جستجوی استاد راهنمای دانشگاهی

Kai Xuمشاهده پروفایل

استادیار مهمان

• Geometric Analysis
• Calculus of Variations
• Metric Geometry
• +۴ مورد دیگر

Kai Xu is a Morrey Visiting Assistant Professor in the Mathematics department at the University of California, Berkeley, mentored by Richard Bamler. Appointed in 2025, he holds a PhD from Duke University supervised by Hubert Bray. His research addresses foundational problems at the intersection of differential geometry and analysis. His educational background includes: PhD in Mathematics, Duke University (2025), supervised by Hubert Bray Xu's research spans geometric analysis, calculus of variations, and metric geometry with concentrated focus on 3D scalar curvature geometry, weak inverse mean curvature flow, nonlinear potential theory (p-harmonic functions for $1 \leq p \leq \infty$), and spectral Ricci curvature bounds. His work systematically explores connections between curvature constraints, topological properties, and geometric flows through rigorous analytical methods. His publication record (2022-2025) reveals consistent advancement in scalar curvature theory, inverse mean curvature flow, and spectral Ricci geometry. Key contributions include spectral splitting theorems, drawstring constructions for scalar curvature constraints, and topological gap theorems for positive scalar curvature 3-manifolds. His collaborative work with leading mathematicians appears in journals including Duke Mathematical Journal and Calculus of Variations and Partial Differential Equations. No scientific awards are mentioned in the provided text. Teaching responsibilities include Math 104 in Fall 2025. Information regarding student advising and grant funding is not specified in available materials. No dedicated laboratory or research team structure is described in the source text.

Mona Merlingمشاهده پروفایل

دانشیار

• Algebraic K-Theory
• Equivariant Stable Homotopy Theory
• Manifold Theory
• +۳ مورد دیگر

Mona Merling is an Associate Professor in the Department of Mathematics at the University of Pennsylvania, affiliated with the School of Arts and Sciences. She holds a Ph.D. from the University of Chicago (2014) under Peter May. Prior to Penn, she was a J.J. Sylvester Assistant Professor at Johns Hopkins University. Her research focuses on algebraic K-theory, its applications to number theory and manifold theory, and equivariant stable homotopy theory. She has held research positions at institutions like the Mathematical Sciences Research Institute (MSRI) and the Max Planck Institute for Mathematics. Merling teaches advanced courses in algebraic topology, homotopy theory, and calculus, including innovative programs like the Penn Directed Reading Program and collaborations with the Prison Teaching Initiative to provide education in incarcerated settings. She organizes conferences and workshops, such as the Algebraic Topology Bridge Summer Workshop, fostering accessibility in topology education. Her research explores cutting-edge topics like scissors congruence K-theory, equivariant infinite loop space theory, and parametrized cobordism categories. Recent work includes collaborations on derived scissors congruence and multiplicative equivariant K-theory, with applications to geometric and algebraic structures. Her grants include funding for social justice initiatives in education.

• Nonlinear partial differential equations
• Singularity formation
• Mathematical analysis
• +۲ مورد دیگر

Manuel Del Pino is Professor at the University of Bath's Department of Mathematical Sciences and Royal Society Professor specializing in nonlinear partial differential equations. His research focuses on singularity formation, geometric evolution equations, and asymptotic analysis in fluid dynamics and mathematical physics. His investigations encompass blow-up phenomena in heat equations, vortex dynamics in Euler flows, and minimal surface theory. Current projects examine infinite-time singularity formation in parabolic equations and asymptotic properties of vortex configurations. Del Pino has received the Royal Society Professorship and leads multiple grants including 'Asymptotic patterns in nonlinear evolution problems' (EPSRC). He maintains collaborations with researchers globally through projects on singularity formation in PDEs.

