Find Academic Supervisors

• Stochastic Analysis
• Constructive Quantum Field Theory
• Statistical Mechanics of Multiscale Systems
• +9 more

Professor Massimiliano Gubinelli is the Wallis Professor of Mathematics at the University of Oxford and a Professorial Fellow at St. Anne's College. He leads the Stochastic Analysis Group within the Mathematical Institute, where his research focuses on stochastic analysis, constructive quantum field theory, and the intersection of probability theory with partial differential equations (PDEs) and renormalization group methods. His work spans statistical mechanics of multiscale systems, analysis of PDEs with random terms, homogenisation theory, mathematical quantum mechanics, path-integral formalisms, and non-commutative probability/geometry. He has pioneered paracontrolled distribution techniques to study singular stochastic PDEs and explored rough paths in ramification and transport equations. Recent publications highlight advancements in the sine-Gordon model via stochastic quantization, nonlinear PDEs with modulated dispersion, and ρ-irregularity in stochastic systems. His research bridges stochastic analysis, quantum field theory, and PDEs, emphasizing pathwise behavior and renormalization. Scientific Awards Junior member of the Institut Universitaire de France (2013–2018) Invited session speaker at the 2018 International Congress of Mathematicians (ICM) in Rio He contributes to scientific software development as a lead developer of TeXmacs , an open-source platform for technical documents, and teaches courses such as C8.1 Stochastic Differential Equations (MT22). No formal student advisement or grant details are provided.

Xue-Mei LiView profile

Professor

• Stochastic Analysis
• Geometric Stochastic Analysis
• Malliavin Calculus
• +5 more

Xue-Mei Li is a Professor of Mathematics at Imperial College London and École Polytechnique Fédérale de Lausanne (EPFL). She holds chairs in Probability and Stochastic Analysis at both institutions. Her research focuses on stochastic analysis, geometric stochastic processes, and multi-scale systems, with contributions to areas like Malliavin calculus, fractional dynamics, and coarse curvature. Li has held positions at the University of Warwick, University of Connecticut, and others, supported by fellowships from the Alexander von Humboldt Foundation, Royal Society, and MSRI. Her work addresses fundamental questions in stochastic differential equations, geometric analysis, and their applications to complex systems. Education and Career: PhD in Mathematics, University of Warwick EPSRC Research Associate Faculty positions at the University of Connecticut (tenured Associate Professor) Research Interests: Her research spans stochastic differential equations (SDEs), stochastic partial differential equations (SPDEs), geometric stochastic analysis, and fractional dynamics. Notable contributions include the BEL formula, strict local martingales, and solutions to longstanding problems in strong completeness on non-compact manifolds. She explores interactions between stochastic processes and geometric structures, including coarse Ricci curvature and homogenization theory. Awards and Grants: Supported by NSF, EPSRC/UKRI, and Swiss NSF grants Awarded fellowships from Alexander von Humboldt Foundation, Royal Society, and MSRI Advising and Teams: PhD students: Johann Gehringer, Rhys Steel, Julian Sieber, and others Leading working groups on stochastic analysis and geometric dynamics

Benjamin BrandsView profile

Research Fellow

• Computational Mechanics
• Multiscale Modeling
• Multiscale Material Modeling
• +3 more

Dr. Benjamin Brands is a Research Fellow at the Department of Mechanical Engineering, Faculty of Engineering, Friedrich-Alexander University Erlangen-Nürnberg (FAU), specializing in computational mechanics and multiscale material modeling. He works under the Chair of Engineering Mechanics (LTM), led by Prof. Paul Steinmann. Core Research: Multi-scale, multi-physics modeling of magneto-sensitive polymeric materials and reduced-order modeling techniques. Technical Focus: Computational homogenization, finite element methods, and magneto-mechanical material analysis. Key Projects: Involved in the ERC-funded MOCOPOLY project (2012–2017), which explored process-microstructure-property relationships in smart materials. His publications span computational mechanics, material science, and advanced numerical methods, emphasizing magneto-sensitive polymers and multi-scale simulations. No scientific awards or student advisement details are explicitly mentioned.

