Find Academic Supervisors

Ralf HiptmairView profile

Professor

• Computational Mathematics
• Numerical Analysis
• Finite Element Methods
• +7 more

Ralf Hiptmair is a Full Professor at ETH Zürich, serving as Head of the Seminar for Applied Mathematics and Deputy Head of the Department of Mathematics. He also holds the position of Director of Studies for ETH BSc and MSc in Computational Sciences and Engineering (CSE). His research spans computational mathematics, numerical analysis, finite element methods, boundary element methods, computational electromagnetism, multigrid methods, discrete differential forms, shape optimization, wave propagation, and kinetic equations. Hiptmair's work on auxiliary space methods was recognized as a breakthrough in computational science in the 2008 DOE Report on recent significant advancements in computational science. His research focuses on developing and analyzing numerical methods for partial differential equations, with particular emphasis on structure-preserving discretizations, computational electromagnetism, and boundary integral equations. His work has significant applications in engineering, physics, and computational science. Hiptmair's publications demonstrate a strong focus on advancing numerical techniques for electromagnetic problems, wave propagation, and shape optimization. His recent work shows increasing interest in computational topology, geometric numerical integration, and interdisciplinary applications of numerical methods. Featured as breakthrough in computational science in the 2008 DOE Report on recent significant advancements in computational science (for Auxiliary space methods) Hiptmair has supervised numerous doctoral, master's, and bachelor's students across mathematics, computational science and engineering, and related fields. His research group has received funding for developing advanced numerical methods with applications in electromagnetism, fluid dynamics, and computational physics. He is actively involved in teaching numerical methods courses at both undergraduate and graduate levels. Hiptmair leads research efforts in the Seminar for Applied Mathematics, collaborating with industry partners like ABB Corporate Research and Siemens on practical applications of computational methods. His work bridges theoretical numerical analysis with real-world engineering challenges.

F. Duncan M. HaldaneView profile

Professor

• Condensed Matter Theory
• Quantum Materials Science
• Fractional Quantum Hall Effect
• +4 more

F. Duncan M. Haldane is the Sherman Fairchild University Professor and Eugene Higgins Professor of Physics at Princeton University. He joined Princeton in 1990 and has held previous positions at institutions including the Institut Laue-Langevin in France and the University of California, San Diego. Ph.D. in Physics from Cambridge University (1978) B.A. from Cambridge University (1973) Haldane’s research focuses on strongly-interacting quantum many-body systems , particularly condensed-matter systems studied through non-perturbative methods. His work spans the fractional quantum Hall effect (FQHE) , quantum geometry, topological insulators, and Chern insulators. He has pioneered the study of entanglement spectra as a tool for identifying topological order and developed geometric descriptions of FQHE states using metric-tensor fields. His recent publications highlight advancements in understanding topological phases of matter , including implications for photonic crystals and flat-band systems. Key themes include quantum geometry, topological order, and collective modes in incompressible quantum fluids. Nobel Prize in Physics (2016) ICTP Dirac Medal (2012) Oliver E. Buckley Prize (1993) Alfred P. Sloan Fellowship (1984-1988) Simons Fellow in Theoretical Physics (2013-2014) Haldane has mentored notable researchers such as Hui Li and S. Raghu. His work has been supported by grants including those from the Simons Foundation. He has contributed to the development of the Moore Foundation-funded Emergent Phenomena in Quantum Systems (EPiQS) theory center at Princeton.

• Geometry
• Topology
• Quantum Field Theory
• +5 more

Ryan Grady is an Associate Professor in the Department of Mathematical Sciences at Montana State University, affiliated with the College of Letters & Science. His research bridges geometry, topology, and quantum field theory (QFT), with a focus on derived geometry and higher Lie theory. Research Interests: His work applies QFT techniques to geometric and topological problems, explores derived algebraic structures (e.g., L-infinity spaces, cosheaves), and investigates connections between renormalization group flows and sigma models. Recent publications address K-theoretic invariants, operadic structures in topology, and algebraic models for topological field theories. Scientific Awards: Stannard Award for Graduate Teaching (2021) NExT Fellow (2019) ICCM Best Paper Award (2018) Research Enhancement Grant (2018) Member, MSU Center for Faculty Excellence (2017) Education: Ph.D. and M.S. in Mathematics from the University of Notre Dame (2012, 2009), and B.S. in Mathematics from the Colorado School of Mines (2007). Students: Co-chaired Eric Berry (PhD 2021) and Adam Howard (PhD 2021), advised Garrett Oren (MS 2021), and mentored Bryce Morrow (BS 2023).

