جستجوی استاد راهنمای دانشگاهی

• Numerical analysis
• Partial differential equations
• Level set methods
• +۷ مورد دیگر

Dr. Jean-Christophe Nave is an Associate Professor in the Department of Mathematics and Statistics at McGill University, specializing in applied mathematics, numerical analysis, and computational methods. His research focuses on numerical methods for partial differential equations, fluid mechanics, interface problems, and computer graphics. He holds a PhD from UCSB (2004) and has held academic positions at MIT and McGill since 2005. Currently, he serves on committees such as the Steering Committee of the Institut des Sciences Mathematiques and the CRM Applied Mathematics Lab. His educational background includes a PhD under Professors Xu-Dong Liu and Sanjoy Banerjee. Key research areas include level set methods, fluid-structure interaction, and invariant numerical methods. Notable works include the Correction Function Method for interface problems and the Characteristic Mapping Method for advection problems. Nave’s publications span topics like Poisson equations with discontinuous coefficients, fluid dynamics simulations, and high-order numerical schemes. He has advised numerous graduate and undergraduate students, contributing to their research in applied mathematics and computational science. His work bridges theoretical rigor and practical applications in engineering and physics. He teaches advanced courses such as Numerical Analysis I/II and Computational Methods in Applied Mathematics. His research group collaborates on projects involving fluid dynamics, elasticity, and geometric algorithms, with a focus on developing robust numerical tools for complex systems.

David Nadlerمشاهده پروفایل

استاد

• Geometric Representation Theory
• Symplectic Geometry
• Langlands Duality
• +۳ مورد دیگر

David Nadler is a Professor in the Department of Mathematics at the University of California, Berkeley, appointed in 2012. His research centers on geometric representation theory and symplectic geometry, with significant contributions to the Langlands program, microlocal sheaf theory, and symplectic topology. He maintains an active research group and teaches courses ranging from undergraduate linear algebra to graduate algebraic topology and geometry. Nadler's research explores the interface of algebraic geometry, topology, and representation theory. His work in geometric representation theory focuses on Langlands duality, Springer theory, and Betti geometric Langlands. In symplectic geometry, he investigates microlocal sheaves, Fukaya categories, and Weinstein structures. His recent publications demonstrate a consistent focus on categorical methods in geometric Langlands correspondence and symplectic arborealization. His publications consistently emphasize categorical and geometric approaches to representation theory. Recent works cluster in three areas: (1) extensions of the geometric Langlands program to Betti cohomology settings, (2) microlocal analysis of sheaves on symplectic manifolds, and (3) combinatorial models in symplectic topology. This reflects sustained development of 'Betti geometric Langlands' as a distinct research program bridging topology and automorphic forms. Nadler has advised over a dozen PhD students since 2012, with dissertations spanning geometric representation theory, symplectic geometry, and algebraic topology. Student projects frequently investigate categorical aspects of geometric Langlands, microlocal sheaves, and combinatorial models in symplectic topology.

Ciprian Manolescuمشاهده پروفایل

استاد

• Geometry
• Topology
• Gauge Theory
• +۴ مورد دیگر

Ciprian Manolescu is a Professor of Mathematics at Stanford University, where he joined after serving as a professor at UCLA since 2008. He holds both his undergraduate degree and doctorate from Harvard University, advised by Peter Kronheimer. His research focuses on gauge theory, low-dimensional topology, and symplectic geometry, with notable contributions to Heegaard Floer theory, Khovanov homology, and the resolution of the Triangulation Conjecture. Manolescu’s academic accolades include the 2019 E.H. Moore Research Article Prize, the 2012 European Mathematical Society Prize, and a 2004 Clay Research Fellowship. He delivered an invited lecture at the 2018 International Congress of Mathematicians and became a Fellow of the American Mathematical Society in 2017. His work bridges advanced algebraic structures with geometric problems, particularly in understanding manifold invariants and topological constraints. His teaching includes the Polya Problem Solving Seminar (Math 193) at Stanford, and he advises students competing in the Putnam Mathematics Competition. Research trends in his publications emphasize applications of Floer homology to knot theory, 4-manifold topology, and the interplay between algebraic topology and quantum field theories. Education: PhD and BA in Mathematics, Harvard University Key Research Themes: Floer homology frameworks, geometric topology, knot invariants, and manifold classification Grants & Collaborations: Involved in NSF-funded projects like the FRG: Collaborative Research: Floer Homotopy Theory (2016)

• 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.

