جستجوی استاد راهنمای دانشگاهی

Oscar Randal-Williamsمشاهده پروفایل

استاد

• Algebraic Topology
• Geometric Topology
• Mapping Class Groups
• +۸ مورد دیگر

Oscar Randal-Williams is the Sadleirian Professor of Pure Mathematics at the University of Cambridge, where he is affiliated with the Faculty of Mathematics and the Department of Pure Mathematics and Mathematical Statistics (DPMMS). His work is centered in the Differential Geometry & Topology research group, where he contributes to advancing knowledge in geometric and algebraic topology. Professor Randal-Williams specializes in Algebraic and Geometric Topology, with particular expertise in mapping class groups, moduli spaces, cobordism categories, spaces of manifolds, surgery theory, configuration spaces, characteristic classes, and K-theory. His research explores the deep connections between homotopy theory and geometric structures, with applications across various mathematical domains. His work often bridges abstract algebraic structures with concrete geometric problems, creating new frameworks for understanding topological phenomena. An analysis of Professor Randal-Williams' recent publications reveals a strong focus on homological stability phenomena, mapping class groups of high-dimensional manifolds, and the interplay between algebraic structures and geometric topology. His work frequently involves E ∞ -algebras, general linear groups, and the topology of diffeomorphism groups. A significant portion of his research investigates the structure of moduli spaces of manifolds and their connections to algebraic K-theory, with recent work extending to applications in mathematical physics through studies of symmetries in quantum field theories. Professor Randal-Williams maintains active collaborations with leading mathematicians worldwide, including Søren Galatius, Alexander Kupers, and Jeremy Miller, among others. His research has been published in top-tier mathematical journals including the Annals of Mathematics, Inventiones Mathematicae, and the Journal of the American Mathematical Society.

Lukas Brantnerمشاهده پروفایل

پژوهشگر ارشد

• Geometry
• Topology
• Algebraic Topology
• +۴ مورد دیگر

Lukas Brantner is a Royal Society University Research Fellow at the Mathematical Institute of the University of Oxford. His research focuses on geometry, topology, and derived algebraic structures, with a particular emphasis on partition Lie algebras, deformation theory, and higher algebraic frameworks. His recent work spans topics such as derived foliations, Poincaré-Birkhoff-Witt theorems, and the complexity of geometric objects like Calabi-Yau varieties in characteristic p. This reflects a deep interplay between algebraic topology, homotopy theory, and modern algebraic geometry. Major Themes: Derived Algebraic Geometry, Homotopy Theory, Deformation Theory, Galois Theory Collaborators: Magidson, Nuiten, Antolín-Camarena, Heuts, Taelman, Campos, Waldron, Hahn, Knudsen, Mathew, Arone, Manners Scientific Awards & Honors: Royal Society University Research Fellow Brantner actively contributes to foundational research in algebraic topology and derived structures, often bridging pure algebra with topological phenomena. His publications highlight the evolution of partition Lie algebras, configuration spaces, and Goodwillie calculus in modern mathematics.

Brent Pymمشاهده پروفایل

دانشیار

• Mathematical Physics
• Algebraic Geometry
• Noncommutative Geometry
• +۳ مورد دیگر

Brent Pym is an Associate Professor in the Department of Mathematics and Statistics at McGill University. His research focuses on the intersection of differential, algebraic, and noncommutative geometry, with a particular emphasis on Poisson varieties and deformation quantization. He has held academic positions at the University of Edinburgh, University of Oxford, and was a Postdoctoral Fellow at McGill and the University of Toronto. Education: BScE in Engineering Physics, Queen's University (2007) MSc in Mathematics, University of Toronto (2008) PhD in Mathematics, University of Toronto (2013) Research Interests: Pym studies Poisson structures, their quantizations, and connections to mathematical physics. His work involves classical/derived algebraic geometry, D-modules, moduli spaces, the Stokes phenomenon, and multiple zeta values. Recent projects include holonomic Poisson manifolds, log symplectic structures, and software for symbolic calculations in deformation quantization. Awards: Lichnerowicz Prize (2018) Advising & Grants: Pym has openings for graduate students (admission 2026) and undergraduate projects (2026–27). He develops the Star Products software package for symbolic calculations in Poisson brackets and quantization. His work is supported by research collaborations and institutional grants. Labs & Teams: Pym collaborates with researchers in geometry and mathematical physics, contributing to projects in noncommutative algebra and geometric quantization. His software tools enhance symbolic computation in these fields.

