Find Academic Supervisors

• Arithmetic Geometry
• Algebraic Geometry
• Representation Theory
• +4 more

Prof. Peter Scholze is a leading mathematician at the University of Bonn and the Max Planck Institute for Mathematics (MPIM). He holds a professorship in the Mathematical Institute at the University of Bonn and is affiliated with MPIM as a principal investigator. His research focuses on arithmetic geometry, representation theory, and p-adic geometry, with notable contributions to perfectoid spaces, prismatic cohomology, and the geometrization of the local Langlands correspondence. Scholze has organized several advanced seminars (ARGOS) and taught courses on topics like condensed mathematics, p-adic geometry, and algebraic geometry. He collaborates widely with researchers such as Laurent Fargues and Bhargav Bhatt. His recent work includes groundbreaking papers on wild Betti sheaves, motivic geometrization of the local Langlands correspondence, and the Habiro ring of number fields. Scholze has pioneered the use of prismatic cohomology to unify p-adic Hodge theories and has developed foundational frameworks in derived algebraic geometry. His research also intersects with representation theory and topological cyclic homology. Affiliations: University of Bonn (Mathematical Institute), Max Planck Institute for Mathematics (MPIM) Research Groups: Arbeitsgruppe Arithmetische Geometrie und Darstellungstheorie Teaching: Recent courses include 'Selected Topics in Algebraic Geometry' and 'Six-Functor Formalisms'. His work frequently explores connections between algebraic geometry and number theory, with a focus on geometric approaches to arithmetic problems. Scholze is a key figure in modern arithmetic geometry, influencing both foundational theory and applied areas like the Langlands program.

• Algebraic Geometry
• Number Theory
• Representation Theory
• +3 more

Andreas Bode is a Research Fellow at the University of Wuppertal, where he is part of the group led by Sascha Orlik in the Department of Mathematics. His research focuses on D-modules on rigid analytic spaces, integrating geometric representation theory and nonarchimedean geometry. His research interests span several areas of algebraic geometry and number theory, including the study of p-adic differential operators, nonarchimedean geometry, and representation theory. He explores the interplay between D-modules and rigid analytic spaces, contributing to the understanding of holonomicity, Auslander regularity, and the application of almost mathematics in p-adic contexts. His work bridges geometric and analytic approaches to problems in nonarchimedean settings. Bode's recent publications include advancements in the theory of Auslander regularity for p-adic structures, contributions to the holonomicity of D-cap-modules on rigid analytic spaces, and explorations into locally analytic representations of p-adic groups. His work often intersects with homological algebra and functional analysis, reflecting a deep engagement with both theoretical and methodological challenges in nonarchimedean geometry. He has not been mentioned as having received any scientific awards in the provided texts. Bode's current role as a postdoctoral researcher does not involve formal academic advising of students. No grants are specifically mentioned in the provided information. He is affiliated with the Algebra and Number Theory group at the University of Wuppertal, collaborating with colleagues such as Sascha Orlik and contributing to the broader research community in nonarchimedean geometry.

• Algebraic Geometry
• Mathematical Physics
• Mirror Symmetry
• +7 more

Maxim Kontsevich has been a permanent professor at the Institut des Hautes Études Scientifiques (IHÉS) since 1995, holding the AXA-IHES Chair for Mathematics . He is also Professor at Rutgers University (one month per year since 1997) and was Professor at University of California, Berkeley (1993–1995). Born 25 August 1964 in Khimki, former USSR, he became a French citizen in 1999. Education: Ph.D. in Mathematics, University of Bonn, March 1992. Research Interests: Prof. Kontsevich’s work lies at the intersection of algebraic geometry , mathematical physics , and quantum theory . He introduced revolutionary ideas in mirror symmetry , non-commutative geometry , and deformation quantization , creating new algebraic structures that have found applications far beyond their original contexts. His current ERC Synergy Grant “ReNew Quantum” (2019-2025) explores recursive and exact new quantum theory . Publications & Trends: Across more than 50 influential papers, Kontsevich has consistently pushed the boundaries of enumerative geometry , motivic integration , and topological field theory . His recent work delves into symplectic aspects of homological algebra , motivic Donaldson-Thomas invariants , non-archimedean geometry , and integrable systems , revealing deep connections between geometry, algebra, and physics. Scientific Awards & Honors: Fields Medal (1998) Crafoord Prize (2008) Shaw Prize in Mathematical Sciences (2012) Breakthrough Prize in Fundamental Physics (2012) Breakthrough Prize in Mathematics (2014) ERC Synergy Grant “ReNew Quantum” (2019) AMS Moore Prize (2025) Doctor Honoris Causa: Aarhus University (2014), Universität Wien (2015), Syddansk Universitet (2023) Member of Académie des Sciences, Institut de France, Academia Europaea, National Academy of Sciences (foreign), London Mathematical Society (honorary) Grants & Leadership: As Principal Investigator of the ERC Synergy Grant “ReNew Quantum” (€10 million, 2019-2025), Kontsevich coordinates an international team advancing exact methods and resurgence in quantum field and string theories. Editorial Service & Community Roles: He serves on the editorial boards of Compositio Mathematica , Publications Mathématiques IHÉS , Journal of Noncommutative Geometry , and several other leading journals, shaping the direction of contemporary mathematical research.