Maarten de Hoopمشاهده پروفایل

استاد

• Seismic Wave Analysis
• Inverse Problems
• Deep Learning
• +۵ مورد دیگر

Maarten de Hoop is the Simons Chair and Professor of Computational and Applied Mathematics at Rice University, part of the George R. Brown School of Engineering. He holds visiting roles at MIT and the Chinese Academy of Sciences. His research spans seismic wave analysis, inverse problems, deep learning, and planetary seismology. He earned his Ph.D. in Technical Sciences from Delft University of Technology (1992), and earlier degrees from Utrecht University. Notable awards include the 1996 J. Clarence Karcher Award and 2001 Fellowship from the Institute of Physics. His work integrates computational mathematics with geophysics, focusing on extracting signal information from large datasets, developing novel inverse scattering methods, and applying deep learning to geoscience challenges. Recent studies include transformer models for in-context learning, semialgebraic neural networks, and seismic waveform foundation models like SeisLM. He leads the Geo-Mathematical Imaging Group, fostering interdisciplinary projects in planetary missions and data-driven discovery.

Mikaela Iacobelliمشاهده پروفایل

دانشیار

• Analysis
• Kinetic theory
• Statistical mechanics
• +۷ مورد دیگر

Mikaela Iacobelli is an Associate Professor in the Department of Mathematics at ETH Zürich. During the 2024-25 academic year, she was a von Neumann Fellow at the Institute for Advanced Study in Princeton. Previously, she held faculty positions at Durham University and a research fellowship at the University of Cambridge. Her educational background includes: PhD in Mathematics from Sapienza University of Rome and École Polytechnique in Paris (2015) Master's degree from Sapienza University of Rome (2012) Bachelor's degree from Sapienza University of Rome (2009) Mikaela's research lies at the interface of analysis, kinetic theory, and statistical mechanics. She studies partial differential equations that model the collective behavior of many-particle systems, with a focus on Vlasov-type plasmas and gravitational dynamics. Her current projects range from quasineutral and singular-limit problems for Vlasov-type systems to quantization of measures, ultrafast diffusion, and gradient-flow structures that link microscopic particle models to macroscopic fluid descriptions. She makes extensive use of PDEs techniques, optimal transport, probability, calculus of variations, and Riemannian geometry in her work. Her recent publications demonstrate a strong focus on Vlasov-type equations, particularly examining quasineutral limits, stability properties, and connections to other physical systems like Euler equations and magnetohydrodynamics. She has made significant contributions to understanding Landau damping, quantization problems on manifolds, and the mathematical foundations of plasma physics. Her notable scientific awards include: SNSF Starting Grant (Swiss ERC) Challenges and Breakthroughs in the Mathematics of Plasmas (2025-2030) von Neumann Fellow at the Institute for Advanced Study, Princeton (2024-2025) Invited speaker at the International Congress of Mathematical Physics (2021) CO-PI of the Germaine de Staël Funding Program for French-Swiss cooperation (2021-2023) L'Oréal prize for Women in Science (2015) Mikaela actively mentors postdocs, PhD, Master's, and Bachelor's students. Her current mentees include postdocs Dennis Chemnitz, Rishabh Gvalani, Stefano Rossi, and Simon Becker, as well as PhD students Thérèse Moerschell, Ata Deniz Aydin, and Antoine Gagnebin. She has served as PI for the Starting Research Grant from the University of Rome Sapienza and is currently the PI for the SNSF Starting Grant. She co-organizes several academic seminars including the Zurich Colloquium in Mathematics, the PDE and Mathematical Physics seminar at ETH Zürich and UZH, and the Analysis Seminar. She also serves on various committees including as Chair of the European Mathematical Society Committee for Women in Mathematics.

David Jerisonمشاهده پروفایل

استاد

• Fourier analysis
• partial differential equations
• free boundary problems
• +۲ مورد دیگر

