جستجوی استاد راهنمای دانشگاهی

Marco Castronovoمشاهده پروفایل

استادیار

• Symplectic Topology
• Mirror Symmetry
• Cluster Algebras
• +۳ مورد دیگر

Marco Castronovo serves as an Assistant Professor in the Mathematics Department at Columbia University, with his office located in Mathematics Hall 614. His academic work bridges continuous and discrete mathematical structures through the lens of symplectic geometry and topology. His research focuses on Symplectic Topology , particularly exploring symplectic structures as frameworks for quantization of classical invariants. Key interests include: Developing open-string versions of Schubert calculus Investigating cluster structures in positroid varieties Constructing Landau-Ginzburg models for Grassmannians Studying Lagrangian cobordisms and exotic tori Analyzing connections between Dubrovin spectra and Fukaya algebras His recent publications reveal a consistent trajectory toward unifying symplectic geometry with combinatorial algebraic structures, particularly through Grassmannian varieties and their mirror symmetric counterparts. The work demonstrates increasing sophistication in connecting Fukaya categories with cluster algebraic frameworks, while maintaining strong ties to quantum topological invariants. As an academic mentor, Castronovo supervises undergraduate researchers including B. Basson (Barnard Summer Research Institute) and S. Kesavan (Columbia Summer Research Fellowship). He actively contributes to the mathematical community through refereeing and co-organizing the Columbia SGGTC Seminar, demonstrating commitment to both research dissemination and academic service. His computational work manifests through three significant open-source projects: Posetroids for exploring Zariski closure orders in Grassmannians, DubrovinDynamics for visualizing spectral evolution in truncated Dubrovin operators, and ClusterExplorer for conducting random walks on cluster structures of Grassmannians. These tools have become valuable resources for researchers working at the intersection of symplectic geometry and combinatorics.

• Mathematical Physics
• Number Theory
• Stochastic Analysis
• +۱ مورد دیگر

Jon Keating is a Professor at the University of Oxford affiliated with the Mathematical Institute . His research spans Mathematical Physics , Number Theory , and Stochastic Analysis , with a focus on Random Matrix Theory and its applications to quantum systems and number theory. Research Trends: His recent work explores connections between random matrices and number-theoretic functions, with contributions to understanding moments of L-functions, characteristic polynomials, and quantum chaos. Key themes include asymptotic analysis, recursive structures, and interdisciplinary applications in nonlinear systems. Publications: Highlights include studies on CUE characteristic polynomials, the Ratios Conjecture, and collaborations in Nonlinearity , International Mathematics Research Notices , and Transactions of the American Mathematical Society .

• Mathematics
• Machine Learning
• Quantum Topology
• +۹ مورد دیگر

Sergei Gukov is the John D. MacArthur Professor of Theoretical Physics and Mathematics at the California Institute of Technology (Caltech), where he has been a faculty member since 2005. He serves in the Division of Physics, Mathematics and Astronomy, with primary affiliation in the Department of Mathematics. His research bridges the fields of mathematics and theoretical physics, focusing on deep connections between geometry, topology, and quantum field theory. Gukov received his B.S. from Moscow Institute of Physics and Technology in 1997, followed by an M.S. and Ph.D. from Princeton University in 2001. He joined Caltech as an Associate Professor in 2005, was promoted to Professor in 2007, and was named the John D. MacArthur Professor in 2021. His research spans several interconnected areas at the frontier of mathematics and physics. A central theme is the exploration of quantum topology and its connections to mathematical physics. He has made significant contributions to the geometric Langlands program, gauge theory, and the categorification of knot and 3-manifold invariants. His recent work increasingly incorporates machine learning approaches to mathematical problems, reflecting his interest in the intersection of traditional mathematical research and modern computational techniques. Gukov's work often reveals deep connections between seemingly disparate areas of mathematics and physics, such as the relationship between Rozansky-Witten geometry and Coulomb branches in supersymmetric gauge theories. Gukov's publications demonstrate a consistent focus on the mathematical structures underlying quantum field theories and their topological implications. His recent work shows an increasing emphasis on computational approaches to mathematical problems, particularly through his interest in mathematics and machine learning. The recurring themes across his research include the application of physical insights to solve mathematical problems and the discovery of new mathematical structures through physical reasoning. He serves on the editorial boards of several prestigious journals including the Journal of Knot Theory and Its Ramifications, Communications in Mathematical Physics, and Letters in Mathematical Physics. Gukov is also active in the academic community, having delivered plenary talks at major conferences such as the First International Congress of Basic Science and presenting at String Math 2023 on the potential impact of AI on mathematical research. Gukov teaches Ma 146 ab, Introduction to Knot Theory and Quantum Topology, a course that reflects his research interests. He also runs a seminar on Mathematics and Machine Learning, held Tuesdays from 2-3pm in East Bridge Conference room 114, demonstrating his commitment to fostering interdisciplinary research at the intersection of mathematics and computational methods.