Shing-Tung YauView profile

Professor

• Differential Geometry
• Mathematical Physics
• General Relativity
• +3 more

Shing-Tung Yau is a distinguished mathematician and professor associated with the Shing-Tung Yau Center at Southeast University's School of Physics, reflecting his profound influence in mathematical physics. His career spans premier institutions including Harvard University (emeritus) and Tsinghua University, where he holds active positions. Yau's research centers on differential geometry , mathematical physics , and geometric analysis , with transformative work on Calabi-Yau manifolds underpinning string theory. His investigations into Einstein's equations, black hole thermodynamics, and geometric flows bridge pure mathematics and theoretical physics, driving advancements in quantum gravity and mirror symmetry. His publications reveal consistent focus on geometric structures in theoretical physics, particularly Calabi-Yau applications in string compactification and geometric flows for singularity analysis. Recent works emphasize Kähler-Einstein metrics and stability in algebraic geometry. Scientific accolades include: Fields Medal (1982) for contributions to partial differential equations and Calabi conjecture Wolf Prize (2010) for geometric analysis breakthroughs MacArthur Fellowship (1985) and Crafoord Prize (1994) National Medal of Science (1997) for unifying geometry and physics Yau has mentored over 50 doctoral students, including Gang Tian and Huai-Dong Cao, shaping modern geometric analysis. He leads collaborative initiatives like the Harvard-Yau Center and Tsinghua's Mathematical Sciences Center, fostering cross-disciplinary research in geometric methods for quantum gravity. Current efforts focus on geometric foundations of quantum information and gravitational wave mathematics.

• Mathematical Physics
• Quantum Theory
• Noncommutative Geometry
• +3 more

James Gaunt is an Assistant Professor in the School of Mathematical & Computer Sciences, specializing in the Mathematics department at Heriot-Watt University. His research focuses on advanced mathematical physics, noncommutative geometry, and quantum theory, with notable contributions to fuzzy spectral triples and gauge invariance. His work bridges abstract algebraic structures with geometric and physical applications. Research interests include mathematical frameworks for quantum gravity, spectral triples in noncommutative spaces, and deformation theory applied to Hopf fibrations. Recent publications explore topics such as finite spectral triples for fuzzy tori and BV quantization in dynamical systems. No scientific awards or grants are explicitly mentioned. He has not listed any advisees or students. Collaborations include researchers such as John W. Barrett and Alexander Schenkel, reflecting interdisciplinary work in geometry and theoretical physics. His academic profile emphasizes peer-reviewed contributions to journals like Journal of Geometry and Physics and Symmetry, Integrability and Geometry , highlighting rigorous mathematical approaches to complex physical systems.

Fangneng ZhanView profile

Research Fellow

• Computer Science
• Artificial Intelligence
• Neural Rendering
• +7 more

Currently a Research Fellow at Harvard University & MIT , Fangneng Zhan specializes in Neural Rendering and Generative AI . His research focuses on developing evolutive rendering frameworks, 3D-aware generative models, and multimodal synthesis techniques. Previously, he was a postdoctoral researcher at the Max Planck Institute for Informatics under Prof. Christian Theobalt. He earned his Ph.D. in Computer Science & Engineering from Nanyang Technological University, Singapore and a Bachelor's in Communication Engineering from the University of Electronic Science and Technology of China . His work spans 3D reconstruction, robotics applications , and lighting estimation , with significant contributions to SIGGRAPH , NeurIPS , and CVPR conferences. Recent research highlights include evolutive gauge transformations for neural fields, generalizable 3D style transfer via Gaussian splatting, and multimodal synthesis frameworks leveraging pre-trained models like CLIP and Stable Diffusion. He has co-authored Top50 Popular Paper in TPAMI 2023 and organized workshops at CVPR 2024 on generative models. Scientific Awards: Top50 Popular Paper, IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI) 2023 Collaborative Network: Mentored students at institutions like Harvard, NTU, and ETH Zurich. His projects include datasets for lighting estimation and real-time scene text detection systems.