• Geometric Topology
• Geometric Group Theory
• Low-Dimensional Topology
• +6 more

Prof. Harry Hyungryul Baik is a Tenured Associate Professor at KAIST's Department of Mathematical Sciences since 2017. He holds a PhD from Cornell University (2014) and a B.S. from KAIST (2009), advised by William Thurston, John Hubbard, and Dylan Thurston. His research focuses on geometric topology, geometric group theory, and low-dimensional topology, with notable contributions to mapping class groups, Kleinian groups, and Teichmüller theory. Education: PhD in Mathematics (Cornell, 2014), B.S. in Mathematics (KAIST, 2009). Key research areas include asymptotic translation lengths, laminar groups, and circular orders of groups. He co-leads the KAIST-KIAS joint research group 2K-GATE as Director, emphasizing collaboration between topologists. Research highlights: Characterization of Fuchsian groups via laminations, unsmoothability of mapping class group actions on 1-manifolds, and exponential torsion growth in random 3-manifolds. His work bridges topology with dynamical systems and geometric group theory, often involving collaborations with institutions like KIAS and MPIM. Awards include the Sangsan Prize (2018), Young-KAST membership (2020–2023), and multiple grants from Samsung and POSCO. He advises 7 PhD students and has mentored 15+ alumni, many of whom hold postdoc positions globally. His lab actively hosts conferences like the KAIST Geometric Topology Fair. Labs/Teams: Director of 2K-GATE (KAIST-KIAS), core member of the KAIST Topology Research Group, collaborator with international networks including the Harvard-MIT-Princeton topology axis.

Rohil PrasadView profile

Research Fellow

• Geometry
• Topology
• Dynamical Systems
• +6 more

Rohil Prasad is a Miller Research Fellow at the University of California, Berkeley, appointed in 2023, and will join Princeton University as an Assistant Professor in 2025. His research lies at the intersection of geometry, topology, and dynamical systems, with a particular focus on conservative dynamics, pseudoholomorphic curves, and Floer theory. Education: PhD in Mathematics, Princeton University (2018–2023), advised by Helmut Hofer Research Interests: Prasad’s work spans several deep areas of modern mathematics, including: Conservative Dynamics: Studying systems that preserve volume or symplectic structures. Symplectic Geometry: Exploring geometric structures preserved under Hamiltonian flows. Low-Dimensional Topology: Investigating the topology of 3- and 4-dimensional manifolds. Floer Theory: Using pseudoholomorphic curves to study periodic orbits and invariants. His research has led to significant advances in understanding periodic orbits, invariant measures, and the structure of area-preserving maps. Awards and Honors: 2024 Brin Dynamical Systems Prize for Young Mathematicians Contact: rrprasad@berkeley.edu | Office: 968 Evans Hall

Ciprian ManolescuView profile

Professor

• Geometry
• Topology
• Gauge Theory
• +4 more

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)

Marco CastronovoView profile

Assistant Professor

• Symplectic Topology
• Mirror Symmetry
• Cluster Algebras
• +3 more

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.

Igor KrizView profile

Professor

• Algebraic Topology
• Stable Homotopy Theory
• Equivariant Topology
• +5 more

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.

• Mathematics
• Machine Learning
• Quantum Topology
• +9 more

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.

Thomas LamView profile

Professor

• Algebraic Combinatorics
• Total Positivity
• Cluster Algebras
• +5 more

Thomas Lam is a professor of mathematics at the University of Michigan , specializing in algebraic combinatorics, total positivity, and connections to mathematical physics. His work bridges cluster algebras, positive geometry, and integrable systems, with applications to scattering amplitudes in quantum field theory. Lam has collaborated extensively with physicists such as Nima Arkani-Hamed and mathematicians like Pavlo Pylyavskyy and Mark Shimozono. Key research areas: Cluster algebras, total positivity, electrical networks, positroid varieties, and quantum cohomology. Notable contributions: Defining polypositroids, proving regularity theorems for totally nonnegative flag varieties, and establishing cluster structures in braid varieties. Recent work focuses on positive geometries , including the amplituhedron and moduli spaces of points on projective lines, with implications for particle physics. His articles often explore dual graded graphs, K-theoretic Schubert calculus, and the interplay between combinatorics and algebraic structures. Lam's research has been supported by NSF grants, including DMS-0748636 and DMS-1249708 .