Simon Donaldsonمشاهده پروفایل

استاد

• Differential Geometry
• Topology
• Mathematical Physics
• +۳ مورد دیگر

Sir Simon Donaldson is a Professor and permanent member of the Simons Center for Geometry and Physics at Stony Brook University. He is renowned for groundbreaking work in differential geometry, topology, and mathematical physics, particularly in four-dimensional manifolds. His academic journey includes a B.A. in Mathematics from Pembroke College, Cambridge University (1979) and a Ph.D. from Oxford University (1983), under the supervision of Nigel Hitchin and Michael Atiyah. His research focuses on gauge theory, symplectic geometry, extremal metrics (including Kahler-Einstein metrics), and algebro-geometric stability. Key contributions include Donaldson's theorem, Donaldson polynomial invariants, and the study of pencils of curves in symplectic four-manifolds. His work bridges mathematics and physics, earning global acclaim. Awards: Fields Medal (1986), Crafoord Prize (1994), King Faisal Prize (2006), Shaw Prize (2009), and knighthood (2012). Affiliations: Fellow of the Royal Society, Foreign Member of the US and Royal Swedish Academies of Sciences, and Fellow of the American Mathematical Society. Donaldson’s research continues to explore geometric structures and their applications, anchored at the Simons Center—a hub for interdisciplinary collaboration in geometry and physics.

Steven Sivekمشاهده پروفایل

استاد

• Pure Mathematics
• Topology
• Contact Geometry
• +۴ مورد دیگر

Steven Sivek is a Reader in Pure Mathematics at Imperial College London, affiliated with the Geometry group within the Department of Mathematics. His research focuses on contact and symplectic geometry, knot theory, gauge theory, and low-dimensional topology. He has taught courses on contact geometry, symplectic geometry, mapping class groups, and Morse theory at institutions including Imperial College London, Harvard University, and the University of Bonn. His work includes advanced topics such as Floer homology, Legendrian knots, and the interplay between contact structures and 3-manifolds. Sivek's contributions bridge geometric topology with algebraic structures, addressing questions about knot invariants, representation varieties, and topological field theories. His courses emphasize foundational texts and advanced research topics, such as the classification of tight contact structures, Morse theory applications, and symplectic fiber bundles. He has organized seminars on mapping class groups and taught graduate-level material on advanced geometry and topology. Sivek's research has been published in numerous high-impact papers, exploring themes like Khovanov homology, instanton Floer homology, and the geometry of 3- and 4-manifolds. His academic profile reflects a commitment to both teaching and cutting-edge research, with a focus on geometric and topological questions that intersect algebraic and differential structures.

Richard Hindمشاهده پروفایل

استاد

• Differential Geometry
• Symplectic Geometry
• Complex Manifolds
• +۳ مورد دیگر

Richard Hind is a Professor in the Department of Mathematics at the University of Notre Dame, part of the College of Science. He holds a B.A. from Cambridge University (1992) and a Ph.D. from Stanford University (1997). His research focuses on differential geometry, particularly complex and symplectic geometry, with an emphasis on the interplay between Riemannian metrics and canonical geometric structures. His work explores symplectic embeddings, Lagrangian submanifolds, and geometric rigidity, utilizing pseudoholomorphic curves as a key tool. Key research areas include symplectic packing problems, Stein manifolds, and the topology of symplectic manifolds. Recent work addresses symplectic barriers, packing stability, and geometric invariants of ellipsoids. His publications span journals like Geom. Funct. Anal., Duke Math. J., and Invent. Math., often collaborating with leading researchers in the field. Teaching includes MATH 10270: Mathematics in Architecture, linking geometric principles to historic structures. Professional roles include service on editorial boards and contributions to conferences. Office: 238 Hayes-Healy Bldg, Email: rhind@nd.edu and hind.1@nd.edu.