Irina Bobkovaمشاهده پروفایل

دانشیار

• Algebraic Topology
• Equivariant Homotopy Theory
• Chromatic Homotopy Theory
• +۴ مورد دیگر

Irina Bobkova is an Associate Professor in the Department of Mathematics at Texas A&M University, affiliated with the College of Arts & Sciences. Her research focuses on algebraic topology, particularly computational aspects of equivariant and chromatic homotopy theory. She has received significant support from the National Science Foundation (NSF) via a CAREER Grant and an RTG Grant. Her research interests include equivariant homotopy theory, chromatic homotopy theory, and the study of stable homotopy groups of spheres. She explores computational methods involving Morava stabilizer groups, Picard groups, and topological modular forms. Her work often involves collaborations with leading mathematicians in the field, such as Agnès Beaudry and Vesna Stojanoska. Bobkova has published extensively in top journals like Mathematische Zeitschrift , Journal of Topology , and Algebraic & Geometric Topology . Her recent work includes groundbreaking contributions to K(2)-local homotopy theory, duality resolutions, and the cohomology of Morava stabilizer groups. She co-organizes the South Central Topology Conference, fostering regional collaboration in topology. Her grants and awards reflect her leadership in advancing algebraic topology. She actively engages in academic service, including organizing workshops and mentoring early-career researchers. Despite no listed formal advisees, her collaborative approach shapes the field’s future directions.

• Geometric Representation Theory
• Noncommutative Geometry
• Algebraic Geometry
• +۳ مورد دیگر

Victor Ginzburg is a Professor in the Department of Mathematics at the University of Chicago. His research focuses on geometric representation theory and noncommutative geometry, with contributions to areas such as Hecke algebras, quantum groups, and mirror symmetry. He currently advises seven graduate students, though their specific projects vary widely. His work intersects with algebraic geometry, string theory, and mathematical physics. Key research themes include the application of algebraic geometry to representation theory, including studies on D-modules, quiver varieties, and symplectic reflection algebras. He has authored influential papers such as Non-commutative Symplectic Geometry (2001) and Symplectic reflection algebras (2002). His interests also extend to Calabi-Yau categories and operads, reflecting a deep engagement with modern geometric and algebraic structures.

Mona Merlingمشاهده پروفایل

دانشیار

• Algebraic K-Theory
• Equivariant Stable Homotopy Theory
• Manifold Theory
• +۳ مورد دیگر

Mona Merling is an Associate Professor in the Department of Mathematics at the University of Pennsylvania, affiliated with the School of Arts and Sciences. She holds a Ph.D. from the University of Chicago (2014) under Peter May. Prior to Penn, she was a J.J. Sylvester Assistant Professor at Johns Hopkins University. Her research focuses on algebraic K-theory, its applications to number theory and manifold theory, and equivariant stable homotopy theory. She has held research positions at institutions like the Mathematical Sciences Research Institute (MSRI) and the Max Planck Institute for Mathematics. Merling teaches advanced courses in algebraic topology, homotopy theory, and calculus, including innovative programs like the Penn Directed Reading Program and collaborations with the Prison Teaching Initiative to provide education in incarcerated settings. She organizes conferences and workshops, such as the Algebraic Topology Bridge Summer Workshop, fostering accessibility in topology education. Her research explores cutting-edge topics like scissors congruence K-theory, equivariant infinite loop space theory, and parametrized cobordism categories. Recent work includes collaborations on derived scissors congruence and multiplicative equivariant K-theory, with applications to geometric and algebraic structures. Her grants include funding for social justice initiatives in education.

