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Kirsi PeltonenView profile

Senior Lecturer

• Differential Geometry
• Quasiregular Mappings
• Contact and Symplectic Geometry
• +3 more

Kirsi Peltonen is a Senior University Lecturer at the Department of Mathematics and Systems Analysis, School of Science, Aalto University. Her research bridges differential geometry, quasiregular mappings, and interdisciplinary mathematics-art collaborations. She leads the Math & Arts initiative, curating exhibitions like Collineation Grounds and IN TRANSITION that explore mathematical concepts through artistic mediums. Research interests focus on: Differential and contact geometry applications in topology Dynamics of quasiregular mappings Interdisciplinary mathematics-art-architecture education Geometric analysis of folded structures and material properties Publications reveal strong thematic evolution: early foundational work in quasiregular mappings (1999-2010) transitioned toward computational material science (2016-2023) and interdisciplinary pedagogical research (2019-2024). Recent outputs emphasize mathematics education through artistic mediums and structural analysis of origami-inspired architectures. Supervised doctoral students include Matias Dahl (awarded by Finnish Society of Sciences) and Riikka Kangaslampi. Leads workshops internationally, including collaborations at Shanghai Future Lab. Organized major conferences: Rolf Nevanlinna Colloquium (2013), Quasiweekend, and Lars Ahlfors Centennial Celebration.

• Fractals
• Geometric Measure Theory
• Metric Rectifiability
• +3 more

Tuomas Orponen is a Professor at the Department of Mathematics and Statistics, University of Helsinki, where he serves as a supervisor for the Doctoral Programme in Mathematics and Statistics. His research focuses on fractal geometry, geometric measure theory, and quantitative rectifiability, with particular emphasis on the interplay between geometric configurations and measure-theoretic properties in Euclidean and non-Euclidean spaces. He has led major research projects such as 'Incidences on Fractals' and 'Quantitative Rectifiability of Sets and Measures,' supported by the University of Helsinki. Orponen has published over 40 peer-reviewed articles and actively contributes to academic activities, including organizing conferences like 'Geometric Measure Theory and its Connections' and delivering invited talks at events like the Barcelona Analysis Conference 2019. His work bridges pure mathematics and applications in harmonic analysis and combinatorics, addressing questions about fractal structures, projection theorems, and metric dimensions. Orponen has collaborated internationally, visiting institutions such as the Institute of Mathematics of the Polish Academy of Sciences (IMPAN) and hosting researchers at the University of Helsinki. His research has advanced understanding in areas like Hölder-regular surfaces, self-similar measures, and continuous analogues of combinatorial problems.

Luca CapognaView profile

Professor

• Analysis
• Partial Differential Equations
• Quasiconformal Mappings
• +5 more

Luca Capogna is the Mary Augusta Jordan Professor of Mathematical Sciences at Smith College. Prior to joining Smith, he held positions as a Courant Instructor at NYU, a Rademacher Instructor at the University of Pennsylvania, and tenured positions at the University of Arkansas and Worcester Polytechnic Institute (where he served as department head from 2013-2020). From 2011-2013, he was a visitor at the University of Minnesota, serving as associate director of the Institute for Mathematics and its Applications (IMA). Capogna earned his Ph.D. from Purdue University and his B.S. from the Second University of Rome, Tor Vergata (Italy). His research spans analysis and partial differential equations, with specific interests in quasiconformal mappings, sub-Riemannian geometry, and geometric flows. In recent years, he has expanded his research to include machine learning applications, particularly using neural networks for system identification problems. His work demonstrates a strong connection between classical mathematical analysis and modern computational techniques. Capogna's publication record shows a clear evolution from pure mathematical analysis (particularly in sub-Riemannian geometry and PDE theory) to more applied work incorporating machine learning. His recent publications (2021-2024) increasingly focus on neural networks, system identification, and deep learning applications, while maintaining strong connections to his foundational work in analysis. Mary Augusta Jordan Professorship at Smith College Capogna has collaborated extensively with researchers including Giovanna Citti, Mario Bonk, and Enrico Le Donne. His work has been supported by various research grants, including an NSF RUI grant titled 'PDE and Geometry in non-smooth spaces' (2024). He has served in leadership roles, including as department head at Worcester Polytechnic Institute and associate director of the IMA at the University of Minnesota. His research has significant implications for both theoretical mathematics and practical applications in system modeling and identification, bridging the gap between pure mathematical analysis and modern computational approaches.