Dima Arinkinمشاهده پروفایل

استاد

• Algebraic Geometry
• Geometric Langlands Program
• Moduli Spaces
• +۳ مورد دیگر

Dima Arinkin is a Professor in the Department of Mathematics at the University of Wisconsin–Madison, specializing in algebraic geometry with significant contributions to geometric representation theory and mathematical physics. His research focuses on: Geometric Langlands Program: Developing frameworks connecting automorphic forms and Galois representations through geometric methods Moduli Spaces: Analyzing spaces of algebraic connections, Higgs bundles, and their compactifications D-modules: Studying systems of linear differential equations via algebraic geometry Integrable Systems: Investigating geometric structures in soliton theory and Painlevé equations Irregular Singularities: Exploring connections with irregular behavior on algebraic curves Analysis of his publications (2008-2016) reveals consistent advancement in geometric Langlands through derived algebraic geometry techniques, particularly in relating singular support of sheaves to automorphic forms and establishing oper structures for connections. No scientific awards are documented in the provided materials. No information regarding student advisement or research grants appears in the source texts.

Zsolt Patakfalviمشاهده پروفایل

دانشیار

• Algebraic Geometry
• Commutative Algebra
• Birational Geometry
• +۳ مورد دیگر

Zsolt Patakfalvi is an Associate Professor at École Polytechnique Fédérale de Lausanne (EPFL), holding positions in the School of Basic Sciences (SB) within the Department of Mathematics (MATH). He is affiliated with the Chair of Algebraic Geometry (CAG) and the Section of Mathematics for Engineers (SMA-ENS). Additionally, he serves as Director of SMA-GE and holds roles in academic governance bodies like the Conference of Section Directors (CDS) and SB Faculty Management. His research focuses on Algebraic Geometry, particularly in birational geometry, positive characteristic methods, moduli theory, and mixed characteristic algebra. He explores topics such as Hodge theory, singularities, and applications to arithmetic geometry. Notable contributions include work on the minimal model program, test ideals, and counterexamples to classical conjectures in positive characteristics. He supervises doctoral students in areas like algebraic geometry and commutative algebra, including Jefferson Baudin, Léo Navarro Chafloque, and Linus Rösler. His past advisees include Emelie Arvidsson and Quentin Posva. Patakfalvi’s publications frequently address foundational questions in geometry, with recent work extending into perfectoid spaces and globally-regular varieties. He coordinates courses such as 'Algebra III - Rings and Fields' and 'Perfectoid spaces' at EPFL, reflecting his commitment to both research and education. His academic service includes managing educational programs within SB-SMA and contributing to institutional decision-making through CDS membership.

Jaime Peraireمشاهده پروفایل

استاد

• Computational Fluid Dynamics
• Finite Element Methods
• Aerodynamics
• +۷ مورد دیگر