Elissa EggenweilerView profile

Researcher

• Homogenisation
• Boundary Layer Theory
• Coupling Free-Flow and Porous-Medium Systems
• +3 more

Elissa Eggenweiler holds the position of Researcher at the University of Stuttgart, affiliated with the Institute of Applied Analysis and Numerical Simulation under the Chair of Applied Mathematics. She specializes in multiscale problems, particularly in homogenization, boundary layer theory, and the coupling of free-flow and porous-medium systems. Her work bridges theoretical analysis and numerical simulation techniques. Her research focuses on interface conditions for fluid-porous medium interactions, with applications in Stokes-Darcy systems and uncertainty quantification. Notable contributions include modifications to classical boundary conditions (e.g., Beavers-Joseph) and Bayesian validation frameworks for coupled flow systems. Eggenweiler’s publications (2020–2023) emphasize rigorous mathematical analysis and computational methods for multiscale phenomena. While no explicit awards are listed, her involvement in projects like the validation of pore-scale resolved models highlights her collaborative and applied research ethos. Currently, she contributes to the development of effective coupling conditions and numerical frameworks at the Institute, with a focus on advancing porous-medium and free-flow system modeling.

• Calculus of Variations
• Partial Differential Equations
• Homogenisation
• +9 more

Lucia Scardia is an Associate Professor in the Department of Mathematics at Heriot-Watt University (Edinburgh EH14 4AS). Her research focuses on calculus of variations, partial differential equations, homogenisation (deterministic and stochastic), and harmonic analysis, with applications in material science including plasticity, dislocations, non-local aggregation problems, nonlinear elasticity, and fracture theories. Research Focus Primary research domains include: Variational methods for PDEs and homogenisation Mathematical modeling of dislocations and plasticity Stochastic analysis of material defects Nonlocal interaction problems and fracture mechanics Anisotropic energy minimization Publication Trends Recent publications (2019-2025) demonstrate strong focus on: Homogenisation techniques in stochastic/perforated domains; variational analysis of anisotropic/nonlocal energies; explicit minimisers for Coulomb/Riesz interactions; free-discontinuity problems; and mathematical descriptions of dislocation patterns. Work consistently employs Gamma-convergence and variational methods. Student Supervision & Grants Supervised 18+ students including PhD candidate Xavier Pellet (2015-2019) and numerous Bachelor/Master projects on variational methods, dislocations, and PDEs. Major grants include: EPSRC EP/V00204X/1: Mathematical Theory of polycrystalline materials (£576,848, 2021-2024) EPSRC EP/V008897/1: Generalised Solutions of Nonlinear PDEs (£35,960, 2021-2024) EPSRC First Grant EP/N035631/1: Dislocation Patterns beyond equilibrium (£95,699, 2016) Academic Leadership Organizes major conferences including 'Optimal Transport and Calculus of Variations' (ICMS 2023) and 'Polycrystals: Microstructure and Plasticity' (ICMS 2022). Co-founder of the 'One World PDE seminar' (2021-present).

Karsten MatthiesView profile

Senior Lecturer

• Partial Differential Equations
• Dynamical Systems
• Kinetic Theory
• +3 more

Dr. Karsten Matthies is a Senior Lecturer in the Department of Mathematical Sciences at the University of Bath . He actively contributes to research in Analysis Group , the Probability Laboratory , and the Centre for Nonlinear Mechanics , with affiliations to KineticNet and the EPSRC Network on generalized PDE solutions. Research Interests : Infinite-dimensional dynamics (PDEs, lattice ODEs), many-particle systems and kinetic equations, averaging/homogenisation for PDEs, and exponentially small effects. Teaching : Courses include Dynamical Systems (MA40045) and Functional Analysis (MA40057) for 2024/25. Recent Publications focus on kinetic equations derived from particle models, solitary waves in nonlinear systems, and geometric analysis in Hamiltonian frameworks. Key themes include wave propagation in lattices, thermodynamic interpretations of fast-slow systems, and rigorous derivations of PDEs from microscopic models. Collaborations & Grants : Co-Investigator in EPSRC network on nonlinear PDEs , Leverhulme grant with Florian Theil , and funding through SAMBa for PhD students. Advising : Supervised PhD candidates include Theodora Syntaka (2020-2024), Matthias Klar (2017-2021), and others with joint supervision.

