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Ricky Ini Liu is an Associate Professor in the Department of Mathematics at the University of Washington. Previously, he held positions at North Carolina State University, the University of Michigan, and the University of Minnesota. He earned his Ph.D. in Mathematics from MIT in 2010 under Alexander Postnikov. His research focuses on algebraic combinatorics, particularly its intersections with algebraic geometry, combinatorial geometry, and representation theory. Key interests include Schubert polynomials, polytopes, Hopf algebras, and Kronecker coefficients. He has contributed to foundational work on birational rowmotion, Gelfand-Tsetlin polytopes, and Fomin-Kirillov algebras. Liu has taught a wide range of courses at UW, including special topics in dynamical algebraic combinatorics, combinatorial theory, and problem-solving. He has also been a key instructor at the Mathematical Olympiad Summer Program since 2007 and mentored undergraduates in research programs at the University of Minnesota, Duluth. His publications span high-impact journals like Selecta Mathematica and Journal of Combinatorial Theory , with recent work addressing topics such as determinantal formulas for Schubert polynomials and applications of flow polytopes to diagonal harmonics. Though no specific awards are listed, his extensive publication record and academic roles reflect significant contributions to combinatorial mathematics.

• Algebraic Combinatorics
• Algebraic Geometry
• Combinatorial Geometry
• +5 more

Mircea Mustata is a Professor in the Department of Mathematics at the University of Michigan. His research focuses on singularities of algebraic varieties and their role in higher-dimensional geometry, with significant work on invariants like log canonical thresholds, minimal log discrepancies, multiplier ideals, and Hodge ideals derived from Saito's mixed Hodge modules. He collaborates extensively, notably with Mihnea Popa on Hodge ideals and with other researchers on topics such as square-free polynomials and F-thresholds. Contact: 3064 East Hall, mmustata@umich.edu Education: Ph.D. from UC Berkeley (2001) Research Interests: Mustata's work bridges algebraic geometry and singularity theory, utilizing tools from resolutions of singularities, jet schemes, D-modules, and positive characteristic methods. His long-term collaboration with Popa explores Hodge ideals, while other projects address Du Bois complexes, stable rationality, and cohomological dimension. Teaching: Courses include Algebraic Geometry I/II, D-modules, commutative algebra, and advanced linear algebra. Lecture notes for topics like toric varieties, rationality, and cohomology are publicly available. Editorial & Organizational Roles: Managing editor of the Michigan Mathematical Journal and member of editorial boards for Compositio Mathematica, Journal de l'École polytechnique-Mathématiques, and Journal of Singularities. Organized events like the Spring School in Ann Arbor and conferences on algebraic geometry.

• Algebraic Geometry
• Singularities of Algebraic Varieties
• Hodge Theory
• +4 more

Jinhyung Park is an Associate Professor in the Department of Mathematical Sciences at KAIST, Daejeon, Korea. He obtained his Ph.D. from KAIST in 2014 under Prof. Sijong Kwak and was mentored as a CMC Fellow at KIAS (2014–2019). His research focuses on Algebraic Geometry , particularly syzygies of algebraic varieties , secant varieties , and positivity of line bundles . Education: Ph.D., KAIST (2014); MS/BS, KAIST and University of Chicago (2002/2001). Research Interests: His work explores geometric properties of projective manifolds, singularities in algebraic geometry, and applications of Okounkov bodies to divisors and syzygies. Recent trends include Castelnuovo-Mumford regularity bounds (e.g., for threefolds with rational singularities) and subadditivity of Okounkov bodies in fiber spaces. Teaching: Courses include Matrix Groups, Algebraic Geometry, and Calculus. He previously taught at Sogang University and Purdue University. Professional Affiliations: Member of the Korean Mathematical Society, American Mathematical Society, and other international societies. Organized the 8th East Asia Number Theory Conference at KAIST (2019).

• Algebraic Geometry
• Syzygies of Algebraic Varieties
• Secant Varieties
• +6 more

