Ryan Grady is an Associate Professor in the Department of Mathematical Sciences at Montana State University. His research and teaching focus span advanced mathematical disciplines. Education: Ph.D. and M.S. (2012, 2009) from University of Notre Dame B.S. (2007) from Colorado School of Mines Ryan's research lies at the intersection of geometry, topology , and quantum field theory (QFT) , with a focus on rigorous mathematical frameworks. He explores connections between QFT, derived geometry , and higher Lie theory , aiming to bridge physical intuition with formal mathematical structures. His recent publications highlight trends in topological data analysis , homotopy theory , and quantization . Key areas include factorization algebras , K-theory , and non-linear sigma models , reflecting a synthesis of abstract mathematics and physical applications. Ryan has advised multiple graduate students, including Eric Berry, Adam Howard, Garrett Oren, and Bryce Morrow, whose work spans cohomology of Grassmanians , surface immersions , algebraic structures , and infinite-dimensional linear algebra .
Claire Zukowski is an Assistant Professor of theoretical physics in the Department of Physics & Astronomy at the University of Minnesota, Duluth, within the Swenson College of Science and Engineering. Her research program focuses on fundamental questions in quantum gravity, with particular expertise in holography, black holes, and cosmology. She is an affiliated member of the QuRIOS collaboration, which investigates observational consequences of quantum gravity theories. Dr. Zukowski received her Ph.D. from the University of California, Berkeley in 2015. Following her doctoral studies, she completed postdoctoral research appointments at Columbia University and the University of Amsterdam, where she further developed her expertise in theoretical physics and quantum gravity. Her research interests center on quantum gravity, particularly exploring the AdS/CFT correspondence, de Sitter space holography, black hole information paradox, and connections between quantum information theory and gravity. Her work often examines how quantum gravitational effects might manifest in observable phenomena, with a particular focus on three-dimensional gravity models that serve as tractable theoretical laboratories. She has made significant contributions to understanding Wilson lines in quantum gravity, modular flow, and the geometric structures underlying holographic duality. Analysis of her publication record reveals a consistent trajectory of high-impact research in theoretical physics. Her recent work shows increasing focus on the intersection of quantum information and gravity, particularly exploring modular Berry phases, quantum extremal surfaces, and the island formalism for resolving the black hole information paradox. She frequently employs mathematical tools from conformal field theory, differential geometry, and topological field theory to address fundamental questions in quantum gravity. Her research demonstrates strong international collaboration, with co-authors from institutions worldwide including Amsterdam, Columbia, Cambridge, and Arizona State University. Dr. Zukowski's research program represents a vital contribution to theoretical physics, particularly in advancing our understanding of quantum aspects of gravity and spacetime. Her work bridges mathematical physics with potential observational consequences, making her research relevant to both theoretical developments and potential future experimental tests of quantum gravity.
Roles and Affiliations: Dan Freed holds the Shiing-Shen Chern Professorship in Mathematics at Harvard University and serves as Director of the Center of Mathematical Sciences and Applications (CMSA). His research bridges global analysis, topology, and mathematical physics, with particular focus on quantum field theory, string theory, and geometric quantization. He actively contributes to Harvard's academic community through seminars like the Geometry and Quantum Theory (GQT) seminar, which explores cutting-edge topics in topological field theories and non-invertible symmetries. Research Interests: His work centers on global geometric analysis, topological quantum field theories (TQFTs), and the interplay between geometry and physics. Key themes include the application of K-theory to string theory, the mathematical formulation of Chern-Simons theories, and the study of anomalies in quantum field theories. Freed collaborates with physicists to translate abstract mathematical concepts into physical frameworks, exemplified by his work on twisted K-theory and orientifold models. Teaching and Mentorship: Freed has taught advanced courses on differential geometry, index theory, Morse theory, and mathematical gauge theory. His mentorship is reflected in the list of students involved in seminar presentations and problem sets, covering topics like Dirac operators, Hodge theory, and boundary conditions in TQFTs. His courses emphasize rigorous foundations while connecting to modern research problems. Key Contributions: Through expository books and lecture series (e.g., CBMS lectures on Field Theory and Topology), Freed synthesizes complex ideas for broader academic audiences. His collaborations with Michael Hopkins and Constantin Teleman on loop groups and twisted K-theory have redefined connections between representation theory and topological invariants. Recent work explores topological symmetries and their implications in quantum systems, including particle-soliton degeneracies.