• Interacting particle systems
• Excluded-volume interactions
• Hydrodynamic behaviour via macroscopic PDEs
• +2 more

Maria Bruna is a Professor and Royal Society University Research Fellow at the Mathematical Institute of the University of Oxford, affiliated with the Oxford Centre for Industrial and Applied Mathematics, Mathematical Biology group, and Oxford Centre for Nonlinear PDE. Her research integrates mathematical modeling with biological and physical systems to uncover fundamental principles of collective behavior. Her core interests include interacting particle systems with excluded-volume effects, hydrodynamic behavior via macroscopic PDEs , and active matter dynamics . She develops theoretical frameworks for multi-species systems and asymptotic homogenisation, focusing on how microscopic interactions drive emergent macroscopic phenomena in complex media. Recent publications reveal a cohesive research trajectory spanning ant traffic self-organization (2024-2025) and phase transitions in active matter (2023). Her work consistently applies stochastic modeling, topological analysis, and PDE techniques to biological contexts like coral reef resilience and physical systems such as Brownian needle suspensions, demonstrating cross-disciplinary methodological innovation. Scientific recognition: Royal Society University Research Fellow No details regarding academic advising or specific research grants are provided in the current profile, though her fellowship position implies independent research leadership. She actively contributes to Oxford's Mathematical Biology and Nonlinear PDE research groups within the Centre for Industrial and Applied Mathematics, fostering collaborations that bridge theoretical mathematics with real-world biological and industrial applications through shared seminars and joint projects.

Kirill CherednichenkoView profile

Professor

• Partial Differential Equations
• Asymptotic Analysis
• Mathematical Physics
• +3 more

Kirill Cherednichenko is a Professor in the Department of Mathematical Sciences at the University of Bath. His research focuses on multi-scale asymptotic analysis of materials and media, particularly the effective behavior of partial differential equations (PDEs) and their applications to metamaterials. He is affiliated with the EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa) and the Centre for Nonlinear Mechanics. His work bridges operator theory, calculus of variations, and applied mathematics, addressing challenges in homogenization, high-contrast media, and wave propagation phenomena. Cherednichenko has led eight research projects funded by institutions like the EPSRC and the London Mathematical Society, exploring topics such as quantitative tools for upscaling micro-geometry, resolvent estimates in periodic problems, and collaborative research with international partners. His research interests include the asymptotic analysis of operator families, functional models for boundary-value problems, and the mathematical foundations of metamaterials. His work has produced over 50 research outputs, with recent contributions emphasizing norm-resolvent convergence, operator-norm estimates in elastic and electromagnetic systems, and the spectral properties of composite materials. He has organized major academic events, including the British Mathematical Colloquium 2023 and the LMS-Bath Symposium, and has supervised four doctoral students. His research underscores the interplay between physical phenomena and advanced mathematical techniques, contributing to both theoretical and applied domains of mathematical physics.

Matteo CapoferriView profile

Professor

• Analysis of PDEs
• Spectral Theory
• Microlocal Analysis
• +4 more

Matteo Capoferri is a Professor at University of Milan and an Associate Professor at Heriot-Watt University within the School of Mathematical and Computer Sciences , Department of Mathematics . He is also a Visiting Professor at Yale University (Mar 2025–Apr 2025) and an Honorary Professor at University College London (since 2021). BSc and MSc in Theoretical Physics (summa cum laude), University of Pavia PhD in Pure Mathematics, University College London (UCL), supervised by Professor Dmitri Vassiliev Research interests span Analysis of PDEs , Spectral Theory , Microlocal Analysis , Stochastic Homogenisation , and Mathematical Physics . His work focuses on spectral asymmetry, Dirac operators, and high-contrast random PDE systems, bridging geometric analysis with applications in quantum field theory and mathematical physics. Scientific awards include: EPSRC Fellowship (2023) Simons Foundation Fellowship (2026) Grants from EPSRC , London Mathematical Society , and Heilbronn Institute for Mathematical Research . Collaborations include Dr. Mikhail Cherdantsev, Dr. Igor Velčić, and Dr. Stefan Murro. He actively chairs the UK Spectral Theory Network since 2023.