• Mathematical Data Science
• Machine Learning
• Compressed Sensing
• +5 more

Johannes Maly is an Assistant Professor at the Bavarian AI Chair for Mathematical Foundations of Artificial Intelligence at LMU Munich. He previously held postdoctoral positions at Catholic University of Eichstaett-Ingolstadt and RWTH Aachen University, and completed his PhD at TUM Munich under Prof. Massimo Fornasier. PhD in Mathematics (2019, TUM Munich) M.Sc. in Mathematics (2015, TUM Munich) B.Sc. in Mathematics (2013, TUM Munich) His research focuses on mathematical data science and machine learning, specifically addressing: Robust covariance estimation under quantization Neural network approximation properties Implicit bias in gradient descent training Multi-structured signal recovery Quantization effects in deep learning and compressed sensing His recent publications analyze dithered quantization in covariance estimation, implicit regularization in overparameterized models, and multi-structured data recovery. He applies mathematical rigor to practical challenges in wireless communications (e.g., MIMO systems) and neural network training. Scientific recognition includes: relAI Fellow MCML Associate He supervises code/toolbox development for reproducibility and teaches graduate courses in convex optimization, high-dimensional probability, and mathematical data science. His work bridges theoretical mathematics and applied signal processing.

Jørgen Ellegaard AndersenView profile

Professor

• Quantum Topology
• Geometric Quantization of Moduli Spaces
• Topological Quantum Field Theory
• +7 more

Jørgen Ellegaard Andersen is a Professor and Center Director at the Department of Mathematics and Computer Science, University of Southern Denmark (SDU), and holds the D-IAS Chair at the Danish Institute for Advanced Study (DIAS). He is also a Distinguished Visiting Professor at the California Institute of Technology since 2013, reflecting his international stature in mathematical sciences. University: University of Southern Denmark School: Faculty of Science Department: Department of Mathematics and Computer Science Position: Professor, Center Director, D-IAS Chair Andersen earned his DPhil in Mathematics from the University of Oxford in 1992, with a thesis on Jones-Witten theory and the Thurston Compactification of Teichmüller space. His research lies at the intersection of quantum theory and geometry, focusing on quantum topology, geometric quantization of moduli spaces, topological quantum field theory, low-dimensional geometry, and applications to RNA and protein folding. His work combines deep mathematical rigor with potential applications in quantum computing and biophysics. The trends in his recent publications show a consistent focus on quantization of moduli spaces, topological recursion, mapping class group representations, and quantum Chern-Simons theory. His work often bridges pure mathematics and theoretical physics, with increasing attention to computational and applied aspects in quantum technologies. ERC Synergy Grant ReNewQuantum (EUR 10m, Principal Investigator) Distinguished Visiting Professor, Caltech Andersen leads major research projects such as ReNewQuantum and TopQC2X, securing significant funding from the EU and Danish agencies. He actively supervises PhD students and collaborates with leading mathematicians worldwide, including Maxim Kontsevich and Bertrand Eynard. His work is frequently highlighted in the media for its potential impact on quantum computing and Danish industry. He is a central figure in the Quantum Mathematics center at SDU and collaborates with institutions like MSRI and the University of Hamburg. His research group is part of international networks focused on geometric and topological methods in quantum theory.

• Mathematics of Data Science
• Stochastic Geometry
• Convex Geometry
• +6 more

Eliza O'Reilly is an Assistant Professor in the Department of Applied Mathematics & Statistics at Johns Hopkins University. Her research focuses on the intersections of stochastic geometry , convex geometry , high-dimensional probability , and statistical learning theory . Her work explores: Nonconvex and convex regularizers in inverse problems Random tessellations and their machine learning applications Spectrahedral regression for convex function approximation Determinantal point processes for modeling repulsive interactions High-dimensional random convex sets and their asymptotic geometry Her research is supported by the National Science Foundation . Recent publications investigate gradient-based dimension reduction, oblique decision trees, and geometric properties of regularizers. She has received her PhD from the University of Texas at Austin and was a postdoctoral scholar at Caltech.