Eva Miranda is a Full Professor of Mathematics at the Universitat Politècnica de Catalunya (UPC), Barcelona, and a Researcher at the Centre de Recerca Matemàtica (CRM). She leads the Geometry, Topology, Algebra, and Applications Group (GEOMVAP) and directs the Laboratory of Geometry and Dynamical Systems. Her research focuses on symplectic and Poisson geometry, with applications to dynamical systems, fluid dynamics, and mathematical physics. Key areas include singular symplectic manifolds, integrable systems, and the interplay between geometry and computation. Affiliations: Full Professor at UPC (Department of Mathematics) ICREA Academia Researcher Chercheur Affilié at Observatoire de Paris Member of BGSMath and European Mathematical Society Her research explores connections between geometry and computational complexity, notably demonstrating Turing universality in 3D Euler flows (a breakthrough resolving a decades-old problem). She also investigates singularities in Hamiltonian systems, symplectic reduction, and Poisson geometry. Her work bridges disciplines like celestial mechanics, fluid dynamics, and computer science. Notable achievements include the ICREA Academia Prize (2021), Bessel Research Prize (2022), and Hardy Lectureship (2023). She supervises a vibrant team of PhD students and postdocs, fostering interdisciplinary collaborations through networks like SYMCREA and COMPLEXFLUIDS. Her recent projects include exploring topological Kleene field theories, entropy in Turing-complete systems, and desingularization of Poisson manifolds. She actively promotes women in mathematics and contributes to scientific outreach through lectures and media articles.
Petalidou Fani serves as Assistant Professor in the Department of Mathematics at the Faculty of Sciences, Aristotle University of Thessaloniki since July 2015, following her appointment as Lecturer at the same institution from 2012-2015. Her academic career includes significant international experience as Postdoctoral Researcher at Institut de Mathématiques de Jussieu (1998-2000) and Centro de Matemática de Universidade de Coimbra (2000-2001), along with teaching positions at University of Peloponnese, University of Cyprus, and University of Macedonia. Her educational qualifications include: Ph.D. in Mathematics from Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie – Paris VI (1998) M.Sc. in Mathematics from Université Paris Sud, Orsay (1992) B.Sc. in Mathematics from Aristotle University of Thessaloniki (1988) Dr. Petalidou specializes in advanced geometric structures with applications in mathematical physics, focusing on Poisson and Symplectic Geometry, Integral Systems, Lie Algebroids/Groupoids, and Courant Algebroids/Dirac Structures. Her research explores the differential geometric foundations of mechanical systems and integrability, particularly through bihamiltonian structures and twisted geometries. She employs sophisticated techniques from global analysis and Lie theory to investigate quantization problems and structural properties of non-standard geometric manifolds. Her publication record (2000-2012) reveals a consistent trajectory in geometric mathematical physics, with increasing sophistication in handling twisted structures and integration problems. The works demonstrate progressive deepening from symplectization of bihamiltonian systems to Casimir-preserving Poisson brackets, reflecting evolving expertise in manipulating complex geometric constraints while maintaining physical relevance for mechanical systems.
Dr. Oliver Fabert is an Associate Professor in the Department of Mathematics at the Faculty of Science, Vrije Universiteit Amsterdam. His research focuses on advanced topics in symplectic geometry, Hamiltonian systems, and Floer theory. He teaches courses such as Differential Geometry, Non-linear Dynamical Systems, and Partial Differential Equations. Key research interests include Hamiltonian systems, periodic solutions, symplectic manifolds, and the application of Floer theory to nonlinear PDEs. His work often intersects with algebraic topology and geometric analysis, addressing challenges like the small divisor problem in Hamiltonian PDEs and the development of regularization techniques in polysymplectic geometry. Dr. Fabert has published extensively on topics such as hyperkähler Floer theory, pseudoholomorphic curves, and topological recursion relations. His contributions span foundational work in symplectic field theory and polyfold theory, with applications to both finite and infinite-dimensional Hamiltonian systems. He has supervised at least one PhD thesis and actively engages in teaching advanced mathematical concepts, reflecting his commitment to both research and education in theoretical mathematics.