Jaime Peraire is the H.N. Slater Professor of Aeronautics and Astronautics at MIT, affiliated with the School of Engineering. He leads research in computational mechanics, aerodynamics, and numerical methods for partial differential equations, with key roles as former Department Head (2011-2018) and Director of the Aerospace Computational Design Lab (1993-2011). His expertise spans finite element methods, shock capturing algorithms, and high-order numerical techniques applied to hypersonic flows, space weather, and metamaterials. Education includes a Ph.D. from the University of Wales (1986) and engineering degrees from the University of Barcelona (1983, 1987). He holds prestigious awards like the T.J. Hughes Medal (2015) and the Ildefons Cerdá Medal (2015). His work bridges computational science and engineering, with contributions to discontinuous Galerkin methods, mesh adaptivity, and GPU-accelerated simulations. Research interests emphasize high-fidelity modeling of compressible flows, plasma dynamics, and terahertz spectroscopy. Notable projects include MIT’s space weather modeling initiative and metamaterial fabrication using atomic layer lithography. His labs collaborate across MIT’s Schwarzman College of Computing, IDSS, and CCSE to advance computational tools for aerospace and environmental systems. Awards: Over 10 major prizes, including NASA Exceptional Achievement (1997) and IACM Young Researchers Award (1998). Grants/Advising: Led NSF-funded space weather projects and advised numerous PhD students in computational engineering. Labs: Aerospace Computational Design Lab, MIT Schwarzman College of Computing collaborations.

Mark Haskinsمشاهده پروفایل

استاد

• Differential Geometry
• Partial Differential Equations
• Holonomy Groups
• +۵ مورد دیگر

Mark Haskins is a Professor of Mathematics at Duke University, affiliated with the Trinity College of Arts & Sciences. He holds a Ph.D. from the University of Texas at Austin (2000) and has held academic positions at institutions including the University of Bath and Imperial College London. His research focuses on differential geometry, special holonomy metrics, and geometric flows, particularly G₂-holonomy manifolds and Laplacian flow solitons. He is a Fellow of the Learned Society of Wales (2014). Research interests include Riemannian geometry, Einstein manifolds, and geometric analysis. Notable contributions involve constructing G₂-manifolds from asymptotically conical Calabi-Yau 3-folds and studying solitons in Laplacian flow. He has led grants from the Simons Foundation (2016–2024) and organized programs like the 2024 Special Geometric Structures and Analysis at MSRI. Teaching includes courses like Real Analysis II and Smooth Manifolds. He mentors students, including Yijia Liu and Anuk Dayaprema, and collaborates with researchers like Nordström and Foscolo. Professional activities include roles as Director of Graduate Studies at Duke and service in academic leadership.

Anton Mellitمشاهده پروفایل

دانشیار

• Algebraic Geometry
• Enumerative Geometry
• Representation Theory
• +۴ مورد دیگر

Anton Mellit is an Associate Professor in the Faculty of Mathematics at the University of Vienna. He holds a Doctor of Natural Sciences from the University of Bonn (2008) and completed postdoctoral positions at institutions including the Hausdorff Center for Mathematics (Bonn), Scuola Internazionale Superiore di Studi Avanzati (Trieste), and the Institute of Science and Technology Austria (Klosterneuburg). His research focuses on algebraic geometry, enumerative geometry, and their connections to representation theory, combinatorics, and number theory, with particular emphasis on moduli spaces, categorification, and character varieties. Education: Doctor of Natural Sciences (2008), University of Bonn Master in Applied Mathematics (2004), National Technical University of Ukraine Bachelor in Applied Mathematics (2002), National Technical University of Ukraine Research Interests: Investigates Poincaré polynomials of moduli spaces, Higgs bundles, and character varieties Studies Khovanov-Rozansky homology and torus knots Explores connections between Macdonald polynomials and affine Springer fibers Develops combinatorial approaches to algebraic geometry via Hilbert schemes and categorification Grants & Projects: ERC Consolidator Grant: Macdonald polynomials and related structures in geometry FWF Standalone Project: Refined invariants in combinatorics, low-dimensional topology, and geometry of moduli spaces Labs/Teams: Collaborates with researchers in geometric representation theory, quantum cohomology, and algebraic combinatorics, including notable co-authors like Erik Carlsson, Eugene Gorsky, and Maxim Smirnov.