Tobias Dyckerhoffمشاهده پروفایل

استاد

• Higher Structures in Algebra and Geometry
• Algebraic Topology
• Homological Algebra
• +۳ مورد دیگر

Prof. Dr. Tobias Dyckerhoff is a Professor of Mathematics at the University of Hamburg , specializing in Higher Structures in Algebra and Geometry . He is affiliated with the Cluster of Excellence "Quantum Universe" and the Center for Mathematical Physics . His academic career includes positions at the University of Bonn, University of Oxford, Yale University, and the University of Pennsylvania. Research Interests : Higher category theory, homological algebra, perverse sheaves, Fukaya categories, and applications to symplectic geometry and quantum topology. Editorial Roles : Managing Editor of Abhandlungen aus dem mathematischen Seminar der Universität Hamburg (since 2023) and Editor of Applied Categorical Structures (since 2023). Publications & Articles focus on advanced topics like stable ∞-categories, spherical functors, and Calabi-Yau structures. Notable trends include interconnections between algebraic topology, category theory, and symplectic geometry. Scientific Awards : Bonn Junior Fellow (2014–2018) Titchmarsh Postdoctoral Fellow (2013–2014) Simons Postdoctoral Fellow (2010–2013) Students & Collaborations : Mentors active researchers like Angus Rush, Till Heine, and Jonte Gödicke. Collaborates with institutions such as MPI Bonn and international experts in higher structures.

• Algebraic Geometry
• Symplectic Geometry
• Mathematical Physics
• +۱ مورد دیگر

Kazushi Ueda is an Associate Professor at the Graduate School of Mathematical Sciences, The University of Tokyo, where he has been since April 2015. His research spans algebraic geometry, symplectic geometry, and mathematical physics, with a focus on homological mirror symmetry and its applications to moduli spaces, Calabi-Yau manifolds, and singularities. He previously held academic positions at Osaka University from 2006 to 2015, including roles as Assistant Professor and Associate Professor. Ueda has also had visiting appointments at institutions such as the University of Oxford, Max Planck Institute for Mathematics, and Korea Institute for Advanced Study. Bachelor of Science, Kyoto University (1997-2001) Master of Science, Kyoto University (2001-2003) Doctor of Science, Kyoto University (2003-2006) Ueda's research explores the deep interplay between complex and symplectic geometry through mirror symmetry, particularly in the context of Calabi-Yau varieties, toric degenerations, and dimer models. His work addresses derived categories, stability conditions, and moduli problems, with recent contributions to noncommutative algebraic geometry and applications in mathematical physics. He has collaborated extensively with researchers like Akira Ishii, Masahiro Futaki, and Shinnosuke Okawa. His publications highlight homological mirror symmetry for K3 surfaces, Grassmannians, and singularities, as well as studies on modular forms, cluster transformations, and the Grothendieck ring. Ueda is a member of the Mathematical Society of Japan and has contributed to educational programs, including graduate lectures on mirror symmetry and symplectic geometry.

Alexei Kovalevمشاهده پروفایل

دانشیار

• differential geometry
• global analysis
• mathematical physics
• +۱ مورد دیگر

Alexei Kovalev is an Associate Professor in the Department of Pure Mathematics and Mathematical Statistics (DPMMS) at the University of Cambridge . His research focuses on differential geometry and global analysis , with a particular emphasis on special holonomy manifolds, geometric analysis, and connections to mathematical physics. Publications Highlights : Major contributions to G2-holonomy manifolds, coassociative submanifolds, and Yang-Mills instanton reductions to Nahm’s equations. Research Group : Differential Geometry & Topology, University of Cambridge. Kovalev's work explores the intersection of differential geometry and topology, including asymptotically cylindrical manifolds, Calabi-Yau deformations, and K3 surface involutions. His publications demonstrate deep connections between geometric structures and physical theories like Yang-Mills. Notable collaborations include JD Lotay, J Nordstrom, and M Singer. He maintains an active research program, with recent work (2019) on calibrated submanifold deformations and compact G2-holonomy constructions. Earlier works (2000–2007) established foundational results in anti-self-dual metrics, Nahm’s equations, and twisted connected sums.

