yamabe problem. He has contributed to understanding singular solutions, asymptotic behaviors, and curvature equations in geometric contexts. His work often intersects differential geometry and global analysis. His office is located in HLL-522 on the Busch Campus, and he maintains an active research program with recent contributions spanning from foundational PDE theory to applications in materials science. While no specific awards are listed, his extensive publication record reflects sustained academic impact. Research interests include nonlinear elliptic equations, geometric identities (e.g., Kazdan-Warner type), and the interplay between curvature and conformal metrics. His articles address topics like σk-Yamabe equations, renormalized volume coefficients, and the Nirenberg problem, demonstrating expertise in both pure and applied mathematical analysis.

• Geometric Analysis
• Metric Geometry
• Riemannian Geometry
• +۲ مورد دیگر

Raquel Perales serves as a Research Fellow at the National Autonomous University of Mexico (UNAM), affiliated with the Mathematics Institute at the Oaxaca campus. Her scholarly work centers on advanced geometric structures and non-smooth spaces within mathematical analysis. Her research program focuses on: Rigidity phenomena in integral current spaces Curvature constraints under Ricci and scalar bounds Singular Riemannian foliations and Yamabe-type problems Topological invariants for RCD metric measure spaces Recent publications (2021-2023) reveal consistent investigation into stability theorems for tori, rigidity of Lipschitz mappings, and geometric analysis of singular spaces. These contributions appear in high-impact journals including Commentarii Mathematici Helvetici and Journal of Mathematical Analysis and Applications , demonstrating expertise in synthetic curvature frameworks. Scientific Awards: No awards documented in source material. Advising and Grants: No student supervision or grant funding information provided. Labs and Teams: No laboratory affiliations or research teams specified.