David Jerison is a Professor of Mathematics at the Massachusetts Institute of Technology (MIT), where he conducts research in Fourier analysis and partial differential equations. His work focuses primarily on free boundary problems and, more recently, on internal Diffusion Limited Aggregation (internal DLA), a stochastic growth model. He maintains an active research program with numerous publications in leading mathematical journals. Professor Jerison's research spans several interconnected areas of mathematical analysis. His primary interests include Fourier analysis and partial differential equations, with particular emphasis on free boundary problems. In recent years, he has expanded his research to include internal Diffusion Limited Aggregation, a stochastic growth model that has connections to probability theory and mathematical physics. His work often bridges geometric analysis, spectral theory, and probabilistic methods, demonstrating the deep connections between different branches of mathematics. Analysis of Professor Jerison's recent publications reveals a consistent focus on geometric aspects of partial differential equations, particularly free boundary problems. His research shows progression from classical PDE theory toward more stochastic and probabilistic approaches, as evidenced by his work on internal DLA. The publications demonstrate interdisciplinary connections between mathematical analysis, probability theory, and mathematical physics, with applications ranging from geometric measure theory to quantum mechanics. Professor Jerison is actively involved in teaching and mentoring at MIT. He has taught courses including Differential Equations (18.03), Fourier Analysis and Applications (18.103), and Differential Analysis (18.155). He also directs the Summer Program for Undergraduate Research (SPUR), which is exclusively for MIT undergraduates, and organizes the mathematics section of the Research Science Institute (RSI) for high school students. His teaching materials are available through MIT's Open Courseware platform, indicating his commitment to educational outreach and accessibility.

Paata Ivanisviliمشاهده پروفایل

دانشیار

• Analysis
• Partial Differential Equations
• Probability
• +۵ مورد دیگر

Paata Ivanisvili is an Associate Professor at the University of California, Irvine (UCI), Department of Mathematics, School of Physical Sciences. His research focuses on Analysis, Probability, Harmonic Analysis, and Functional Analysis, with a particular emphasis on isoperimetric inequalities, functional inequalities, and discrete structures such as the Hamming cube. He has held visiting positions at institutions including the Hausdorff Research Institute for Mathematics and Princeton University. Ivanisvili has organized conferences such as the Dual Trimester Program at the Hausdorff Institute on Boolean Analysis in Computer Science (2024) and annual Summer/Fall Schools since 2021. He earned his PhD in Mathematics from Michigan State University (2015) and a BS from Saint Petersburg State University (2011). His research interests include sharp inequalities in analysis (e.g., Poincaré, Beckner, Ehrhard), hypercontractivity, and applications to discrete mathematics and probability. He has collaborated with prominent mathematicians such as Fedor Nazarov, Alexander Volberg, and Roman Vershynin. Notable awards include the NSF CAREER Award (2021–2025) and Simons Fellowship in Mathematics (2025–2026). Ivanisvili’s recent work explores the interface between harmonic analysis and discrete mathematics, including studies on additive energies, convex hulls of space curves, and learning theory. His articles frequently address foundational questions in geometric functional analysis, often using tools like Bellman functions and optimal control theory. He actively advises PhD students and has mentored visiting researchers at UCI.

Peter McGrathمشاهده پروفایل

استادیار

• Geometric Analysis
• Minimal Surfaces
• Partial Differential Equations
• +۳ مورد دیگر

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.

• Geometric Measure Theory
• Calculus of Variations
• Minimal surfaces
• +۱ مورد دیگر

Andrea Marchese is an Associate Professor in the Department of Mathematics at the University of Trento since 2019. He holds a PhD from the University of Pisa (2013) and has held academic positions at the University of Pavia, University of Zurich, and Max Planck Institute for Mathematics in the Sciences (Leipzig). His research focuses on Geometric Measure Theory, Calculus of Variations, and Optimal Transport, with contributions to minimal surfaces, branched transportation networks, and singular measure analysis. Education: PhD in Mathematics, University of Pisa (2013), Thesis: 'Two applications of the theory of currents' Master's in Mathematics, University of Milan (2008), Thesis: 'Singular points for coverings of Banach spaces' Bachelor's in Mathematics, University of Milan (2006), Thesis: 'Weak topologies and their metrizability in Banach spaces' Research Interests: Geometric Measure Theory, Calculus of Variations, Optimal Transport, Minimal Surfaces, and their applications to real analysis and geometric flows. Awards & Grants: Habilitation for Full Professor in Mathematical Analysis (2022) ERC Starting Grant (2020, ranked A with a score of 484/3272 proposals) Coordinated multiple INdAM/GNAMPA projects totaling over €25,000 Awarded grants from the University of Pavia, SNF, and Marie Sklodowska-Curie Actions Teaching: Has taught courses on Mathematical Analysis, Geometric Measure Theory, and Functional Analysis at the University of Trento, Pavia, Zurich, and Freiburg. Professional Activities: Organized international workshops, served as referee for over 30 journals (e.g., Inventiones Mathematicae , Journal of Differential Geometry ), and contributed to conferences worldwide.