• Algebraic Geometry
• Moduli Spaces
• Stability Conditions
• +۴ مورد دیگر

Arend Bayer is a Professor of Algebraic Geometry at the University of Edinburgh's School of Mathematics, where he has been a faculty member since 2012. He specializes in areas such as stability conditions, moduli spaces, and derived categories, contributing to the understanding of Fano varieties, K3 surfaces, and wall-crossing phenomena. His research emphasizes collaboration, reflecting his belief in mathematics as a social endeavor. Education: Arend holds degrees from prestigious institutions, including a PhD from the University of Bonn, with earlier studies at Heidelberg University and a year at the University of Cambridge. His academic journey reflects a deep commitment to advancing algebraic geometry through rigorous research and interdisciplinary collaboration. Research Interests: Arend’s work focuses on algebraic geometry, particularly in stability conditions, Fano varieties, and moduli spaces. He explores the interplay between algebraic structures and geometric objects, often employing derived categories and wall-crossing techniques. His contributions include foundational insights into Kuznetsov components and the geometry of cubic threefolds. Collaborations are central to his approach, emphasizing problem-solving through shared ideas and sustained intellectual exchange. Scientific Awards: No specific scientific awards were mentioned in the provided text. Advising and Grants: While specific advising records or grant details are not detailed in the text, Arend’s collaborative approach suggests active involvement in mentoring and securing research funding. Labs and Teams: Arend contributes to a thriving research group within the School of Mathematics at Edinburgh, focusing on structural and symmetrical aspects of algebraic geometry. His work aligns with broader initiatives in the department, fostering a collaborative environment for advanced mathematical inquiry.

• Pure Mathematics
• Symplectic Topology
• Singularity Theory
• +۱ مورد دیگر

Dr Jonny Evans is a Reader in Pure Mathematics at the School of Mathematical Sciences, Lancaster University . He specializes in Symplectic Topology and its intersections with Singularity Theory and Algebraic Geometry. His research explores geometric structures and topological phenomena in mathematical spaces like S² × S². His recent work focuses on Lagrangian Klein bottles , advancing understanding of symplectic embeddings and singularities. Evans actively supervises PhD students, including Matthew Buck, Elliot Gathercole, and Patrick Ramsey, in the Algebra and Geometry research group. Contact: j.d.evans@lancaster.ac.uk .

• Algebraic Geometry
• Calabi-Yau Manifolds
• Derived Categories
• +۴ مورد دیگر

Richard Thomas FRS is a Royal Society Research Professor in the Department of Mathematics at Imperial College London, affiliated with the Faculty of Natural Sciences. His research focuses on algebraic geometry, Calabi-Yau manifolds, derived categories of coherent sheaves, and moduli problems. He holds a prestigious position as a Fellow of the Royal Society (FRS). His work bridges pure mathematics and theoretical physics, particularly in areas like mirror symmetry and string theory. Key themes include enumerative geometry, stability conditions, and geometric invariants. Recent publications (2020–2025) explore advanced topics such as wall-crossing phenomena, K-theoretic invariants, and applications of derived categories to moduli spaces. His contributions have significantly impacted modern algebraic geometry and its interdisciplinary connections.

Kai Cieliebakمشاهده پروفایل

استاد

• Symplectic geometry
• Contact geometry
• Hamiltonian dynamics
• +۵ مورد دیگر

Prof. Dr. Kai Cieliebak is a Professor of Mathematics at the University of Augsburg, where he holds the Chair of Analysis and Geometry within the Institute of Mathematics under the Faculty of Mathematics, Natural Sciences, and Materials Engineering. He has been at Augsburg University since 2012, following a professorship at Ludwig-Maximilians-Universität München from 2001-2012. His research group includes several researchers and postdocs working on symplectic geometry and related fields. Dr. Cieliebak earned his Diplom in mathematics summa cum laude from Ruhruniversität Bochum in 1992, with thesis on "Pseudo-holomorphe Kurven und periodische Orbits auf Cotangential Bündeln" under advisor H. Hofer. He completed his PhD in mathematics at ETH Zürich in 1996, with thesis "Symplectic boundaries: closed characteristics and action spectra," also advised by H. Hofer. His academic journey included positions at Harvard University, Stanford University, and research at IBM Zürich before his professorships in Munich and Augsburg. Prof. Cieliebak's research focuses on symplectic and contact geometry , with significant contributions to understanding symplectic manifolds, Lagrangian and Legendrian knots, Stein manifolds, and string topology. His work in Hamiltonian dynamics explores variational methods, periodic orbits, and celestial mechanics problems, particularly the restricted three-body problem. In global analysis , he investigates solution spaces of elliptic PDEs and symplectic field theory. His approach often bridges differential geometry, topology, and dynamical systems, with applications to mathematical physics. Over the past decade, Prof. Cieliebak's publications reveal a consistent focus on symplectic homology, Floer theory, and their applications to geometric problems. His work shows increasing integration of algebraic structures with geometric methods, particularly in cyclic homology and string topology. Recent research demonstrates strong collaboration with Urs Frauenfelder on celestial mechanics problems, applying symplectic techniques to the restricted three-body problem and related orbital dynamics. Prof. Cieliebak has secured significant research funding throughout his career, including multiple DFG grants under project codes CI 45/1 through CI 45/12, NSF grants, and participation in European Science Foundation networking programs. His most notable grants include "Foundations of Symplectic Field Theory" (2009-2015) and the current "Rabinowitz Floer Homology" project (since 2023), both in collaboration with U. Frauenfelder. He has mentored numerous researchers and maintains an active research group at Augsburg University, including postdocs and collaborators working on symplectic geometry problems. His team includes researchers such as Dr. Filip Broćić, Zhen Gao, Dr. Hanna Häußler, Emilia Konrad, Shuaipeng Liu, Dominik Meidert, Dr. Airi Takeuchi, Dr. Evgeny Volkov, Milan Zerbin, and PD Dr. Lei Zhao. Prof. Cieliebak has also organized numerous workshops on symplectic geometry, including the annual "Symplectic Field Theory" workshop series.