Allen Knutsonمشاهده پروفایل

استاد

• Algebra
• Algebraic Geometry
• Algebraic Combinatorics
• +۳ مورد دیگر

Prof. Allen Knutson is a Professor of Mathematics at Cornell University, affiliated with the College of Arts and Sciences. He earned his Ph.D. from the Massachusetts Institute of Technology in 1996. His research focuses on algebraic geometry, algebraic combinatorics, and geometric representation theory, with an emphasis on Schubert calculus, quiver varieties, and the combinatorial structures underlying geometric problems. Education: Ph.D. (1996) from MIT. His work often involves degenerating complex algebraic varieties into simpler combinatorial pieces, bridging geometry and discrete mathematics. Notable contributions include foundational results in Schubert calculus, honeycomb models, and the use of puzzles in cohomology computations. Research Interests: Algebraic geometry, algebraic combinatorics, Schubert calculus, quiver varieties, geometric representation theory, and applications to integrable systems. His interdisciplinary approach integrates algebraic, geometric, and combinatorial methods to solve problems in mathematics and theoretical physics. Advising: Current students include Portia Anderson, Raj Gandhi, and others. Past advisees have contributed to areas like flag manifolds, Frobenius splitting, and Bruhat atlases. He has taught advanced courses on topics such as symplectic resolutions, differentiable manifolds, and algebraic geometry. Labs/Teams: Collaborates widely, with contributions to projects like the ICM 2022 paper on Schubert calculus and quiver varieties. His work often involves visual tools like puzzles and pipe dreams to encode geometric invariants.

Yanki Lekiliمشاهده پروفایل

استاد

• Symplectic Topology
• Low Dimensional Topology
• Algebraic Geometry
• +۳ مورد دیگر

Yankı Lekili is a Professor of Geometry at the Department of Mathematics, Imperial College London, affiliated with the Faculty of Natural Sciences. His research focuses on symplectic topology, low-dimensional topology, and their connections to algebraic geometry and geometric representation theory. He explores topics including mirror symmetry conjectures, Fukaya categories, and homological mirror symmetry for various geometric structures. Education: PhD in Mathematics from MIT (2009), specializing in broken Lefschetz fibrations and Heegaard-Floer homology. Teaching: Courses include Elliptic Curves, Commutative Algebra, Algebraic Topology, and Representation Theory. Research Interests: Symplectic manifolds, Lagrangian submanifolds, derived equivalences, and categorical mirror symmetry applications. His work bridges symplectic geometry with algebraic geometry, particularly through mirror symmetry. Recent studies involve Fukaya categories of singularities, noncommutative crepant resolutions, and equivariant cohomology. He collaborates internationally, contributing to topics like the Fargues-Fontaine curve and Auslander algebras.

Vasily Krylovمشاهده پروفایل

پژوهشگر ارشد

• Representation Theory
• Mathematical Physics
• Algebraic Geometry
• +۵ مورد دیگر

Vasily Krylov is a Benjamin Peirce Postdoctoral Fellow at Harvard University's CMSA, mentored by Prof. Dan Freed and supported by the Simons Foundation via the Simons Collaboration on Global Categorical Symmetries. He completed his PhD in Mathematics at MIT under Prof. Roman Bezrukavnikov. His research focuses on the intersection of representation theory, mathematical physics, and algebraic geometry, with a special emphasis on symplectic resolutions, integrable systems, 3D-mirror symmetry, and Coulomb branches. Affiliations: Harvard CMSA (2020–present), MIT PhD (2015–2020) Education: PhD in Mathematics (MIT, 2020), Prior studies include seminars on geometric representation theory and quantum groups. His work spans geometric realizations of algebraic structures, such as asymptotic affine Hecke algebras and Bethe subalgebras in Yangians, with applications to character formulas and symplectic duality conjectures. He co-organizes the Geometry and Quantum Theory (GQT) seminar at Harvard and has presented at institutions like the Perimeter Institute and Skoltech. Key research directions include: Proving Hikita-Nakajima conjecture for ADHM spaces and Slodowy slices Geometric Satake equivalence and Coulomb branch constructions Applications of Kazhdan-Lusztig theory to affine Lie algebras His recent articles address symplectic resolutions, Frobenius pushforwards on compactifications, and integrable crystal structures in representation theory.