• Hamiltonian dynamics
• Topological entropy
• Pseudoholomorphic curves
• +3 more

Dr. Lucas Dahinden is a researcher in the Fundamental Mathematics group at the Mathematical Institute , Utrecht University. His work lies at the intersection of dynamical systems, symplectic geometry, and geometric analysis. Current affiliation: Research group of Alvaro del Pino (Utrecht University) Research Focus : Dahinden specializes in Hamiltonian dynamics , particularly studying topological entropy as a measure of chaos in dynamical systems. He has applied pseudoholomorphic curve theory and Floer homology to demonstrate entropy robustness under perturbations and, in collaboration with M. Alves, M. Meiwes, and A. Pirnapasov, established generic lower semi-continuity of topological entropy in 3D systems. Additional Contributions : He has advanced sub-Riemannian geometry through work on billiards (with A. del Pino) and contributed to Lorentz geometry by disproving the Borde-Sorkin conjecture (with L. Jin).

• Hamilton-Jacobi PDE
• Viscosity solutions
• Mean Field Games
• +3 more

Claudio Marchi is an Associate Professor of Mathematical Analysis at the University of Padua's Department of Mathematics "Tullio Levi-Civita". He maintains an active teaching and research schedule, with courses in Mathematical Analysis 1 for Biomedical Engineering students and Introduction to Partial Differential Equations for Mathematics students scheduled for the 2025-26 academic year. Professor Marchi's research focuses on Hamilton-Jacobi PDEs and viscosity solutions , Mean Field Games , and multiscale problems in partial differential equations . His work frequently addresses analytical challenges in non-standard geometries including networks and the Heisenberg group. Recent publications demonstrate his expertise in convergence rates, homogenization, and singular perturbation methods for partial differential equations. His publication record shows consistent scholarly output with approximately 3-4 papers annually in recent years, appearing in top mathematics journals including SIAM Journal on Mathematical Analysis, Mathematische Annalen, and Calculus of Variations and Partial Differential Equations. This sustained research activity indicates an established academic career with significant contributions to the field of mathematical analysis. Professor Marchi collaborates extensively with researchers including Fabio Camilli, Paola Mannucci, and Nicoletta Tchou, among others. His international collaborations reflect the global relevance of his work in partial differential equations and game theory. As an educator, Professor Marchi teaches core mathematics courses for engineering and mathematics students, maintaining regular office hours and providing detailed course materials through the university's Elearning platform. His teaching schedule includes specific exam periods scheduled through 2026, demonstrating his ongoing commitment to academic instruction.

• Analysis in Carnot groups
• Geometric inequalities
• Calculus of Variations
• +3 more

Davide Vittone serves as Associate Professor in the Department of Mathematics "T. Levi-Civita" at the University of Padua, Italy. His institutional affiliation is well-documented across university directories with consistent contact information including office room 5AB8 and direct phone line 049 827 1338. Professor Vittone's research focuses on advanced geometric analysis within constrained mathematical spaces, specifically examining Analysis in Carnot groups, Geometric inequalities in the Calculus of Variations, Geometric Measure Theory, Minimal surfaces, and Subriemannian geodesics. His work investigates how classical geometric concepts behave in non-holonomic environments where traditional Euclidean methods don't apply, requiring innovative analytical approaches to address the unique challenges of these constrained geometries. The analysis of his 15 most recent publications reveals a consistent trajectory in sub-Riemannian geometric analysis, with increasing focus on the interplay between measure-theoretic properties and variational principles in Carnot groups. His work demonstrates sophisticated mathematical techniques applied to fundamental questions about minimal surfaces, isoperimetric inequalities, and regularity theory within these specialized geometric frameworks. While no specific awards are documented in the available materials, Professor Vittone maintains an active research program as evidenced by his consistent publication record in geometric analysis. His work contributes to advancing mathematical understanding in sub-Riemannian geometry, a field with growing importance in both pure mathematics and applied contexts. For prospective students, Professor Vittone offers supervision opportunities in geometric analysis, particularly for those with strong backgrounds in differential geometry and real analysis. His research direction suggests potential projects examining minimal surface theory in Carnot groups, geometric measure theory applications, or calculus of variations problems in constrained environments. Collaborators would find opportunities in extending geometric analysis techniques to new sub-Riemannian settings or exploring applications in control theory and mathematical physics.