• Symplectic topology
• Homological Mirror Symmetry
• Floer theory
• +۴ مورد دیگر

Alexander Ritter is a Professor of Mathematics at the University of Oxford, affiliated with the Mathematical Institute and Wadham College. Holding a PhD from MIT (2009), he maintains active research and teaching roles, including Michaelmas 2025 Linear Algebra instruction. Education PhD, Massachusetts Institute of Technology (MIT), 2009 Research Focus Professor Ritter specializes in symplectic topology, homological mirror symmetry, Floer theory, and Gromov-Witten theory. His work bridges symplectic geometry with algebraic geometry through quantum cohomology invariants, Fukaya categories, and spectral sequence techniques. Key innovations include filtrations on quantum cohomology using C*-actions and Morse-Bott-Floer theory to analyze semiprojective toric manifolds and singularities. Publication Evolution Recent publications (2023-2025) reveal intensified collaboration with Filip Živanović on quantum cohomology filtrations, yielding eight joint papers. This work integrates Hilbert-Poincaré series, equivariant cohomology, and McKay correspondence applications, demonstrating progression from foundational symplectic cohomology (2009-2013) toward geometric topology and birational geometry implications. Honors and Recognition Junior Research Fellowship, Trinity College, Cambridge (2009-2013) Research Fellowship, MIT (2007-2008) McCormick Fellowship, University of Chicago (2004-2006) Rouse Ball Prize & Heilbronn Prize, Trinity College, Cambridge (2003) Senior/Junior Scholarships, Trinity College, Cambridge (2001-2002, 2023) Research Funding As Principal Investigator for EPSRC grant EP/Z535977/1 (2025-2028; £806K), he leads research on "Orbifold Floer cohomology and birational geometry." Previously, he served as Co-Investigator with Dominic Joyce on EPSRC grant EP/T012749/1 (2019; £653K) exploring Bridgeland stability in Fukaya categories of Calabi–Yau 2–folds. Academic Environment Based in Oxford's Geometry research group, Ritter collaborates extensively within symplectic topology networks. His 2022-2023 Visiting Associate Professorship at Stanford University underscores international recognition, while consistent teaching of advanced courses (e.g., Morse homology, Algebraic Topology) reflects commitment to graduate education.

Jan de Gierمشاهده پروفایل

استاد

• Mathematical Physics
• Statistical Mechanics
• Solvable Lattice Models
• +۳ مورد دیگر

Jan de Gier is a Professor at the School of Mathematics and Statistics, The University of Melbourne . He is also the Founding Director of MATRIX , Australia’s residential research institute in the mathematical sciences, and a former Deputy Director and Chief Investigator in the Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS) . Additionally, he co-founded the Australian and New Zealand Association for Mathematical Physics (ANZAMP) in 2011 and served as its inaugural Chair. His research focuses on solvable lattice models at the intersection of mathematical physics and statistical mechanics . Key areas include the application of quantum integrability , algebraic structures like the Yang-Baxter equation, Hecke algebras, and quantum groups, as well as analytical methods such as complex analysis and elliptic curves. His work bridges pure and applied mathematics through connections between enumerative combinatorics , representation theory , and real-world phenomena like traffic flow modeling via exclusion processes . The 15 most recent articles reflect his expertise in integrable systems , non-equilibrium statistical mechanics , and algebraic combinatorics . Topics span Macdonald polynomials , stochastic duality , quantum spin chains , and traffic modeling , with methodologies involving matrix product forms , exact solutions , and critical phenomena analysis. He has contributed to editorial efforts through the AustMS Gazette and MATRIX Annals, and has been involved in public science communication via opinion pieces on mathematics funding and applications. His work emphasizes the importance of fundamental research in driving technological innovation, as highlighted in media articles discussing pi calculation , zero-knowledge proofs , and mathematics education .