Aise Johan de Jong is a Professor in the Department of Mathematics at Columbia University, where he teaches courses including representations of finite groups and organizes the algebraic geometry seminar. He is a leading figure in algebraic geometry with a particular focus on stacks theory and arithmetic aspects of algebraic varieties. Institution: Columbia University, Department of Mathematics Research Focus: Algebraic stacks, arithmetic geometry, moduli spaces Major Project: The Stacks Project (open-source collaborative textbook) De Jong's research primarily centers on algebraic stacks, arithmetic geometry, and the foundations of algebraic geometry. His work bridges abstract theoretical frameworks with concrete computational aspects, particularly in positive characteristic. He has made significant contributions to understanding Brauer groups, period-index problems, and the geometry of moduli spaces. His research often connects number theory with geometric structures, exploring how arithmetic properties manifest in geometric settings. His publication record shows a consistent focus on fundamental structures in algebraic geometry, with particular emphasis on stacks theory (evident in The Stacks Project), Brauer groups, rational connectivity, and arithmetic properties of algebraic varieties. The trajectory of his work demonstrates increasing sophistication in handling complex geometric structures while maintaining connections to arithmetic questions. His most recent work continues to explore the interplay between algebraic geometry and number theory, particularly through the lens of stacks and moduli spaces. De Jong actively mentors graduate students, with numerous descendants listed in the Mathematics Genealogy Project. His academic lineage includes researchers working across various subfields of algebraic geometry. He has organized multiple conferences including "Moduli spaces and moduli stacks" (2012) and "Spaces of curves and their interaction with diophantine problems" (2009), demonstrating his leadership in the field. He leads The Stacks Project, a major collaborative open-source initiative that has become an essential reference for algebraic geometers worldwide. This project provides comprehensive foundations for algebraic stacks and related concepts, with regular updates and community contributions. De Jong also maintains the Stacks Project Blog where he discusses mathematical topics related to the project and shares updates.

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

Mihnea Popa is a Professor at Harvard University's Department of Mathematics. He is actively involved in research and teaching, focusing on Algebraic Geometry and related fields. His current teaching includes Algebraic Geometry (Math 137) in Spring 2025. Research Interests: Mihnea Popa's research spans several areas within Algebraic Geometry, including Birational Geometry, Hodge Theory, Singularities, Kodaira dimension, and D-modules. His work often explores the interplay between these topics, as evidenced by his lecture notes such as Singularities and Hodge Theory and Kodaira dimension of algebraic varieties . Editorial and Academic Contributions: He serves on the editorial boards of several prestigious journals, including Algebraic Geometry (2013-2019), Journal of Algebraic Geometry (2019-), and Selecta Mathematica (2020-). He has organized conferences and contributed to edited volumes, such as Hodge Ideals (co-authored with Mircea Mustață) and proceedings from the 2015 Salt Lake City Algebraic Geometry conference.

• Algebraic Geometry
• Birational Geometry
• Hodge Theory
• +3 more

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.

• Algebraic Geometry
• Symplectic Geometry
• Mathematical Physics
• +1 more

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.

• Algebraic Geometry
• Moduli Spaces
• Stability Conditions
• +4 more

David Savitt is a Professor and Chair of the Department of Mathematics at Johns Hopkins University, affiliated with the Krieger School of Arts & Sciences. His research focuses on algebraic number theory, with emphasis on Galois representations, modular forms, and p-adic Hodge theory. He holds a PhD from Harvard University and has served on the board of directors for Canada/USA Mathcamp, a summer program for high school students. His work spans theoretical contributions to arithmetic geometry, including studies on moduli stacks of Galois representations and geometric aspects of the p-adic Langlands program. Education: PhD in Mathematics from Harvard University. Research interests include the interplay between Galois representations and modular forms, p-adic Hodge theory, and moduli spaces. His recent work explores geometric structures in the Emerton-Gee stack and the Breuil-Mézard conjecture. Over 20 years of research has produced influential papers on topics like Serre weight conjectures and crystalline lifts of Galois representations. Professional contributions include editorial roles for journals and books, such as co-editing p-adic Geometry: Lectures from the 2007 Arizona Winter School . His involvement with Mathcamp highlights his dedication to nurturing young talent in mathematics.

• Algebraic Number Theory
• Galois Representations
• Modular Forms
• +3 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.

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

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.

