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Tom CoatesView profile

Professor

• Pure Mathematics
• Algebraic Geometry
• Mirror Symmetry
• +5 more

Tom Coates is a Professor of Pure Mathematics in the Department of Mathematics at Imperial College London's Faculty of Natural Sciences. He holds affiliations with the Artificial Intelligence Network, the CNRS-Imperial Abraham de Moivre UMI, and the Pure Mathematics research group. His office is located in the Huxley Building (662) on the South Kensington Campus, London SW7 2AZ, and he can be contacted via email at t.coates@imperial.ac.uk or phone at +44 (0)207 594 3607. Professor Coates' research spans pure mathematics with emphasis on algebraic geometry, mirror symmetry, and Gromov-Witten theory. He investigates quantum cohomology and Fano variety classification to construct a 'Periodic Table for shapes' through computational algebra, data mining, and machine learning. His work integrates geometric methods with cluster-scale computing to identify structural patterns in algebraic varieties, focusing on quantum periods, toric degenerations, and Laurent polynomial applications. His recent publications (2021-2024) demonstrate a strong trend toward computational classification of Fano varieties and polytopes, leveraging machine learning for dimension prediction and database construction. Key themes include mirror symmetry via Laurent inversion, toric geometry applications, and connections between Gromov-Witten invariants and modular forms. These works often utilize custom tools like PCAS and Fanosearch for large-scale algebraic computations. While specific student names are not listed, Professor Coates mentors PhD and Master's students in algebraic geometry and computational mathematics. His research is supported by the Simons Foundation, member institutions, and contributors, enabling international collaborations through networks like the CNRS-Imperial Abraham de Moivre UMI. He leads a research team developing the Periodic Table for shapes framework, utilizing high-performance computing resources. The team maintains open-source tools including PCAS (Periodic Table for Algebraic Shapes) and Fanosearch for Fano variety exploration, with code repositories hosted on Bitbucket and quantum period databases published in Scientific Data.

Matteo PeneginiView profile

Associate Professor

• Algebraic Geometry
• Complex Geometry
• Birational Geometry
• +3 more

Matteo Penegini serves as an Associate Professor in the Department of Mathematics at the University of Genoa, where he holds a seat on the Department Board. His teaching portfolio spans multiple degree programs including Economic and Financial Sciences, Biomedical Engineering, and Mathematical Statistics, with courses such as General Mathematics, Geometry, and Linear Algebra and Analytic Geometry. His research centers on advanced Algebraic Geometry, specializing in the classification and structural analysis of algebraic surfaces and threefolds. Key investigations include triple covers of K3 surfaces, surfaces with pg=q=2 invariants, and projective varieties of general type. His work integrates cohomological methods, birational transformations, and moduli space theory to explore geometric genus constraints and Albanese map properties. Recent publications reveal a consistent focus on geometric invariants and covering spaces, with collaborative studies examining K3 surface covers (2022), surface families with specific Chern numbers (2021), threefold classification (2021), cohomology of irregular surfaces (2020), and Zariski multiplets from isogenous surfaces (2020). This trajectory demonstrates deepening engagement with Hodge theory and moduli problems in complex algebraic geometry.

Joe WaldronView profile

Assistant Professor

• Algebraic Geometry
• Birational Classification
• Positive Characteristic
• +3 more

Joe Waldron is an Assistant Professor in the Department of Mathematics at Michigan State University (MSU), located in C335 Wells Hall. His research focuses on algebraic geometry, particularly the birational classification of algebraic varieties in positive and mixed characteristic, with connections to commutative algebra and arithmetic geometry. He holds a PhD from the University of Cambridge under Caucher Birkar, followed by postdoctoral positions at Princeton University and the École Polytechnique Fédérale de Lausanne (EPFL). His work is supported by NSF Grant #2401279 and a Simons Foundation Gift #850684. Waldron is actively involved in academic outreach, co-organizing the First-Generation/Low-Income (FGLI) mentorship program in MSU's mathematics department. This initiative connects FGLI students with faculty and graduate student mentors to support their academic and career goals. He also contributes to the Michigan algebraic geometry symposium and the MSU algebra seminar. His research interests include advanced topics such as Mori fibre spaces, test ideals in mixed characteristic, and the log minimal model program (LMMP) for threefolds. He has published extensively on geometrically non-reduced varieties, singularities in positive characteristics, and purely inseparable Galois theory. Waldron’s grants fund explorations into foundational algebraic geometry problems, emphasizing cross-disciplinary connections with commutative algebra. His involvement in departmental initiatives reflects his commitment to fostering inclusive academic environments and mentoring underserved student populations.