• Calculus on metric measure spaces
• Carnot-Caratheodory spaces
• Geometric analysis
• +3 more

Andrea Orazio Caruso is an Assistant Professor of Mathematical Analysis at the Department of Mathematics and Informatics within the College of Engineering at the University of Catania. He has held this position since January 2, 2004, following his appointment as a Research Assistant in 2003. His research primarily focuses on calculus in metric measure spaces, particularly Carnot-Caratheodory (sub-Riemannian) spaces and Carnot Lie groups, with special emphasis on geometric aspects. His work investigates the relationships between calculus, measure properties, and regularity properties of real functions. Caruso has presented his research at numerous conferences and workshops, including meetings on partial differential equations and metric space analysis. As an educator, Caruso has taught Calculus 1 and Calculus 2 courses continuously since the 2002/03 academic year, demonstrating remarkable teaching consistency. He has also developed preparatory courses for engineering and medical programs, as well as advanced mathematics courses for high school students preparing for university studies. Caruso serves as President of the Catania Section of the 'Accademia Italiana per la Promozione della Matematica,' a ministry-accredited organization that promotes mathematical excellence through competitions involving hundreds of thousands of students annually. His technical expertise includes proficiency with Windows, Mac, and Linux operating systems, as well as office applications, HTML, and TeX/LaTeX. He is fluent in English (spoken and written) and has reading knowledge of French, enabling him to participate in international mathematical discourse. His academic journey began with a cum laude Mathematics degree from the University of Catania in 1998, followed by a PhD in Mathematics in 2003.

• Functional Analysis
• Harmonic Analysis
• Operator Theory
• +4 more

Dmitriy Zanin is a Senior Lecturer in the School of Mathematics and Statistics at the University of New South Wales (UNSW), Faculty of Science. He is an active member of the Functional and Harmonic Analysis Group, which specializes in theoretical studies of functions and operators with applications spanning quantum physics and signal processing. His academic role involves research and instruction in advanced mathematical theories within a globally recognized institution. Zanin's research is deeply rooted in functional and harmonic analysis, extending into operator theory, noncommutative geometry, and mathematical physics. Key domains include: Operator algebras (von Neumann algebras, symmetric operator spaces) Noncommutative geometric structures (quantum tori, spectral invariants) Functional inequalities and embedding theorems Applications to quantum systems and signal processing frameworks His work consistently bridges abstract mathematical constructs with physical models. Analysis of Zanin's 15 most recent publications (2024–2025) reveals a strong focus on operator-theoretic frameworks in noncommutative settings. Predominant themes include: Sobolev embeddings and interpolation inequalities on quantum spaces Compactness criteria in quasi-Banach operator algebras Schatten-class commutator estimates and trace formulas Geometric invariants of deformed noncommutative manifolds This corpus demonstrates rigorous theoretical development at the intersection of functional analysis and quantum geometry.