Dr Edwin Beggs is a Reader in Mathematics within the School of Mathematics and Computer Science at Swansea University, located at the Computational Foundry on Bay Campus. His research spans Algebra, Differential Geometry, Noncommutative Geometry, Theoretical Physics, and the computability of physical systems. He co-authored the influential 2020 Springer book Quantum Riemannian Geometry , contributing to the Grundlehren series. His work bridges mathematical formalism with physical applications, focusing on quantum structures, geometric frameworks, and computational models interfacing with physical systems. Research interests include noncommutative differential operators, quantum geodesic flows, and the interplay between algebraic topology and physics. Notable contributions address quantum gravity models, soliton dynamics, and the theoretical limits of measurement and computation in physical systems. He is actively involved in postgraduate supervision and has explored computational paradigms using physical oracles, such as the Wheatstone bridge and kinematic systems, to redefine computational boundaries. His interdisciplinary approach is reflected in publications spanning quantum geometry, analogue-digital computation models, and the mathematical foundations of measurement theory. Collaborations with Shahn Majid highlight his role in advancing noncommutative geometry's applications to modern physics.
Bojko Bakalov is a Professor in the Department of Mathematics at North Carolina State University (NC State), serving as Director of Graduate Programs in Mathematics and Applied Mathematics. He also holds the role of Associate Director of the NC State Quantum Initiative. His research focuses on mathematical physics, quantum computing, representation theory, signal processing, and integrable systems. Bakalov earned his PhD in Mathematics from the Massachusetts Institute of Technology (MIT) in 2000. He has made significant contributions to quantum information processing, including work on barren plateaus in quantum circuits and geometric quantum machine learning. He leads a $10M DOE-backed quantum computing research project and is involved in organizing the Quantum Information Processing conference series. His research is supported by grants such as the NSF-funded Quantum Information Science initiative. Education: PhD in Mathematics, MIT (2000) His research interests span quantum computing algorithms, representation theory of vertex algebras, and applications of algebraic methods to integrable systems. Notable achievements include the development of quantum coherent state transforms and the classification of dynamical Lie algebras in spin systems. Bakalov is actively involved in advancing quantum technologies through interdisciplinary collaborations. His publications explore topics such as logarithmic vertex algebras, Poisson pseudoalgebras, and quantum signal processing. He is affiliated with the Algebra and Combinatorics Research Group and the Topology, Geometry, and Mathematical Physics Research Group at NC State. Grants and Leadership: Leads DOE quantum computing projects and directs graduate programs, shaping the next generation of mathematicians and quantum scientists. Labs/Teams: Part of the NC State Quantum Initiative, fostering collaborative research in quantum technologies.
Alexander Goncharov is the Philip Schuyler Beebe Professor of Mathematics at Yale University's Department of Mathematics. His research focuses on arithmetic algebraic geometry, geometry, representation theory, and mathematical physics. He has received the European Mathematical Society Prize for his contributions to mathematics. His work spans topics such as motives, moduli spaces, polylogarithms, and quantum geometry. Education: Ph.D. 1987 (USSR). His research explores connections between algebraic geometry, number theory, and physics, with a focus on motivic cohomology, Hodge theory, and geometric representation theory. He has contributed to the understanding of scattering amplitudes, cluster varieties, and quantum invariants of moduli spaces. Research highlights include studies on Hodge correlators, motivic fundamental groups, and the geometry of moduli spaces. His recent work integrates quantum geometry with algebraic structures, such as cluster algebras and non-commutative systems. Key publications address exponential volumes of hyperbolic surfaces, spectral descriptions of non-commutative systems, and quantum aspects of moduli spaces. He has authored over 100 papers and is a leading figure in the field, with contributions to both pure mathematics and its intersections with theoretical physics. His lab or team collaborations are not explicitly detailed in the provided texts.
