Find Academic Supervisors

• Geometric Measure Theory
• Calculus of Variations
• Optimal Transportation
• +3 more

Andrea Marchese is an Associate Professor in Mathematical Analysis at the University of Trento, Department of Mathematics. His research focuses on geometric measure theory, calculus of variations, and optimal transportation networks. He actively participates in organizing academic events such as the Analysis seminar and international workshops on geometric measure theory and partial differential equations. His work addresses topics like minimal surfaces, modulo p problems, and singular set analysis in geometric flows. Marchese collaborates with leading institutions and frequently presents at conferences worldwide, including recent talks in Munster and upcoming events in Pisa and Trento. Education: Completed his Ph.D. in 2014 with a thesis on optimal irrigation networks. Professional activities include seminar organization across multiple academic years and participation in high-impact international conferences. His research interests bridge pure mathematics with applied problems in network optimization and geometric analysis. Scientific contributions include over 38 publications in top journals like Journal of Functional Analysis and Communications on Pure and Applied Mathematics . His work emphasizes rigorous analysis of geometric variational problems and their applications to real-world transportation models.

• Metric Measure Spaces
• Sobolev Spaces
• Calculus of Variations
• +3 more

Danka Lučić is a Researcher at the University of Jyväskylä, specializing in advanced mathematical analysis with a focus on metric measure spaces, Sobolev spaces, and non-smooth geometry. Her work bridges functional analysis, geometric measure theory, and calculus of variations, addressing foundational questions in these areas through innovative axiomatic and analytical approaches. Education: Ph.D. in Mathematics, 2019 (Thesis: Universal infinitesimal Hilbertianity of sub-Riemannian manifolds) Her research explores topics such as BV functions, normed modules, and optimization problems in metric settings. She has contributed to representation theorems, density results, and Gamma-convergence techniques in non-smooth frameworks. Collaborations with leading mathematicians like Nicola Gigli, Enrico Pasqualetto, and Tapio Rajala highlight her role in advancing interdisciplinary mathematical analysis. Her recent work emphasizes metric Sobolev spaces, Lebesgue differentiation in measure spaces, and applications to geometric optimization. Notable results include equivalence of Sobolev space definitions, BV-extension set approximations, and analysis of Hilbertian structures in non-Euclidean spaces.

• Mathematical Analysis
• Partial Differential Equations
• Functional Analysis
• +3 more

Diego Pallara is a Full Professor at the Department of Mathematics and Physics of the University of Salento (Lecce). His research focuses on mathematical analysis, particularly partial differential equations, functional analysis, calculus of variations, and geometric measure theory. He has contributed extensively to studies on fractional calculus, nonlocal functionals, and subelliptic equations in stratified Lie groups. His work often intersects with stochastic processes and spectral theory, with a strong emphasis on analytical techniques such as semigroup theory and regularity estimates. Key research areas include isoperimetric inequalities, BV functions in infinite-dimensional spaces, and the analysis of degenerate elliptic and parabolic operators. He has organized international conferences and seminars, such as the 19th Internet Seminar on Infinite Dimensional Analysis and CDV2016 (Lecce Conference on Calculus of Variations and PDEs). His research has been published in prestigious journals like Annali di Matematica Pura e Applicata and Journal of Functional Analysis. Diego Pallara’s contributions span over 70 publications, with notable works on fractional Gaussian perimeters, stability of geometric inequalities, and mean value properties in sub-Riemannian geometries. His work frequently addresses the interplay between functional inequalities, geometric structures, and stochastic models.