Jean-Baptiste CaillauView profile

Professor

• Optimization
• Control Theory
• Applied Mathematics
• +5 more

Jean-Baptiste Caillau is a Professor of Applied Mathematics at Université Côte d'Azur, where he holds positions with CNRS, Inria, and the Laboratoire J.A. Dieudonné (LJAD). He is an active member of the CNRS research team Géométrie, Dynamique & Topologie and the Inria team McTAO in Sophia-Antipolis. His academic work spans multiple institutions including Polytech Nice Sophia where he teaches in the Department of Applied Mathematics and Modeling. Caillau's research focuses on optimization and control theory, with particular expertise in geometric control, orbital mechanics, and applications to aerospace engineering and systems biology. His work bridges theoretical mathematics with practical applications, especially in spacecraft trajectory optimization, bacterial resource allocation models, and computational methods for optimal control problems. He has developed significant software tools including the control-toolbox project, HamPath, and cotcot, which have become important resources in the optimal control community. Analysis of his recent publications reveals a strong trend toward interdisciplinary applications of control theory, particularly in biological systems (bacterial growth models, resource allocation) and aerospace engineering (solar sails, orbital mechanics). His work consistently combines deep mathematical analysis with practical computational methods, demonstrating expertise in both theoretical developments and numerical implementations. Recent publications show increasing focus on applications in systems biology while maintaining strong connections to geometric control theory and aerospace applications. best paper award at the 18th IFAC Workshop on Control Applications of Optimization, Paris, July 2022 Caillau actively participates in the academic community through seminar organization (Analyse & dynamique seminar, OptAzur), conference participation, and collaborative projects including the PDE-AI project (PEPR IA). His research has evolved from fundamental geometric control theory toward increasingly interdisciplinary applications while maintaining strong theoretical foundations. His GitHub activity shows ongoing development of computational tools for optimal control, reflecting his commitment to making theoretical advances accessible through practical software implementations. Caillau leads or participates in multiple research teams including the McTAO Inria team and the Géométrie, Dynamique & Topologie CNRS team at LJAD. His work connects mathematical theory with practical applications through collaborations with researchers across disciplines, particularly in aerospace engineering and systems biology.

Valentina FranceschiView profile

Associate Professor

• Mathematical Neuroscience
• Sub-Riemannian Geometry
• Cortical-Inspired Models
• +3 more

Valentina Franceschi is an Associate Professor at the Department of Mathematics of the University of Padua. Her academic journey includes a post-doctoral research career in France (Inria Paris, Université Paris-Sud, Sorbonne Université) and international collaborations through projects like RUBIN-VASE funded by ANR. She specializes in cortical-inspired models for vision and sub-Riemannian geometry. Current affiliation: Department of Mathematics, University of Padua Education: MSc in Mathematics (University of Bologna, 2012), PhD in Mathematics (University of Padova, 2016) Research focus: Mathematical modeling of visual perception, geometric analysis, and image processing applications Selected projects: RUBIN-VASE (ANR-funded), MesuR (Marie Curie Fellowship) Professional memberships: Member of UMI group 'Matematica delle immagini, della visione e delle loro applicazioni'

• Differential Geometry
• Geometric Analysis
• Sub-Riemannian Geometry
• +3 more

Aleksander Vladimirov Petkov is an Associate Professor at the Department of Geometry within the Faculty of Mathematics and Informatics at the University of Sofia. His research focuses on differential geometry, geometric analysis, and spectral geometry, particularly in the context of quaternionic contact manifolds and sub-Riemannian structures. He holds a PhD in geometry, with a dissertation titled Riemannian and Sub-Riemannian Manifolds with Structures . His work explores eigenvalue problems, heat equations, and the qc Yamabe problem, contributing to the understanding of geometric properties and spectral behavior in non-Riemannian settings. Recent publications include studies on HKT manifolds, Obata sphere theorems, and sharp eigenvalue bounds for sub-Laplacians. Petkov has authored/co-authored papers in journals like International Mathematics Research Notices and Journal of Geometric Analysis , with ongoing preprints focusing on geometric flows and conformal structures. His research bridges pure geometry with analytical methods, emphasizing both theoretical foundations and specific manifold classifications.

Michel RuminView profile

Lecturer

• Differential Geometry
• Spectral Theory
• Contact Geometry
• +5 more

Michel Rumin is a Lecturer at the Orsay Institute of Mathematics, University of Paris-Sud, France, with his office located in Building 307, Office 2N22 at the Orsay campus. He teaches advanced mathematics courses for engineering and physics students, including the Master M2 MSV deterministic modeling module and first-year Polytech engineering pathway covering linear algebra, differential equations, and numerical integration using Scilab practical work. Rumin's research centers on differential geometry and spectral theory, with specialized expertise in contact manifolds, sub-Riemannian geometry, and Carnot groups. His work explores cohomology, spectral invariants, and analytic torsions, bridging geometric structures with analytical methods. Key contributions include foundational results on differential forms for contact manifolds (1990) and recent advances in topological aspects of spectral invariants (2024). Analysis of his 13 publications from 1990-2024 reveals a consistent trajectory in geometric analysis: early work established frameworks for contact geometry, evolving through Carnot group cohomology (2018) toward dynamical/topological investigations of spectral invariants (2024). His research demonstrates persistent focus on non-Riemannian geometric structures, with increasing integration of topological and dynamical systems perspectives in recent years. Scientific awards: No awards or fellowships are documented in the available materials. Rumin actively mentors students through structured teaching materials including worksheets, test annals (2014-2016), and Scilab practical sessions for linear algebra and differential equations. His S2 PMCP course prepares students for physics competitive exams with comprehensive notes on vector spaces and matrix calculus. No research grants or laboratory affiliations are specified in the provided documentation.