Steven SivekView profile

Professor

• Pure Mathematics
• Topology
• Contact Geometry
• +4 more

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.

Markus LandView profile

Academic

• Algebraic Topology
• Homotopy Theory
• K-Theory
• +3 more

Markus Land is a Tenure Track Professor at the Department for Mathematics, Ludwig Maximilian University of Munich, affiliated with the Algebraic Geometry Working Group. His research bridges algebraic topology, homotopy theory, and K-theory, focusing on their interplay with L-theory and manifold topology. He has held postdoctoral positions at the University of Copenhagen (supported by an EU Marie Curie Fellowship and DFG Grant) and the University of Regensburg, and earned his PhD at the University of Bonn under Wolfgang Lück. Education : PhD in Mathematics (University of Bonn, 2016) Positions : Postdoctoral (University of Copenhagen, 2019–2022; University of Regensburg, 2016–2019) Research Interests : Markus Land explores algebraic topology and homotopy theory , particularly algebraic K-theory , hermitian K-theory , and their connections to L-theory and manifold topology . His work often applies infinity-categories to foundational problems in operator K-theory and geometric topology. Recent Publications : His research includes groundbreaking studies on chromatic localization in K-theory, Grothendieck-Witt groups in ring theory, and additivity in cobordism categories . Collaborations with leading mathematicians like Georg Tamme and Ulrich Bunke highlight interdisciplinary approaches to algebraic and geometric problems. Awards & Grants : EU Marie Curie Individual Fellowship (2020–2022) DFG Individual Research Grant (2019–2020) Teaching & Academic Leadership : He has designed advanced courses including Topology I–V , Algebraic K-Theory , and Condensed Mathematics , emphasizing homotopy theory and infinity-categories . Future initiatives include student seminars on arithmetic and algebraic geometry to foster academic collaboration. Working Group : As part of the Algebraic Geometry Working Group at LMU Munich, he contributes to seminars and research projects on arithmetic geometry , manifold classification , and spectral algebra .

• Algebraic Geometry
• Calabi-Yau Manifolds
• Derived Categories
• +4 more

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.

Maggie MillerView profile

Research Fellow

• Low-Dimensional Topology
• 3-Manifolds
• 4-Manifolds
• +7 more

Maggie Miller is a mathematician specializing in low-dimensional topology, currently serving as an NSF Postdoctoral Fellow at the Massachusetts Institute of Technology. She previously held a position at the University of Texas, Austin, and earned her Ph.D. in 2020 from Princeton University under the supervision of David Gabai. Education: Ph.D. in Mathematics (Princeton University, 2020) Her research focuses on 3- and 4-manifolds, leveraging algebraic, combinatorial, geometric, and topological techniques to solve long-standing problems. Key contributions include developing a theory of singular fibrations in 4-manifolds and resolving a 35-year-old problem by Casson and Gordon related to fibered ribbon knots. She actively collaborates on diverse topics such as topological versus smooth isotopy, taut foliations, concordance, trisections, and knot Floer homology. Maggie's work intersects multiple subfields within topology, including Knot Theory , Manifold Theory , and Differential Topology , with a strong emphasis on geometric structures and their applications. While her recent publications aren't listed here, her research trends center on topological invariants and their implications in mathematical physics. Scientific Awards: Clay Research Fellow

Frank CalegariView profile

Professor

• Algebraic Number Theory
• Langlands Programme
• Galois Representations
• +3 more

Frank Calegari is a Professor of Mathematics at the University of Chicago. His primary research interests include algebraic number theory, the Langlands program, Galois representations, and arithmetic geometry. He has made significant contributions to understanding reciprocity laws linking Galois representations to automorphic forms. His work often intersects with cohomology of arithmetic groups, motives, and the arithmetic of periods. Prof. Calegari has advised numerous PhD students, including Maria Stadnik, Shiva Chidambaram, and Eric Stubley. He serves on editorial boards for prestigious journals such as Algebra & Number Theory, Essential Number Theory, and the Annals of Mathematics. He actively participates in academic conferences and programs, including organizing the 2020 Arithmetic of the Langlands Program in Bonn. His research spans modularity theorems for abelian varieties, cohomology of arithmetic groups, and the study of L-functions. Key recent work includes resolving the unbounded denominators conjecture and advancing potential automorphy results over CM fields. Calegari frequently collaborates with leading mathematicians, including George Boxer, Vincent Pilloni, and Yilin Yang. He teaches advanced courses such as Honors Calculus (Math 16100) at the University of Chicago. His expository work includes lecture notes on motives and L-functions, as well as a blog compiling mathematical insights (Persiflage). Calegari’s contributions to number theory have been recognized through his editorial roles and invited lectures at institutions like the ICM and Clay Mathematics Institute.