• Sub-Riemannian Geometry
• Mathematical Analysis
• Neurogeometry
• +3 more

Giovanna Citti is a Full Professor in the Department of Mathematics at the University of Bologna. Her research focuses on sub-Riemannian geometry, mathematical analysis, and neurogeometry, with a particular emphasis on modeling the functional architecture of the visual and motor cortices. She develops geometric frameworks to understand neural processing in the brain, including models of visual perception and motor control. Her work integrates concepts from differential geometry, partial differential equations (PDEs), and Lie group theory to analyze sub-Riemannian structures. She explores regularity properties of subelliptic PDEs and applies these to biological systems, such as the cortical organization of the visual cortex and motor pathways. Recent efforts include developing brain-inspired neural networks and studying neurogeometric models of stereo vision and 3D perception. Key contributions include sub-Riemannian models of perceptual completion, cortical-based optimal transport frameworks, and analysis of geometric optical illusions. Her research bridges pure mathematics and neuroscience, addressing challenges in both fields through innovative interdisciplinary approaches.

Claudio GorodskiView profile

Professor

• Differential Geometry
• Lie Groups and Representations
• Riemannian Geometry
• +3 more

Claudio Gorodski is a Full Professor at the Department of Mathematics of the University of São Paulo (USP), affiliated with the Institute of Mathematics and Statistics (IME). His research focuses on Differential Geometry, particularly in areas such as Riemannian geometry, symmetric spaces, Lie group representations, and geometric structures. He serves as Editor-in-Chief of the São Paulo Journal of Mathematical Sciences . He teaches advanced courses including Geometric Analysis, Riemannian Geometry, and Differential Topology. Recent courses include 'Geometria Riemanniana' (Riemannian Geometry) and 'Grupos de Lie Compactos e Suas Representações' (Compact Lie Groups and Their Representations). His research group organizes a bi-weekly seminar on Differential Geometry. Key research interests include the geometry of isometric actions, submanifold theory, and the interplay between algebraic structures (Lie groups) and geometric objects. His work often explores curvature properties, symmetry, and classification problems in geometric spaces. He has authored over 60 research articles and a textbook on Smooth Manifolds. His contributions span topics like orbit space geometry, polar actions, and geometric analysis in symmetric spaces. Current projects include studies on positively curved manifolds, diameter gaps in sphere quotients, and representation-theoretic aspects of geometric actions.

Bolys SabitbekView profile

Research Fellow

• Partial Differential Equations
• Hyperbolic Equations and Systems
• Functional Inequalities
• +7 more

Bolys Sabitbek is a Postdoctoral Research Assistant in the School of Mathematical Sciences at Queen Mary University of London, working under the supervision of Claudia Garetto and Michael Ruzhansky on an EPSRC-funded project. He is also affiliated with the Ghent Analysis and PDE research group at Ghent University, Belgium. His research is centered on advanced topics in partial differential equations and harmonic analysis. Research Interests: His work primarily investigates hyperbolic equations and systems with multiplicities, functional inequalities on stratified Lie groups, and the global existence and nonexistence of solutions to PDEs. These areas lie at the intersection of pure and applied analysis, with deep connections to geometry and mathematical physics. Publication Trends: His recent articles (2021–2025) demonstrate a strong focus on inequalities (Hardy, Rellich, Caffarelli-Kohn-Nirenberg) on stratified and sub-Riemannian structures, blow-up phenomena in nonlinear PDEs on Lie groups (especially Heisenberg and stratified groups), and well-posedness of hyperbolic systems with singular or non-diagonalisable coefficients. His work combines functional analysis, microlocal techniques, and geometric insights. Scientific Engagement: He is actively involved in the international analysis community, as evidenced by his participation in the ISAAC Congress. While no specific awards are listed, his consistent publication output in high-level journals reflects strong scholarly impact. Advising and Grants: Currently, there is no public information about students he may be advising. He is supported by an EPSRC grant, indicating competitive external funding for his research. Collaborative Environment: He is part of a vibrant research group led by Michael Ruzhansky, known for work in analysis and PDEs on Lie groups. His dual affiliation with Queen Mary and Ghent University highlights a collaborative, international research profile.