Ieke Moerdijkمشاهده پروفایل

استاد

• Algebraic Topology
• Differential Topology
• Mathematical Logic
• +۳ مورد دیگر

Prof. Dr. Ieke Moerdijk is a distinguished Professor of Mathematics at the Mathematical Institute of Utrecht University, part of the Faculty of Science. Previously, he held positions at Radboud University (2011–2016) and has been affiliated with institutions like the University of Chicago, Cambridge, and the University of Amsterdam, where he earned his PhD in Mathematics (1985, Cum Laude). His research focuses on algebraic and differential topology, homotopy theory, and applications of topological structures to mathematical logic. He is renowned for co-authoring influential books such as Sheaves in Geometry and Logic (with S. Mac Lane) and Introduction to Foliations and Lie Groupoids (with J. Mrcun). Moerdijk has received prestigious awards including the Spinoza Prize (2012) and the Descartes-Huygens Prize (2011), and is a member of the KNAW and Academia Europaea. His current research emphasizes the theory of dendroidal sets and homotopy operads. He has held visiting positions at institutions like Cambridge, McGill, and Sydney. His academic contributions span editorships, teaching, and supervising numerous students. Moerdijk’s work bridges foundational mathematics with advanced categorical and topological frameworks, influencing areas from algebraic geometry to logic. Education: Bachelor’s/Master’s in Mathematics, Philosophy, and Linguistics at University of Amsterdam PhD in Mathematics, University of Amsterdam (1985) Awards: Spinoza Prize (2012), Descartes-Huygens Prize (2011) Member of KNAW (2006), Academia Europaea (2014) Huygens Fellowship (1986), PIONIER Grant (1995) Research Interests: Algebraic topology, homotopy theory, operads, category theory, and mathematical logic. Moerdijk’s publications include foundational works on dendroidal sets and simplicial methods, with recent contributions addressing ∞-operads and univalent completion. His research often explores connections between algebraic structures and topological spaces, with applications to higher category theory.

Igor Krizمشاهده پروفایل

استاد

• Algebraic Topology
• Stable Homotopy Theory
• Equivariant Topology
• +۵ مورد دیگر

Igor Kriz is a Professor of Mathematics at the University of Michigan, specializing in algebraic topology. He is affiliated with the Department of Mathematics within the College of Literature, Science, and the Arts (LSA). His research focuses on advanced topics in algebraic topology, particularly stable homotopy theory and related areas. Kriz received his Ph.D. from Charles University in 1988. His academic journey has led him to become a prominent researcher in algebraic topology, with significant contributions to the field over several decades. Professor Kriz's primary research interests lie in algebraic topology , which studies topological spaces through algebraic invariants. He specializes in equivariant stable homotopy theory, Mackey functors, cobordism, and motivic homotopy theory . His work involves calculations of stable homotopy groups and other generalized homology theories, including Morava K-theories of classifying spaces of finite groups. He has made significant contributions to the study of operads and structures up to homotopy, with applications extending to differential geometry and physics, particularly string theory. His research often bridges multiple mathematical disciplines, creating connections between topology, algebra, and geometry. His recent publications (2022-2025) demonstrate a strong focus on equivariant topology and its connections to algebraic structures. Kriz frequently collaborates with researchers like P. Hu, P. Somberg, and others, producing work that explores the intersection of homotopy theory with representation theory and algebraic geometry. His research program shows consistent evolution from foundational work in stable homotopy to more recent applications in motivic contexts and topological Hochschild homology. Professor Kriz teaches both undergraduate and graduate courses at the University of Michigan. His teaching portfolio includes Math 425 (Introduction to Probability), Math 592 (Introduction to Algebraic Topology), and advanced graduate courses Math 695 and Math 696 (Algebraic Topology I and II). His course materials are regularly updated, reflecting his commitment to education in mathematical topology. Based in East Hall (room 3846) at the University of Michigan, Professor Kriz maintains an active research program while contributing to the academic community through teaching and mentorship. His work continues to advance our understanding of complex topological structures and their algebraic representations.

Jianqi Liuمشاهده پروفایل

پژوهشگر ارشد

• Vertex Operator Algebras
• Conformal Field Theory
• Mathematical Physics
• +۳ مورد دیگر

Jianqi Liu is a Hans Rademacher Research Fellow in the Department of Mathematics at the University of Pennsylvania, affiliated with the School of Arts and Sciences. His research focuses on vertex operator algebras (VOAs) and 2D conformal field theory (CFT), with an emphasis on algebraic structures such as fusion rules, Zhu’s algebras, Borel-type subalgebras, and connections to the classical Yang-Baxter equation. He also explores geometric aspects of VOAs and their physical interpretations. He earned his Ph.D. in Mathematics from the University of California, Santa Cruz (2018–2023), under the supervision of Chongying Dong. Prior to his current role, he held teaching roles at both UPenn and UCSC, instructing courses ranging from advanced linear algebra to complex analysis and number theory. His research publications address topics such as twisted conformal blocks, Rota-Baxter operators, and the interplay between algebraic structures and integrable systems. Liu collaborates with researchers like Angela Gibney and Daniel Krashen, focusing on advancing theoretical frameworks in mathematical physics and algebraic geometry.