Yi Laiمشاهده پروفایل

استادیار

• Geometric Analysis
• Ricci Flows
• Steady Gradient Ricci Solitons
• +۳ مورد دیگر

Yi Lai is an Assistant Professor in the Department of Mathematics at the University of California, Irvine (UCI). He earned his Ph.D. from UC Berkeley in 2021 under Richard Bamler and served as a Szego Assistant Professor at Stanford University (2021–2024), mentored by Otis Chodosh. His research centers on geometric analysis, with a focus on Ricci flows, steady gradient solitons, and the geometry of 3-manifolds. Dr. Lai's work explores the construction and classification of geometric structures like flying wing solitons, convergence properties of Ricci flow, and curvature behavior in low-dimensional manifolds. His publications frequently address long-time existence of geometric flows and symmetry in solitons, blending PDE theory with differential geometry. At UCI, he teaches courses such as Linear Algebra (Math 121A). No awards, grants, or supervised students are mentioned in available sources.

Betsy Stovallمشاهده پروفایل

استاد

• Harmonic Analysis
• Fourier Analysis
• Partial Differential Equations
• +۲ مورد دیگر

Betsy Stovall is a Professor of Mathematics at the University of Wisconsin–Madison and holds the Letters and Science Mary Herman Rubenstein Professor chair. She serves as the AMS Associate Secretary for the Central Section . Education : Not explicitly stated in provided text. Appointments : Regular faculty at UW–Madison since at least 2012 Organizer of graduate analysis seminars Research Interests : Stovall specializes in harmonic analysis , focusing on operators involving curvature, oscillatory integrals, and Fourier restriction phenomena. Her work intersects with partial differential equations (PDEs) through the study of dispersive equations and geometric analysis problems. Teaching : Complex Analysis (Math 623) - Fall 2021 Calculus III (Math 234) - Fall 2020 Graduate Analysis Seminar - Spring 2022 Organized UW Madison undergraduate summer school in Analysis (2018) Scientific Contributions : Sole or joint author of 15+ publications NSF RTG grant in Analysis and PDE Active in harmonic analysis seminars and educational initiatives Administrative Roles : AMS Associate Secretary Co-organizer of RTG/Student seminars Summer school director

Peter Schroederمشاهده پروفایل

استاد

• Computer Graphics
• Geometric Modeling
• Computational Physics
• +۳ مورد دیگر

Peter Schroeder is the Shaler Arthur Hanisch Professor of Computer Science and Applied and Computational Mathematics at the California Institute of Technology (Caltech). He holds a B.S. from the Technical University of Berlin (1987), M.S. from MIT (1990), M.A. and Ph.D. from Princeton University (1992–1994). His academic roles at Caltech include Assistant Professor (1995–1998), Associate Professor (1998–2001), Professor (2001–2013), and Hanisch Professor since 2013. He served as Division Deputy Chair (2012–2015) and Acting Director of the Center for Advanced Computing Research (2013–2014). Schroeder’s research focuses on numerical algorithms for computer graphics, geometric modeling, and physical simulation. His work emphasizes Discrete Differential Geometry, rebuilding classical differential geometry for computational applications. Key areas include cloth deformation, fluid dynamics, and vortex simulations. Notable contributions include 'Schrödinger’s smoke' and fluid visualization techniques using Clebsch maps. His publications span ACM Transactions on Graphics and address topics like constrained Willmore surfaces, filament-based plasma models, and shape reconstruction from metrics. He has received the ACM Fellowship and Best Paper in Geometry Processing Award. His research often bridges computational mathematics with artistic and engineering challenges, such as simulating ink chandeliers and solar flares. Schroeder’s academic leadership includes co-founding the ACM SIGGRAPH Academy and mentoring students like James R. McLaughlin and Yanke Song, both recipients of the Henry Ford II Scholar Award.