• Differential Geometry
• Riemann-Finsler Geometry
• Geometric Analysis
• +2 more

Bankteshwar Tiwari is Professor in Mathematics at Banaras Hindu University, Varanasi, India, with additional affiliation at Slovakia's Lepage Research Institute. His academic profile centers on advanced geometric structures, particularly within Finsler geometry frameworks. Research focuses on Differential and Riemann-Finsler Geometry, specializing in Randers, Kropina, and Funk metric spaces. Key investigations include curvature properties, isoperimetric problems, geodesic behavior, and stability analysis. Recent work bridges pure geometry with biological modeling through predator-prey systems and cancer dynamics. Analysis of 2023-2025 publications reveals intensifying interdisciplinary applications: geometric methods now address ecological stability (Jacobi vs linear stability in predator-prey models) while maintaining core contributions to Finsler curvature theory, metric measure spaces, and homogeneous group inequalities. Collaborations span Czech, Slovak, Hungarian, Italian, Romanian, and Polish institutions through the International Visegrad Fund.

• Metric Measure Spaces
• Optimal Transport
• Geometric Analysis
• +3 more

Tapio Rajala is an Associate Professor at the University of Jyväskylä. His research focuses on geometric analysis, metric measure spaces, optimal transport, and functional analysis. He has contributed to areas such as Sobolev extensions, BV spaces, and geometric measure theory in non-smooth settings. His work often intersects with calculus of variations, partial differential equations, and the study of geometric properties in metric spaces. Recent publications explore topics like Laplacian bounds in metric measure spaces, entropy-transport problems, and dimension estimates for fractal-like structures. Rajala has organized academic events such as the Sub-Riemannian Geometry workshops (2017–2019) and the Optimal Transport and Applications conferences (2011–2018). His research trends emphasize interdisciplinary approaches to geometric analysis and functional inequalities.

• Sub-Riemannian Geometry
• Optimal Transport
• Control Theory
• +4 more

Ludovic Rifford is a Professor of Mathematics at Université Côte d'Azur and holds the CNRS-AIMS Chair in Mathematics at AIMS-Senegal (2023-2027). He has held visiting positions at institutions including Universidad de Chile, Mathematical Sciences Research Institute (Berkeley), and Centro de Modelamiento Matemático. His research focuses on Sub-Riemannian Geometry, Optimal Transport, and Control Theory. Education: PhD in Mathematics, Université Lyon I (2000) Habilitation à Diriger des Recherches, Université Paris XI (2005) Rifford's work addresses fundamental problems in geometric control theory, including the Sard Conjecture for sub-Riemannian structures, regularity of optimal transport maps, and Hamilton-Jacobi equations. His 2025 preprints explore mixed convex integration and analytic minimal rank Sard conjectures. Scientific Awards: Junior Member, Institut Universitaire de France (2011-2016) He has organized numerous international workshops in Africa, including the Conference at the Frontiers of Sub-Riemannian Geometry (2024) and Differential Geometry at AIMS-Senegal (2024), emphasizing his commitment to scientific collaboration between France and Africa.

• Probability
• Analysis
• Differential Geometry
• +3 more

Jing Wang is an Associate Professor of Mathematics and Statistics at Purdue University with a joint appointment in the Department of Mathematics and Department of Statistics. She holds affiliations within the College of Science. Her research is supported by the National Science Foundation (NSF) under grant DMS-2246817. Prior to her current position, she was a J.L. Doob Research Assistant Professor at the University of Illinois at Urbana-Champaign (2015–2018) and a postdoctoral fellow at the Institute for Mathematics and its Applications (IMA) at the University of Minnesota (2014–2015). She earned her Ph.D. in Mathematics from Purdue University in 2014. Her research focuses on probability, analysis, and differential geometry, with applications to stochastic processes on manifolds, sub-Riemannian geometry, and geometric analysis. Key areas include spectral bounds for exit times, stochastic areas and winding numbers, and heat kernel analysis on non-Euclidean spaces. Notable contributions include work on the Hot Spots conjecture, hypoelliptic diffusions, and geometric stochastic models such as the Parabolic Anderson model on Heisenberg groups. Her recent studies explore large deviations principles for sub-Riemannian random walks and asymptotic behaviors of stochastic processes on complex manifolds. Funding: NSF DMS-2246817 supports her ongoing research in stochastic analysis and geometric probability.