• Differential Geometry
• Geometric Analysis
• Riemannian Geometry
• +۳ مورد دیگر

Bianca Santoro is an Investigator in Mathematics Münster and a member of the Collaborative Research Center (CRC) 1442 'Geometry: Deformations and Rigidity' at the University of Münster. She is affiliated with the Mathematisches Institut within the Faculty of Mathematics and Computer Science. Her research focuses on differential geometry, geometric analysis, and related areas such as Riemannian geometry and partial differential equations. She has contributed to topics including Ricci-flat metrics, Hamiltonian stationary Lagrangian submanifolds, and singularities in geometric problems. Education and career highlights include her work at the Instituto Nacional de Matemática Pura e Aplicada (IMPA), where she authored foundational texts like Introduction to evolution equations in geometry (2009) and Holonomy Groups in Riemannian Geometry (2012). Her research spans projects such as 'Curvature, shape, and global analysis' (T5) and 'Singularities and PDEs' (T6) under Mathematics Münster’s framework. Her publications reflect expertise in geometric PDEs, bifurcation theory, and complex geometry, with contributions to both theoretical developments and applied methodologies. Santoro’s work is supported through collaborative initiatives like the CRC 1442, emphasizing interdisciplinary approaches to geometric deformations and rigidity phenomena.

• Mathematical Physics
• Algebraic Geometry
• Symplectic Geometry
• +۷ مورد دیگر

Travis Schedler is a Professor of Mathematics at Imperial College London's Department of Mathematics within the Faculty of Natural Sciences. His research focuses on algebraic and geometric structures in mathematical physics, including symplectic resolutions, Poisson varieties, and representation theory. He has developed novel homology theories such as Poisson-de Rham homology and introduced nondegeneracy conditions like 'holonomicity.' Education history is not explicitly detailed in the text, but his academic career includes a five-year fellowship (2008–2013) from the American Institute of Mathematics and NSF funding. He teaches advanced modules such as Representation Theory and Algebraic Geometry, offering both handwritten lecture notes and typed materials. In Spring 2019, he delivered a TCC course on Symplectic Resolutions and Singularities, with comprehensive lecture notes and problem sheets. His research spans Hochschild (co)homology, log symplectic manifolds, preprojective algebras, and A-infinity/L-infinity algebras. He actively contributes to academic discourse through lectures like his talk on Toric Poisson Structures at the 2020 Fields Institute event. Awards include his AIM fellowship and NSF grants. Teaching materials include problem sheets and Slack-based course forums. His work bridges algebraic geometry with mathematical physics, emphasizing structural analysis of geometric and algebraic objects.

Dan Abramovichمشاهده پروفایل

استاد

• Algebraic Geometry
• Resolution of Singularities
• Logarithmic Geometry
• +۳ مورد دیگر

**Dan Abramovich** is a Professor in the Department of Mathematics at Brown University, affiliated with the College of Arts and Sciences. His research focuses on algebraic geometry, particularly in resolution of singularities, logarithmic geometry, moduli spaces, and birational geometry. He has authored numerous papers and contributed to foundational work in these areas, supported by NSF and BSF grants. **Teaching**: He teaches courses like Math 1540 (Galois theory and representations of finite groups) and has extensive past teaching records dating back to 2015. His seminars include Algebraic Geometry and Topology. **Research**: Abramovich's work bridges algebraic structures and geometric applications, with notable contributions to logarithmic geometry and moduli theory. His recent articles address weighted blow-ups, dynamical systems in resolution, and functorial monomialization. **Grants & Collaboration**: He collaborates internationally, organizing conferences like AGNES and BATMoBYle. His work is disseminated via arXiv, with over 50 publications since the 1990s.