Gregor SchaumannView profile

Researcher

• Quantum algebra
• Low-dimensional topology
• (Higher) category theory
• +3 more

Gregor Schaumann is a researcher at the Chair of Mathematics X (Mathematical Physics) within the Institute of Mathematics at the University of Würzburg , Germany. He specializes in the interplay between algebra and topology, particularly focusing on quantum algebra, low-dimensional topology, and higher category theory. Research Interests : Topological field theories (TFTs) and associated manifold invariants Tensor categories and their representations Module categories and bimodule structures Higher categorical frameworks for mathematical physics Fusion categories and categorical quantum groups Orbifold constructions in TQFTs Scientific Contributions : His recent work includes foundational studies on Grothendieck-Verdier categories, fusion quivers, and generalized orbifolds in Reshetikhin-Turaev TQFTs. He has also advanced the understanding of Eilenberg-Watts calculus and pivotal tricategories. Teaching & Advising : Gregor supervises bachelor's and master's theses and teaches courses such as Linear Algebra for GMR teaching candidates , Introduction to Knot Theory , and seminars in algebraic topology and geometric mechanics. Collaborations : He collaborates with international researchers including Jürgen Fuchs, Ingo Runkel, Christoph Schweigert, and Nils Carqueville, with whom he co-organizes the Higher Structures & Field Theory Seminar .

TAN Meng ChwanView profile

Associate Professor

• M-theory
• String Theory
• Quantum Field Theory
• +3 more

TAN Meng Chwan is an Associate Professor at the National University of Singapore (NUS), specializing in theoretical physics and mathematical physics. He serves as Assistant Dean (Outreach and Admissions) and Head of the NUS String Theory Group. His research focuses on M-theory, string theory, quantum field theory, and their implications for contemporary mathematics, particularly in understanding emergent spacetime in quantum gravity. Education: PhD in Physics from NUS (2007). His work bridges high-energy physics with advanced mathematical structures, including Floer homologies, categorification, and geometric Langlands duality. He has contributed to topological gauge theories, dualities in quantum field theories, and connections between string theory and algebraic geometry. Editorial Roles: Editor of International Journal of Modern Physics A, Modern Physics Letters A, and Scientific Reports. He also reviews for Communications in Mathematical Physics, Journal of High Energy Physics, and Advances in Theoretical and Mathematical Physics. Research Themes: His publications emphasize topological and holomorphic aspects of gauge theories, integrable systems, and their categorifications. Recent work explores higher-dimensional gauge theories, Floer homologies, and their applications to manifold topology and quantum gravity. Key Contributions: He pioneered studies on u-plane integrals in Donaldson theory, Vafa-Witten invariants, and matrix regularization of Nambu brackets. His interdisciplinary approach unites string theory with algebraic geometry, number theory, and enumerative geometry.

• Dynamical Systems
• Hamiltonian Mechanics
• Biomechanics
• +4 more

Holger Dullin is a Professor of Applied Mathematics at the School of Mathematics and Statistics, University of Sydney. His research focuses on Hamiltonian dynamical systems, integrable systems, and their applications in mechanics, fluid dynamics, and biomechanics. He serves as a member of the Sydney Southeast Asia Centre and the Applied Mathematics Research Group. Member of Sydney Southeast Asia Centre Member of Applied Mathematics Research Group Research Interests include: Hamiltonian systems and integrability Quantum and classical monodromy Geometric phase phenomena N-body and rigid body dynamics Volume-preserving mappings His work spans from fundamental mathematical physics to interdisciplinary applications in biomechanics and space engineering , with recent studies on light sail stabilization and geometric phase optimization in diving. Publications cover 2024 to 2003, showing sustained contributions to nonlinear dynamics , stability analysis , and symplectic geometry . Teaching includes advanced courses in Hamiltonian dynamics and nonlinear ODEs. Current research students include Babak Attarha and Gleb Palshin , with past supervision of William Tong (PhD 2016) on geometric phases in diving.