Matthew BadgerView profile

Associate Professor

• Geometric Measure Theory
• Geometric Function Theory
• Harmonic Analysis
• +2 more

Matthew Badger is an Associate Professor at the University of Connecticut specializing in Geometric Measure Theory and its interdisciplinary applications. His research bridges geometric analysis, harmonic functions, and metric geometry with significant implications for partial differential equations and free boundary problems. His primary research focuses on rectifiability criteria for measures and sets, harmonic measure analysis, and parameterization problems in metric spaces. Badger has pioneered multiscale analysis techniques for 1-rectifiable measures and made fundamental contributions to the Analyst's Traveling Salesman theorem in Banach spaces, with recent work extending to Carnot groups and parabolic geometries. Analysis of his 15 most recent publications reveals a consistent trajectory in geometric measure theory, with increasing emphasis on connections between rectifiability, harmonic analysis, and nonlinear PDEs. His work demonstrates particular innovation in handling non-Euclidean settings like Banach spaces and Carnot groups while maintaining deep connections to classical problems in potential theory. Scientific recognition includes: NSF Postdoctoral Research Fellowship (2012) NSF CAREER Award for "Analysis and Geometry of Measures" (2017) Badger actively participates in collaborative research initiatives including the Northeast Analysis Network (2019). While specific student names aren't publicly listed, his publication record indicates ongoing mentorship of graduate researchers in geometric analysis. His teaching responsibilities include advanced mathematics courses with structured office hours for student engagement.

Filip RindlerView profile

Professor

• Partial Differential Equations (PDEs)
• Geometric Measure Theory
• Mathematics of Material Science
• +5 more

Filip Rindler is a Professor of Mathematics at the University of Warwick, based at the Mathematics Institute. His research focuses on the intersection of Applied and Theoretical Mathematics, particularly oscillation and concentration phenomena in Material Science, such as elasto-plasticity and dislocation dynamics. He has held significant grants, including ERC Starting and Consolidator Grants, and has supervised numerous PhD students and postdocs. Rindler is an editor for journals like Mathematical Models and Methods in Applied Sciences (M3AS) and Revista Matemática Iberoamericana. He earned his DPhil from the University of Oxford and a Diplom from TU Berlin. Education: 2009–2011: DPhil (PhD) in Mathematics, University of Oxford 2004–2008: Diplom in Mathematics (with distinction), TU Berlin Research Interests: Rindler’s work spans PDEs, Geometric Measure Theory, and the Mathematics of Material Science. He investigates singularities in nonlinear PDEs, particularly those arising in elasto-plasticity and dislocation mechanics. His research combines geometric and analytic techniques to understand concentration and oscillation effects, with applications to material deformation and fracture mechanics. Grants & Awards: Over £4 million in funding, including ERC grants, Lloyds Register Foundation grants, and the 2025 Blavatnik UK Awards for Young Scientists. His work has been recognized with the Whitehead Prize (2018) and multiple research fellowships. Advising & Labs: Leads the ERC-funded SINGULARITY and CONCENTRATE projects, supervising postdocs and PhD students in topics like dislocation dynamics and shape optimization. His team explores applications in data science and anomaly detection in streaming data. Labs/Teams: Principal Investigator of the ERC SINGULARITY and CONCENTRATE projects, collaborating with institutions globally on topics such as dislocation-driven plasticity and geometric measure theory.