Julie Bergnerمشاهده پروفایل

استاد

• Homotopy Theory
• Algebraic Topology
• Algebraic K-Theory
• +۳ مورد دیگر

Julie Bergner is a Professor in the Department of Mathematics at the University of Virginia. She is currently on sabbatical during 2024-25 as a Visiting Fellow at Clare Hall, University of Cambridge. Her research focuses on Homotopy Theory, Algebraic Topology, Algebraic K-Theory, and Category Theory, with a particular emphasis on higher category theory and homotopical algebraic structures. University of Virginia (Professor, Department of Mathematics) University of Cambridge (Visiting Fellow at Clare Hall, 2024-25) Her work spans 2-Segal objects, model categories, Waldhausen constructions, and applications to topological field theories. She has received NSF CAREER awards for her research on equivariant topological field theories and higher cluster categories. Her recent publications explore combinatorial models, enriched categories, and homotopy limits in the context of functor calculus and higher structures. Julie Bergner contributes to mathematical exposition through articles on writing papers in the mathematical sciences and homotopy theory applications. She is actively involved in the department's topology seminar and supports collaborative learning initiatives. Her research has implications in algebraic topology, category theory, and their interdisciplinary applications.

Maxim Kontsevichمشاهده پروفایل

استاد

• Mathematical Physics
• Algebraic Geometry
• Deformation Quantization
• +۵ مورد دیگر

Maxim Kontsevich is a permanent professor at the Institut des Hautes Études Scientifiques (IHÉS), holding the AXA Chair for Mathematics since 1995 and a visiting chair at Rutgers University (one month annually since 1997). Born in 1964 in Khimki, USSR, he earned his PhD from Bonn University in 1992. His career includes visiting positions at Harvard, the Institute for Advanced Study, and Berkeley, where he was a professor from 1993 to 1995. His research spans mathematical physics, algebraic geometry, and non-commutative geometry. Notable contributions include deformation quantization, mirror symmetry, and motivic integration. His work bridges algebraic structures with geometric and physical concepts, influencing areas like topological field theories, string theory, and integrable systems. Awardees of Fields Medal (1998), Crafoord Prize (2008), and Breakthrough Prize (2014), he also holds editorial roles at Compositio Mathematica and Publications Mathématiques IHÉS. His over 50 publications explore advanced topics such as quantum cohomology, Hodge theory, and categorical structures in geometry.

Tom Leinsterمشاهده پروفایل

استاد

• Category Theory
• Metric Geometry
• Algebra
• +۳ مورد دیگر

Tom Leinster is a mathematician at the University of Edinburgh, specializing in category theory, metric geometry, and their applications to areas such as algebra, topology, and mathematical biology. His research focuses on the concept of magnitude, a measure for metric spaces and enriched categories, as well as entropy and diversity. He has authored influential books including *Basic Category Theory* and *Entropy and Diversity: The Axiomatic Approach*. Leinster's work bridges foundational mathematics with interdisciplinary applications, emphasizing the interplay between abstract structures and concrete problems. His research interests span category theory, metric geometry, algebraic topology, and mathematical biology. Key contributions include foundational work on magnitude and its connections to geometric measure theory, entropy characterization, and categorical frameworks for diversity measurement. Leinster also engages in mathematical education and ethics, advocating for responsible research practices. Notable publications include recent advancements in magnitude homology of Euclidean sets, extremal magnitude in metric spaces, and entropy modulo primes. His work often highlights interdisciplinary applications, such as biodiversity quantification and information-theoretic foundations.

Richard Garnerمشاهده پروفایل

مدرس

• Category Theory
• Algebraic Structures
• Homotopy Type Theory
• +۳ مورد دیگر

Richard Garner is a lecturer at Macquarie University's School of Mathematical and Physical Sciences, Faculty of Science and Engineering. He specializes in teaching mathematics to engineering and computing students in units like MATH2055 and MATH1007, focusing on problem-solving and real-world applications. His teaching philosophy emphasizes authentic mathematical experiences, blending abstract concepts with practical examples, such as connecting multivariable calculus to AI technologies. School: School of Mathematical and Physical Sciences University: Macquarie University Teaching Areas: Mathematics for engineering and computing, convolution, multivariable calculus Richard won a Student Nominated Award in the 2023 Vice Chancellor’s Learning and Teaching Awards, reflecting his commitment to student-centered education. He prioritizes clarity in course design, using visual tools and accessible materials to enhance learning, and fosters a supportive environment where students feel comfortable asking questions. Key Teaching Strategies Organized iLearn layouts following Macquarie University's standards Multiple formats for lecture materials (diagrams, color-coded slides) Weekly task clarity and real-world problem framing Live worked examples and transparent success criteria His research spans category theory, computational effects, and homotopy theory, with publications on topics like comodels, monoidal bicategories, and enriched categories. Richard's work bridges abstract mathematics with applications in computer science and logic. Scientific Awards 2023 Vice Chancellor’s Learning and Teaching Award (Student Nominated) Students praise his ability to make complex concepts intuitive, his enthusiasm for mathematics, and his dedication to explaining the 'why' behind the subject. His teaching design, including time-sensitive banners and structured weekly content, has been highlighted as exemplary.