Urs Schreiber is a Professor at New York University in Abu Dhabi (NYU AD), working in the Mathematics Division of Science. He leads the Research Center for Quantum and Topological Systems (CQTS) under the group of Prof. Hisham Sati. His work bridges mathematical physics, quantum theory, and topology, with significant contributions to understanding strongly-coupled quantum systems and their applications to topological quantum technology. His research focuses on applying tools from algebraic topology and geometric homotopy theory to fundamental problems in quantum physics. His major projects include Hypothesis H on flux quantization in M-theory, geometric engineering of anyons on M5-branes, and developing quantum language via linear homotopy types. His work represents a unique synthesis of advanced mathematical techniques with cutting-edge theoretical physics, particularly in the areas of M-theory, topological quantum computing, and differential cohomology. Schreiber has established himself as a leading figure in the application of higher categorical and homotopical methods to physics. His research demonstrates a clear trajectory toward developing mathematical frameworks for next-generation quantum technologies, with particular emphasis on topological approaches that could provide fault-tolerant quantum computing platforms. His work shows strong connections between abstract mathematical structures and practical quantum computing applications, particularly through homotopy type theory implementations. Monograph: The Character Map in Non-Abelian Cohomology (with D. Fiorenza & H. Sati, 2023) Monograph: Equivariant Principal ∞-Bundles (with H. Sati, 2025) Contributor: Mathematical Foundations of Quantum Field and Perturbative String Theory (2011) Schreiber has advised numerous graduate students in areas spanning homotopy theory, quantum field theory, and mathematical physics. His teaching portfolio includes courses on Mathematical Quantum Field Theory, Topological K-Theory, and Stable Homotopy Theory. He is also the founder of the nLab research wiki project (started in November 2008), which has become an essential resource for researchers working at the intersection of mathematics and physics. His research group actively develops mathematical foundations for quantum and topological systems with practical implications for quantum technology development.
Michela Zedda is an Associate Professor at the Department of Mathematical, Physical and Computer Sciences of the University of Parma. Her research focuses on differential and symplectic geometry, particularly in Kähler metrics, Sasakian manifolds, and geometric quantization. Department: Mathematical, Physical and Computer Sciences (University of Parma) Academic Rank: Associate Professor Email: michela.zedda@unipr.it Her work explores the interplay between Kähler and symplectic structures, with key contributions to projectively induced metrics, immersions into complex space forms, and the geometry of Cartan-Hartogs domains. Recent publications (2024–2025) address scalar flat metrics on line bundles and symplectic cones over Sasakian manifolds. Zedda's research spans geometric analysis, including the Yamabe problem, Ricci solitons, and stability under Lie group actions. She has extensively studied diastasis functions, TYZ expansions, and balanced metrics in both Cartan and Hartogs domains. Teaching appointments include Geometry courses for Mathematics and Management Engineering students at the University of Parma (2022–2025) and previous roles in Mathematics and Dental Medicine programs. No scientific awards or advisees are documented in the provided texts.