• Metric Geometry
• Optimal Transport
• Ricci Curvature
• +3 more

Dr. Mattia Magnabosco is a Research Fellow at the Mathematical Institute, University of Oxford, based at the Andrew Wiles Building. His primary research affiliations include: Geometry research group Oxford Centre for Nonlinear PDE Contact details consist of a direct phone line (+44 1865 615105) and an online contact form. His research centers on metric geometry and geometric analysis, with specialization in the curvature-dimension (CD) condition, sub-Finsler geometry, and Brunn-Minkowski inequalities. He investigates metric measure spaces with non-constant dimensionality, Ricci curvature bounds, and optimal transport theory. His work bridges pure mathematics with applications in nonlinear partial differential equations, particularly examining geometric structures where classical curvature conditions fail or manifest unexpectedly. Analysis of his 2023-2025 publications reveals a cohesive trajectory focused on the CD condition across diverse geometric contexts. Key trends include: failure mechanisms in sub-Finsler and almost-Riemannian settings; equivalence between Brunn-Minkowski inequalities and curvature conditions; and novel behaviors in spaces with negative dimension parameters. His contributions consistently address foundational questions in metric measure spaces while advancing theoretical frameworks for geometric analysis. Scientific awards: None documented in available sources. Advising and grants: No information provided regarding doctoral students, master's advisees, or research funding. Labs and teams: Dr. Magnabosco actively collaborates within Oxford's Geometry research group and the Oxford Centre for Nonlinear PDE, contributing to interdisciplinary projects at the intersection of geometry, analysis, and mathematical physics.

Tai MelcherView profile

Associate Professor

• Probability
• Geometry
• Analysis
• +6 more

Tai Melcher is an Associate Professor at the Department of Mathematics , University of Virginia. Their research intersects Probability , Geometry , and Analysis , focusing on infinite-dimensional analysis, Gaussian measures, stochastic differential equations on Lie groups, Markov processes, differential operators, and hypoellipticity theory. Co-organizer of the UVa Probability Seminar Founder and coordinator of Women in Probability Faculty coordinator for UVa Math Ambassadors Email: melcher@virginia.edu Recent publications explore stochastic differential equations with degenerate noise, sub-Riemannian random walks , and quasi-invariance in infinite-dimensional settings. These works connect probability theory with geometric structures like Lie groups and Heisenberg manifolds, emphasizing functional inequalities, heat kernels, and Malliavin calculus. Key contributions include: Advancing understanding of hypoelliptic heat kernels on infinite-dimensional groups Developing large deviations principles for geometric stochastic processes Establishing smoothness properties of heat kernel measures Current projects involve collaborations with researchers like F. Baudoin, M. Gordina, and B. Driver. The work appears in journals such as Journal of Functional Analysis , Annales Henri Lebesgue , and Transactions of the AMS . For course materials, visit the UVa Canvas platform. Office: 205 Kerchof Hall, University of Virginia, Charlottesville, VA 22903. Phone: (434) 982-2782. Fax: (434) 982-3084.

Bart M.N. SmetsView profile

Researcher

• Partial Differential Equations
• Geometric Deep Learning
• Image Processing
• +3 more

Bart M.N. Smets is a University Researcher at Eindhoven University of Technology, affiliated with the Center for Analysis, Scientific Computing and Applications and the Geometric Learning & Differential Geometry group within the School of Mathematics and Computer Science. His research focuses on geometric deep learning, partial differential equations (PDEs), and their applications in image processing and convolutional neural networks (CNNs). Dr. Smets has contributed to advancing PDE-based CNN architectures, data-driven cartan connections for vascular tracking, and geometric analysis frameworks. He teaches the course Differential Geometry for Image Processing and has presented at international conferences on topics like geometric deep learning and PDE-based morphological convolutions. His work aligns with UN Sustainable Development Goals through innovations in medical imaging and computational methods. Key research themes include equivariant neural networks, sub-Riemannian geometry applications, and mathematical foundations of deep learning. Over 12 publications since 2019 reflect his interdisciplinary approach combining pure mathematics with practical machine learning challenges.