Christine Vespaمشاهده پروفایل

استاد

• Algebra
• Algebraic Topology
• Category Theory
• +۳ مورد دیگر

Christine Vespa is a Professor at Aix-Marseille Université affiliated with the Institute of Mathematics (I2M) in Marseille. Her research lies at the intersection of Algebra , Algebraic Topology , and Category Theory , focusing on polynomial functors , functor homology , and stable homology of group families. Education Habilitation à diriger des recherches (HDR), Université de Strasbourg, 2013. Thesis: Foncteurs polynomiaux et homologie stable à coefficients polynomiaux . Jury: William Dwyer, Vincent Franjou, Hans-Werner Henn, Nick Kuhn, Birgit Richter, Lionel Schwartz. Doctorat en Mathématiques, Université Paris 13, 2005. Thesis: La catégorie F_quad des foncteurs de Mackey généralisés pour les formes quadratiques sur F2 . Director: Lionel Schwartz. Research Interests Her work explores structural properties of polynomial functors and their applications in homology stability. She connects abstract category-theoretic frameworks with concrete algebraic and topological problems, such as stable homology for automorphism groups of free groups and orthogonal groups. Recent preprints address PROP structures , analytic exponential functors , and Jacobi diagrams , highlighting her engagement with algebraic topology and category theory. Article Trends Christine Vespa's publications and preprints emphasize algebraic topology and category theory . Recent trends include analyzing partition PROPs , exponential functors , and Jacobi diagrams in the context of stable homology. Earlier works delve into Hochschild homology , automorphism groups , and generalized Mackey functors , showcasing her contributions to homological algebra and representation theory. Advising Antoine Feltz (2020–2024): Foncteurs polynomiaux sur les catégories FI_d . Arthur Soulié (2015–2018): Foncteurs de Long-Moody et homologie stable des groupes de difféotopie . Andrea Cesaro (2012–2016): Pre-Lie algebras and operads in positive characteristic , co-supervised with Benoit Fresse. Labs & Teams She is a member of the Analyse, Géométrie, Topologie research group at I2M. She has organized academic events, including the 2014 Strasbourg workshop on Mac Lane's cubic construction and the 2015 Strasbourg Masterclass on Topological K-theory.

• algebraic topology
• Goodwillie calculus
• chromatic homotopy theory
• +۴ مورد دیگر

Gijs Heuts is an Associate Professor in the Fundamental Mathematics group at the Mathematical Institute of Utrecht University, part of the Faculty of Science. His research focuses on advanced topics in algebraic topology and higher category theory, with particular expertise in Goodwillie calculus, chromatic homotopy theory, and operads. He is affiliated with the Utrecht Geometry Center, which includes prominent mathematicians Ieke Moerdijk and Lennart Meier. His work is currently funded by prestigious grants including an ERC Starting Grant titled "Chromatic homotopy theory of spaces" and an NWO Vidi grant "Hopf algebras and periodic homotopy theory". Starting September 2025, he will also serve as one of the Principal Investigators on the NWO XL consortium "Symmetry on the interface of topology and higher algebra". Dr. Heuts' research centers around homotopy theory and derived algebraic geometry, with a focus on generalizations of classical algebraic concepts (such as Lie algebras, commutative rings, and Hopf algebras) to homotopy theory. His work has significant applications to chromatic homotopy theory, with Goodwillie calculus and operads serving as central methodological tools. His publication record demonstrates consistent high-impact contributions to the field, with papers appearing in top journals such as Annals of Mathematics and Proceedings of the American Mathematical Society. His research spans theoretical foundations of higher category theory to specific applications in unstable homotopy theory, particularly focusing on connections between spectral Lie algebras and vn-periodic phenomena. ERC Starting Grant "Chromatic homotopy theory of spaces" NWO Vidi grant "Hopf algebras and periodic homotopy theory" PI on NWO XL consortium "Symmetry on the interface of topology and higher algebra" (starting Sept 2025) Dr. Heuts completed his PhD under Jacob Lurie at Harvard University and was previously a postdoc at the University of Copenhagen. He has held research positions at the Isaac Newton Institute and Hausdorff Research Institute. He was an organizer of the MIT Talbot Workshop (2012-2015) and currently organizes the European Autumn School in Topology (EAST).