Abhishek Halder is an Associate Professor in the Department of Aerospace Engineering at Iowa State University and an Associate Adjunct Professor in the Department of Applied Mathematics at the University of California, Santa Cruz. He is also a member of the Translational AI Center at Iowa State University. His academic journey includes joining Iowa State University as an Assistant Professor in July 2023 and previously serving as faculty at UC Santa Cruz starting from October 2017. Dr. Halder's educational background includes studies at IIT Kharagpur and Texas A&M University, where he developed expertise in systems and control theory with applications to matrix analysis, probability, and optimization. His research has been recognized with prestigious awards including the O. Hugo Schuck Best Application Paper Award from the American Automatic Control Council, Applied Mathematics Research Award from UC Santa Cruz, Outstanding Doctoral Student Award from Texas A&M, and Best Dual Degree Thesis Award from IIT Kharagpur. His research focuses on stochastic systems, control and optimization with applications to large scale cyber-physical systems. Dr. Halder has made significant contributions to the fields of optimal transport, Schrödinger Bridge theory, distributional control, and uncertainty propagation in dynamical systems. His work bridges theoretical developments with practical applications in power systems, aerospace engineering, and machine learning. He has secured multiple research grants from NSF, including a CPS Frontier project on Computation-Aware Algorithmic Design for Cyber-Physical Systems. Dr. Halder has demonstrated leadership in the control systems community through editorial roles including Associate Editor for IEEE Transactions on Automatic Control (2025-present), ASME Journal of Dynamic Systems, Measurement, and Control (2025-present), Systems & Control Letters (2022-present), and previously for IEEE Control Systems Society Conference Editorial Board (2019-2025) and IEEE Transactions on Aerospace and Electronic Systems (2019-2022). He is a Senior Member of IEEE and a member of IFAC, SIAM and ASME. His research group has produced numerous publications in top-tier journals and conferences, with recent work focusing on connections between optimal transport theory, stochastic control, and machine learning. The publication trends show increasing integration of Schrödinger Bridge formulations with machine learning techniques for distributional control problems across various domains including power systems, aerospace applications, and resource allocation. O. Hugo Schuck Best Application Paper Award (2024) Applied Mathematics Research Award from UC Santa Cruz (2022) IEEE Senior Member (2021) Outstanding Doctoral Student Award from Texas A&M Best Dual Degree Thesis Award from IIT Kharagpur Dr. Halder has mentored numerous PhD students including Alexis, Georgiy, Iman, Shadi, and Kenneth, many of whom have received prestigious fellowships. His research group maintains strong collaborations with national laboratories including Lawrence Livermore National Lab and Los Alamos National Lab, as well as industry partners. Dr. Halder is also committed to education and outreach, having created and taught the 'Feedback Control' course for high school students in the California State Summer School for Mathematics and Science (COSMOS), introducing complex control theory concepts without calculus or linear algebra.
Raffael Hagger is a researcher at the University of Reading, specializing in operator theory, functional analysis, and mathematical physics. His work focuses on Toeplitz and Hankel operators, spectral theory, and quantization in domains like Fock spaces and bounded symmetric domains. Recent Research Trends: Hagger's publications (2025–2015) span topics such as band-dominated operators on locally compact abelian groups, quantum harmonic analysis for polyanalytic Fock spaces, and spectral properties of Toeplitz operators on the unit ball and Lipschitz domains. His work also addresses compactness criteria, essential spectra, and symmetries in random hopping matrices. Collaborations: He frequently collaborates with researchers like J. Virtanen, W. Bauer, and M. Lindner.
Maxim Braverman is a Professor in the Mathematics Department at Northeastern University. His research focuses on spectral theory, geometric analysis, and mathematical physics, with a particular emphasis on index theorems, differential operators on manifolds, and applications to quantum field theory. He has collaborated extensively on topics such as the Weyl law, symplectic reduction, and the study of mtDNA mutations. Braverman holds a Ph.D. in Mathematics and has authored numerous influential papers in top-tier journals. His work often bridges the gap between pure mathematics and theoretical physics, with notable contributions to the understanding of non-compact manifolds and their spectral properties. Key research interests include the geometry of differential operators, geometric quantization, and the interplay between topology and analysis. His recent work explores the dynamics of mtDNA mutations and their implications in genetics, reflecting his interdisciplinary approach. Braverman has been recognized for his scholarship through publications in prestigious venues and his editorial contributions to academic journals. His research has been supported by various grants, though specific details are not listed here. He is affiliated with Northeastern University’s Mathematics Department and has contributed to academic service, including organizing conferences on spectral theory and geometric analysis.
Michela Zedda is an Associate Professor at the Department of Mathematical, Physical and Informatics Sciences of the University of Parma . Her research focuses on complex geometry, differential geometry, and geometric analysis, with particular emphasis on Kähler and Sasakian manifolds, geometric flows, and quantization techniques. Her work includes studies on isometric immersions of locally conformally Kähler manifolds, stability in Lie group actions, J-flow dynamics on Sasakian manifolds, and Berezin-Engliš quantization of Cartan-Hartogs domains. Recent contributions address convergence properties of geometric flows and asymptotic expansions in geometric quantization. Professional Activities: She organizes workshops such as PREDICT 2025 and Informal Geometry Workshop in Paradiso 2025 , and participates in international conferences on complex and differential geometry.