Karen HabermannView profile

Associate Professor

• Stochastic Processes
• Geometric Analysis
• Mathematical Physics
• +3 more

Karen Habermann is an Associate Professor in the Department of Statistics at the University of Warwick, where she previously held the position of Harrison Early Career Assistant Professor. Her academic journey includes postdoctoral fellowships at Sorbonne Université (funded by FSMP) and the Hausdorff Center for Mathematics at the University of Bonn. She completed her PhD at the University of Cambridge under Prof. James Norris, focusing on sub-Riemannian diffusion processes. Her research interests span stochastic processes, geometric analysis, and differential geometry, with a focus on sub-Riemannian manifolds and their applications in mathematical physics. Education: PhD in Mathematics from the University of Cambridge (Cambridge Centre for Analysis), MMath and BA in Mathematics from the University of Cambridge. Her research explores stochastic processes on geometric structures, including sub-Riemannian diffusions, optimal transport, and stochastic differential equations. Notable contributions include studies on Brownian motion configurations, Lévy area approximations, and Cartan connections in stochastic developments. She has been affiliated with teams such as Inria Paris' CAGE and Prof. Ugo Boscain’s group, reflecting interdisciplinary collaborations in geometric analysis. Her work often bridges probability theory and differential geometry, with applications in mathematical physics and medical imaging (e.g., proton beam radiotherapy modeling). Office hours for Term 3 2024/25 are Wednesdays 14:30–15:30 and Fridays 13:30–14:30 by email appointment.

Erin MartinView profile

Associate Professor

• Partial Differential Equations
• Geometric Analysis
• Graph Theory
• +4 more

Dr. Erin Martin is an Associate Professor of Mathematics at Lindenwood University, located in St. Charles, Missouri. She holds a B.S. in applied mathematics from the University of Missouri–Rolla (now Missouri S&T), and a M.S. and Ph.D. in mathematics from the University of Arkansas. Prior to joining Lindenwood in 2017, she served as faculty and administrator at Westminster College for nine years. Her academic interests span Partial Differential Equations, Geometric Analysis, Graph Theory, and Mathematics Education. She actively engages in undergraduate research, mentoring projects across diverse areas like mathematical biology and applied mathematics. Dr. Martin’s research focuses on geometric analysis and nonlinear PDEs, particularly in Carnot group settings. Her notable publications include studies on parabolic equations and curvature flows. She teaches a broad range of courses from Intermediate Algebra to Advanced Calculus, emphasizing active learning methods like inquiry-based learning. She also contributes to the university’s Data Science and Mathematics programs. No scientific awards are listed for Dr. Martin. Her advising and grants section remains under development, with no specific grants or mentorship programs detailed in the provided text. She is affiliated with the Mathematics department within the College of Science, Technology, and Health. Outside academia, Dr. Martin enjoys swing dancing, baking, and reading science-fiction/fantasy novels with her family.

Rob NeelView profile

Associate Professor

• Geometry
• Topology
• Probability
• +4 more

Rob Neel is an Associate Professor in the Department of Mathematics at Lehigh University. His research focuses on Geometry, Topology, and Probability, with a particular emphasis on sub-Riemannian geometry, stochastic processes, and geometric analysis. He has contributed extensively to understanding heat kernel asymptotics, Brownian motion on manifolds, and applications of probabilistic methods in geometric contexts. Neel's work spans theoretical frameworks such as maximal couplings, geometric boundaries, and wavelet analysis, alongside practical applications in control theory and optimization. His research has been published in leading journals like ESAIM and the Journal of Differential Geometry. Notably, he explores topics like the Dirichlet problem at infinity, sub-Laplacians in sub-Riemannian settings, and the Ricci flow on surfaces. While no specific awards or advisory roles are listed, his scholarly output reflects deep engagement with both pure and applied mathematical challenges.