Antonio De Rosaمشاهده پروفایل

دانشیار

• Geometric Analysis
• Partial Differential Equations
• Geometric Measure Theory
• +۳ مورد دیگر

Antonio De Rosa is an Associate Professor in the Department of Decision Sciences at Bocconi University, Italy. Previously, he held positions at the University of Maryland, College Park (2020–2024), and the Courant Institute of Mathematical Sciences, New York University (2017–2020). He earned his Ph.D. in Mathematics from the University of Zurich in 2017 under Camillo De Lellis and Guido De Philippis. Education: Ph.D. in Mathematics, University of Zurich (2017). His research spans Geometric Analysis , Partial Differential Equations , Calculus of Variations , Geometric Measure Theory , Optimal Transport , and Non-convex Optimization . Recent work focuses on anisotropic geometric variational problems, including existence, regularity, and uniqueness of anisotropic minimal surfaces and CMC (constant mean curvature) surfaces. He has also contributed to interdisciplinary applications in Explainable Risk Assessment and Data Analysis . The 15 most recent articles highlight advancements in anisotropic surfaces , min-max theory , optimal transport , and mathematical programming (e.g., K-means clustering, linear programming). Key trends include the intersection of geometric measure theory with nonlinear PDEs and applications in machine learning and transportation networks . Scientific Awards and Grants: 2023 Maryland Research Excellence Carlo Ciliberto Prize (2019) ERC Starting Grant ANGEVA (101076411, 2023–2028) Air Force Office of Scientific Research (AFOSR) grant (FA9550-23-1-0123) NSF CAREER Award (DMS-2143124) NSF DMS Awards (DMS-1906451, DMS-2112311) AMS Simons Travel Grant Antonio actively supervises research and teaches courses such as Optimization and Introduction to Partial Differential Equations . His work is supported by significant funding totaling approximately €3 million.

Ke Zhangمشاهده پروفایل

استاد

• Dynamical Systems
• Hamiltonian Dynamics
• Weak KAM Theory
• +۳ مورد دیگر

Ke Zhang is a Professor in the Department of Mathematics at the University of Toronto. His research focuses on dynamical systems, particularly Hamiltonian dynamics, weak KAM theory, Arnold diffusion, and smooth dynamics. He also works on thermodynamic formalism and variational methods in Hamiltonian systems. B.S. in Mathematics from Tsinghua University Ph.D. in Mathematics from Pennsylvania State University under Yakov Pesin Postdoctoral research at University of Maryland and Fields Institute Ke Zhang's research explores instability phenomena in Hamiltonian systems (e.g., Arnold diffusion), viscosity solutions of Hamilton-Jacobi equations in weak KAM theory, and normal form/averaging theory. He has also contributed to vector calculus education through interactive Jupyter notebooks and teaching real analysis courses. He teaches courses such as MAT334 (Complex Variables), MAT1000/457 (Real Analysis I), MAT1001/458 (Real Analysis II), and MAT1845 (Dynamical Systems). The recent trends in his work align with geometric and analytical methods in dynamical systems, with applications to physics and nonlinear modeling. Ke Zhang maintains affiliations with institutions including the University of Toronto, University of Maryland, and Fields Institute. His educational background and postdoctoral training reflect a strong foundation in mathematical analysis and dynamical systems.

Chun Liuمشاهده پروفایل

استاد

• Nonlinear Partial Differential Equations
• Complex Fluids
• Multiscale Modeling and Analysis
• +۵ مورد دیگر

Chun Liu is Chair and Professor of Applied Mathematics at the Department of Applied Mathematics, Illinois Institute of Technology (IIT), within the College of Computing. His research focuses on Nonlinear Partial Differential Equations , Complex Fluids , and Multiscale Modeling , with applications in electrophysiology and materials science. He earned a Ph.D. from New York University’s Courant Institute, an M.S. from Duke University, and a B.S. from Fudan University. Prof. Liu leads projects on General Diffusion Systems , Ion Channel Dynamics , and Viscoelastic Fluids . He has secured grants from NSF, BSF, and DAAD for research in energetic variational approaches, multiscale materials modeling, and biomolecular systems. Key contributions include the development of Poisson-Boltzmann models , coarse-grained dynamics , and energetically stable numerical methods . He serves on editorial boards for Communications in Mathematical Sciences , SIAM Journal on Mathematical Analysis , and others. His work bridges applied mathematics with engineering and biophysics, addressing challenges in fluid mechanics, ion transport, and nonlinear systems.