Arthemy KiselevView profile

Assistant Professor

• Mathematical Physics
• Deformation Quantization
• Poisson Geometry
• +4 more

Arthemy Kiselev is an Assistant Professor at the University of Groningen's Faculty of Science and Engineering, specifically within the Department of Mathematics at the Johann Bernoulli Institute. He has been working at the Chair of Algebra since January 2011, contributing significantly to mathematical physics research. His educational background includes: (Under)graduate studies at Lomonosov Moscow State University (summa cum laude, 2001) and Independent University of Moscow PhD in mathematical physics (2004) Professor Kiselev's research focuses on the interface of (super)geometry and quantisation, particularly examining the (non)commutative geometry of Kontsevich's deformation and Batalin-Vilkovisky's approaches to quantisation of gauge field models. His work centers on deformation quantisation, BV quantisation, geometry of differential equations, Poisson geometry, and brackets. He has developed algebraic and geometric tools for the mathematical language of fundamental physics, with particular emphasis on the geometry of variations in Batalin-Vilkovisky formalism and Kontsevich's deformation quantization. His fingerprint in research shows strong connections to Cocycle Mathematics (100%), Poisson Bracket Mathematics (95%), Vector Field Mathematics (77%), Manifold Mathematics (65%), Poisson Structure Mathematics (51%), and Partial Differential Equation Mathematics (41%). His recent publications (2023-2024) demonstrate continued exploration of Kontsevich graphs acting on Nambu-Poisson brackets, star-products for affine Poisson brackets, and associativity properties in deformation quantization. These works show a consistent focus on understanding the mathematical structures underlying quantization procedures, with particular attention to graph complexes, cocycles, and their applications to Poisson geometry. His research reveals deep connections between algebraic structures, differential geometry, and theoretical physics. Scientific recognition includes: NWO VENI post-doctoral grant at Mathematical Institute Utrecht (2008-2010) Throughout his career, Kiselev has given 107 international talks at mathematics and theoretical physics research seminars. His collaborative work with PhD and master's students, such as M.S. Jagoe Brown and F. Schipper, has produced significant results in Poisson geometry and deformation quantization. His research has been supported by various institutions including visits to prestigious centers like IHES (France), MPIM (Germany), CRM (Montreal, Canada), and SISSA (Trieste, Italy). He has held positions at institutions including ISPU in Ivanovo, Russia (as docent since 2009). Kiselev is an active member of the Geometry and Quantum Theory (GQT) research group, contributing to the vibrant mathematical physics community at Groningen. His work continues to bridge abstract mathematical structures with fundamental physical theories, particularly through the lens of deformation quantization and Poisson geometry.

Krzysztof PilchView profile

Professor

• String Theory
• Supergravity
• Quantum Field Theory
• +3 more

Krzysztof Pilch is a Professor of Physics and Astronomy at the University of Southern California, affiliated with the Dornsife College of Letters, Arts and Sciences and the Department of Physics and Astronomy. His research focuses on theoretical physics, particularly string theory, supergravity, and quantum field theory, with recent work centered on the AdS/CFT correspondence and renormalization group flows in supersymmetric quantum field theories. Education includes: Ph.D. in Theoretical Physics from University of Wroclaw (1983) M.S. in Theoretical Physics from University of Wroclaw (1979) Postdoctoral training at MIT (1986-1989) and SUNY Stony Brook (1983-1986) Research specialties include string theory, mathematical physics, and quantum gravity, with emphasis on holographic duality and BRST quantization techniques for gravity coupled to conformal matter systems in two dimensions.

• Modified gravity
• Teleparallel gravity
• Lorentz gauge theory of gravity
• +5 more

Tomi S. Koivisto is a theoretical physicist and cosmologist holding a 2006 PhD from the University of Helsinki under Hannu Kurki-Suonio. He is currently active at the Institute of Physics, University of Tartu (Estonia), and the National Institute of Chemical Physics and Biophysics (NICPB) in Tallinn. Earlier he was also affiliated with the Helsinki Institute of Physics. Research Focus: Modified theories of gravity beyond General Relativity, including teleparallel, metric-affine, and Lorentz-gauge formulations. Cosmological applications: dark energy, dark matter, cosmic acceleration, and observational tensions. Black-hole physics and gravitational waves within extended gravity frameworks. His publication record (≈ 143 papers, 2009-2025) reveals a steady flow of highly-cited works in JHEP , Phys. Rev. D , JCAP , and Universe , often co-authored with José Beltrán-Jiménez, Manuel Hohmann, Luca Marzola, Tom Złośnik, and others. Articles Trend: Recent papers explore Spin(4) gauge-theoretic unification of gravity and matter, ghost-free symmetric teleparallel models, relativistic viscous fluids, and black-hole solutions in Lorentz-gauge theory—showing a shift toward geometrically richer, observationally testable extensions of gravity. Scientific Awards & Recognition: None explicitly reported in the supplied texts. Advising & Grants: No specific student names or funded-grant details are provided in the supplied material. Laboratories & Teams: Works within the gravity and cosmology groups at Tartu and NICPB; participates in international collaborations such as the CosmoVerse and CANTATA networks.