Bryn DaviesView profile

Assistant Professor

• Partial Differential Equations
• Metamaterials
• Spectral Theory
• +3 more

Dr. Bryn Davies is an Assistant Professor in the Mathematics Institute at the University of Warwick. His research focuses on mathematical physics, particularly wave phenomena in complex media including metamaterials and resonator systems. Current investigations explore spectral properties of quasiperiodic structures and topological wave localization. Research Interests: Bryn specializes in asymptotic analysis of partial differential equations with applications to wave propagation in metamaterials. His work bridges theoretical mathematics with practical applications in photonics and acoustic materials, examining phenomena like subwavelength resonance and topological protection in engineered structures. Publications: His recent papers demonstrate consistent focus on spectral theory applications in materials science, including density of states estimation in aperiodic systems, topological mode analysis, and convergence properties of numerical methods. Theoretical frameworks integrate operator theory with wave physics across multiple scales. Research Activities: Leads investigations into non-Hermitian systems and defect-induced localization transitions. Current projects include developing multi-scale models for metamaterial design and analyzing waveguide behavior in damped topological systems.

• Calculus of variations
• Partial differential equations
• Geometric measure theory
• +4 more

Filippo Cagnetti is an Associate Professor (Professore di II fascia) in the Department of Mathematical, Physical and Computer Sciences at the University of Parma , Italy. He regularly teaches foundational courses such as Calculus 2A and Mathematical Analysis A to first- and second-year students enrolled in Mathematics, Geological Sciences (Earth Sciences), and Management Engineering degree programmes, spanning academic years from 2023/2024 through 2025/2026. His research lies at the intersection of calculus of variations , partial differential equations , and geometric measure theory . A recurrent theme is the rigorous derivation of effective models for materials with microstructures via deterministic and stochastic homogenisation , particularly for free-discontinuity problems that describe brittle fracture. Parallel efforts focus on symmetrisation inequalities (Pólya–Szegö, Steiner, Schwarz, Gaussian) and their rigidity properties: under which geometric or analytic conditions equality in an inequality forces the domain to be symmetric or even trivial. Over the past decade his publication portfolio shows a clear evolution from foundational results on viscosity solutions and large-time behaviour of Hamilton–Jacobi equations to highly specialised contributions on Korn- and Poincaré-Korn-type inequalities in spaces of special functions of bounded deformation (GSBD), and on optimal regularity of free boundaries in cohesive fracture models. The techniques employed combine Γ-convergence, fine properties of BV and GSBD spaces, measure-theoretic arguments, and stochastic two-scale convergence. Contact: Email: filippo.cagnetti@unipr.it

C.S. UpadhyayView profile

Professor

• Finite Element Analysis
• Analysis & Design of Composite Structures
• Solid Mechanics

Dr. C.S. Upadhyay is a Professor in the Department of Aerospace Engineering at the Indian Institute of Technology Kanpur, specializing in advanced computational methods and structural mechanics. Education: PhD, Texas A&M University Research Interests: Finite Element Analysis : Adaptive FEM, Goal-based adaptivity, Time-dependent nonlinear problems, Generalized FEM, Nonconforming FEM, Parallel computation Composite Structures : Micromechanics, Homogenisation, Hierarchic plate/shell modeling, Adaptive finite element modeling for laminates, Specialized finite element methods, Shape/topology optimization, Stochastic analysis Solid Mechanics : Constitutive modeling for electro-thermo-elastic materials with losses, Analysis of piezo structures, Crack propagation in 3D solids, Life enhancement of structures, Finite elasticity, Damage in composites Laboratory: Structural Analysis Lab at IIT Kanpur

Guillaume PUELView profile

Professor

• Inverse problems
• Multi-scale identification
• Periodic and stochastic homogenisation
• +3 more

Guillaume PUEL is a Professor at CentraleSupélec, where he holds significant academic and administrative roles. His research focuses on inverse problems, multi-scale identification, periodic/stochastic homogenisation, and advanced vibration modeling. He leads multiple courses including Continuum Mechanics, Dynamics of Undeformable Solids, and Simulation of Multiphysics Couplings with FEM. He has served as Director of the Mechanics and Civil Engineering Department (2015-2021), Head of joint/elective courses (2021-2023), and Deputy Director of Studies for the Centrale engineering curriculum (2016-2020). He co-authored the textbook Mécanique pour l'ingénieur (Dunod, 2021). His contributions include designing 75+ exams, supervising 65 students via recommendation letters, and managing over 1,700 marked copies across courses. Education details unspecified but implies engineering/doctoral training in mechanics. Research emphasizes computational mechanics and material characterization. Active in curriculum design and academic governance, including membership in CSMA Board (2013-2022). Lab/Team involvement not explicitly stated but implies leadership in experimental teaching and material modelling initiatives.