Jonathan M. RosenbergView profile

Professor

• K-theory
• Noncommutative Geometry
• C*-algebras
• +7 more

Jonathan M. Rosenberg is a Professor of Mathematics at the University of Maryland, where he holds the Ruth M. Davis Professorship. His career spans several decades with significant contributions across multiple mathematical disciplines. He maintains active involvement in departmental activities including the Geometry/Topology Seminar, Algebra/Number Theory Seminars, Departmental Colloquium, and Geometry and Physics RIT. Rosenberg's research focuses on the deep connections between topology, geometry, and mathematical physics. His primary interests include K-theory, noncommutative geometry, C*-algebras, index theory of elliptic operators, and positive scalar curvature problems. His work bridges pure mathematics with theoretical physics, particularly in string theory applications. His research has evolved to address increasingly sophisticated questions in manifold theory, pseudomanifolds, and their connections to physical theories. His recent publications show a continued focus on positive scalar curvature problems across various geometric settings including spin c manifolds, pseudomanifolds, and manifolds with boundary. Rosenberg also maintains active collaborations with leading mathematicians like Boris Botvinnik, Varghese Mathai, and others, producing work that connects topology with mathematical physics through T-duality and related concepts. His publications span prestigious journals including Journal of Geometry and Physics, Communications in Mathematical Physics, and Advances in Theoretical and Mathematical Physics. Fellow of the American Mathematical Society Ruth M. Davis Professorship at University of Maryland Co-editor of influential volumes including "Novikov Conjectures, Index Theorems and Rigidity" Author of the graduate textbook "Algebraic K-Theory and its Applications" Principal speaker at multiple NSF/CBMS Regional Conferences Rosenberg serves on editorial boards of several prominent journals including Annals of K-Theory (as Managing Editor Emeritus), Journal of Topology and Analysis (as Managing Editor), Homology Homotopy and Applications, SIGMA, and The New York Journal of Mathematics. He previously served as Secretary of the K-Theory Foundation from 2010 to 2021. His teaching responsibilities span undergraduate courses including Calculus and Differential Equations to advanced graduate courses in K-theory, Homotopy Theory, and Noncommutative Geometry. He has maintained the Novikov Conjecture home page and the UMCP Math Department electronic journals web page as significant service contributions to the mathematical community.

Anne PICHONView profile

Professor

• Algebraic Geometry
• Topology
• Low-Dimensional Topology
• +3 more

Prof. Anne PICHON is a Professor at the University of Aix-Marseille and a member of the Institut de Mathématiques de Marseille (I2M). She holds leadership positions, including membership in the CoNRS (National Committee of CNRS) section 41 since 2021 and directorship of the FRUMAM (Research Federation of Mathematics Units of Marseille) from 2018 to 2022. Her research focuses on topology and geometry of singular spaces, algebraic geometry, and low-dimensional topology. She coordinates the ANR project LISA (2017–2022) and serves as an associate editor for the Journal of Singularities . Her work explores Lipschitz geometry, metric properties of singularities, and their classification. She actively participates in seminars like the Marseille Geometry and Topology Seminar and the Rauzy Seminar. PICHON’s contributions bridge geometric analysis with algebraic structures, emphasizing both theoretical and applied aspects of singularity theory. Research Interests Topology and geometry of singular spaces and morphisms Algebraic geometry, particularly singularities of complex spaces Lipschitz geometry of singularities and metric invariants Low-dimensional topology and fiber structures Key Activities ANR Project LISA Coordinator (2017–2022) Member of GDR Singularities and Applications Editorial Board, Journal of Singularities Leadership roles in FRUMAM and CoNRS Labs/Teams She contributes to the Institut de Mathématiques de Marseille (I2M) and collaborates within the FRUMAM federation, fostering interdisciplinary research in geometry and topology.