• Symplectic topology
• Homological Mirror Symmetry
• Floer theory
• +4 more

Kristin Shaw is a Professor in the Department of Mathematics at the University of Oslo, specializing in Algebra, Geometry and Topology. She leads the research group on Algebraic and Topological Cycles in Tropical and Complex Geometries, funded by the BFS. Her office is located in room 1114 of Niels Henrik Abels hus, with contact information including email krisshaw@math.uio.no and phone +47 22855940. Shaw's research focuses on the connections between combinatorics and algebraic geometry over the real and complex numbers, with particular emphasis on tropical geometry. Her work bridges abstract mathematical theory with concrete geometric structures, exploring how combinatorial methods can illuminate deep properties of algebraic varieties. She has made significant contributions to understanding matroids, real algebraic curves, and the topology of hypersurfaces through tropical techniques. Her research demonstrates how combinatorial structures can reveal fundamental insights about algebraic varieties and their topological properties. Analysis of Professor Shaw's recent publications reveals a consistent focus on tropical geometry and its applications to classical algebraic geometry problems. Her work frequently examines the interplay between real and complex geometries, with particular attention to combinatorial structures underlying algebraic varieties. Key themes include matroid theory, enumerative geometry, and the topology of algebraic varieties, demonstrating how tropical methods can provide new insights into longstanding problems in algebraic geometry. Her research shows remarkable depth across multiple subfields while maintaining a coherent theoretical framework that connects combinatorial and geometric approaches. Professor Shaw leads the research group on Algebraic and Topological Cycles in Tropical and Complex Geometries, which is funded by the BFS. Prior to her position at the University of Oslo, she held postdoctoral positions at the Max Planck Institute Leipzig, the Technical University of Berlin, the University of Toronto, and participated in the Fields' Institute semester in Combinatorial Algebraic Geometry. Her collaborative work spans multiple international institutions, reflecting her active engagement in the global mathematical research community.

• Algebraic Geometry
• Tropical Geometry
• Combinatorics
• +3 more

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.

• Algebraic Geometry
• Commutative Algebra
• Birational Geometry
• +3 more

Yuri Tschinkel is a Professor of Mathematics at the Courant Institute of Mathematical Sciences, New York University, and Director of the Mathematics and Physical Sciences Division at the Simons Foundation since 2012. He previously held positions at the University of Goettingen, Princeton University, and the University of Illinois at Chicago. His research spans algebraic geometry, analytic number theory, and arithmetic geometry, focusing on rational points, birational geometry, and algebraic structures. Ph.D. in Mathematics, MIT (1992) His work addresses stable rationality of algebraic varieties, weak approximation over function fields, and distribution of rational points. Key contributions include studies on Mori cones, log Fano varieties, and quadric surface bundles. Recent publications reflect collaborations with leading mathematicians like Kontsevich and Hassett. Scientific accolades include 2018 Member of Leopoldina, German National Academy of Sciences 2014 Fellow of the American Association for the Advancement of Science 2012 Fellow of the American Mathematical Society As Director of the Simons Foundation division, he oversees grants and research initiatives in mathematics and physical sciences. He has authored 135 papers, edited 19 books, and serves on 8 editorial boards and advisory panels.

• Algebraic geometry
• Analytic number theory
• Arithmetic geometry

Chenyang Xu is a Professor at Princeton University's Department of Mathematics, specializing in Higher Dimensional Geometry with a focus on K-stability, Fano varieties, and moduli spaces. His research bridges algebraic geometry and complex geometry, contributing to foundational questions in birational geometry and geometric invariant theory. Position: Professor at Princeton University Research Interests: Algebraic Geometry, K-stability, Fano varieties, Moduli spaces, Birational Geometry He leads the Simons Collaboration on Moduli of Varieties, advancing understanding of geometric structures and their applications. Notable achievements include resolving key conjectures in K-stability and establishing foundational results on the birational geometry of Fano varieties. Recipient of the 2019 New Horizons in Mathematics Prize for his contributions to algebraic geometry. Active in academic service, he contributes to conferences and editorial roles, including co-editing volumes on higher-dimensional algebraic geometry.

• Algebraic Geometry
• Higher Dimensional Geometry
• K-stability
• +4 more

Sheldon Katz is a Professor of Mathematics at the University of Illinois at Urbana-Champaign (UIUC), with a joint appointment in the Department of Physics. He holds a Ph.D. in Mathematics from Princeton University (1980) and a B.S. from MIT (1976). Previously, he was a Regents Professor of Mathematics at Oklahoma State University before joining UIUC in 2001. Katz's research focuses on algebraic geometry and mathematical physics, particularly string theory and supersymmetric quantum field theories. His work bridges geometry and physics, exploring topics like Gromov-Witten theory, toric varieties, and F-theory. He co-authored the influential book Mirror Symmetry and Algebraic Geometry (1999), a cornerstone in the field. His recent research includes studies on BPS invariants, Calabi-Yau manifolds, and topological string theory. Key contributions include analyses of F-theory, mirror symmetry, and geometric dualities in string compactifications. He teaches advanced courses in algebraic geometry and mathematical physics at UIUC. While no explicit awards are listed, his extensive publication record and academic leadership reflect significant contributions to the field. Katz’s work continues to explore the interplay between algebraic geometry and fundamental physics.

• Algebraic Geometry
• Mathematical Physics
• String Theory
• +3 more