Louis EsserView profile

Lecturer

• Algebraic Geometry
• Equivariant Birational Geometry
• Optimization in Algebraic Geometry

Louis Esser is an instructor in mathematics at Princeton University. He received his PhD from UCLA in 2023 under the supervision of Burt Totaro. Esser co-organizes the Princeton Algebraic Geometry Seminar and the Princeton Algebraic Geometry Preprint Seminar. His research focuses on algebraic geometry, specifically equivariant birational geometry and optimization problems. Esser teaches undergraduate mathematics courses including Algebra I (MAT345), Honors Linear Algebra (MAT217), Multivariable Calculus (MAT201), and Linear Algebra with Applications (MAT202). His publications primarily explore birational geometry, Fano varieties, hypersurfaces, automorphism groups, and singularities. Recent work shows strong emphasis on classification problems in algebraic geometry, minimal model program applications, and geometric structures with group symmetries. Collaborative projects frequently involve topics at the intersection of algebraic geometry, topology, and invariant theory.

Georg HeinView profile

Professor

• Algebraic Geometry
• Vector Bundles
• Moduli Spaces
• +2 more

Prof. Dr. Georg Hein is a Professor in the Department of Mathematics at the University of Duisburg-Essen, Campus Essen. His office is located at WSC-O-3.58, Thea-Leymann-Str. 9, 45117 Essen, with office hours held every Tuesday from 2-3 PM and by appointment. He serves as Director of the Research Group Hein, focusing on Algebraic Geometry. His research centers on Algebraic Geometry with specific expertise in vector bundles, moduli spaces, elliptic surfaces, and sheaf theory. Hein's work demonstrates deep engagement with stability conditions, Fourier-Mukai transforms, and geometric invariant theory. His publications reveal a consistent focus on foundational structures in algebraic geometry, particularly through the lens of vector bundles on curves and surfaces. Analysis of his 15 most recent publications (2017-2007) shows a strong thematic continuity in moduli space theory and vector bundle classification. His work bridges abstract algebraic constructions with computational approaches, as evidenced by algorithmic developments for elliptic surfaces and lattice-theoretic investigations. The publications collectively emphasize stability criteria across diverse geometric contexts. Hein actively supervises PhD students including Asbjørn Michelsen, with former advisees Quyet Thang Truong and Dr. Dario Weißmann. He contributes to academic outreach through the Essen Math Circle for students, organizing weekly sessions for grades 5-13 covering advanced mathematical topics beyond standard curricula. His teaching portfolio includes courses such as Mathematische Miniaturen and Topologie .

• Algebraic Geometry
• Algebra
• Transformation Groups
• +3 more

Ivan Vladimirovich Arzhantsev serves as Dean of the Faculty of Computer Science and Professor at the Department of Big Data and Information Retrieval at the National Research University Higher School of Economics (HSE University). He also heads the Research Laboratory of Algebraic Transformation Groups and is a member of the Academic Council of HSE University. Having joined HSE in 2011, he has over 20 years of scientific and teaching experience in mathematics and computer science. Dean: Faculty of Computer Science Professor: Faculty of Computer Science / Department of Big Data and Information Retrieval Leading Researcher, Head of Laboratory: Faculty of Computer Science / Research Laboratory of Algebraic Transformation Groups Member of the Academic Council of the National Research University Higher School of Economics Arzhantsev's educational background includes a Specialist degree in Mathematics and Applied Mathematics from Moscow State University (1995), a Candidate of Physical and Mathematical Sciences degree (1998), and a Doctor of Physical and Mathematical Sciences degree (2011), all from Moscow State University. He was awarded the academic title of Associate Professor in 2009 and Professor in 2020. His research focuses on Algebraic Geometry, Transformation Groups, Algebraic Groups, and Geometric Invariant Theory. Arzhantsev's work explores homogeneous spaces, flexible varieties, infinite transitivity, locally nilpotent derivations, and algebraic monoids. His research has significant implications for understanding the structure and classification of algebraic varieties and their automorphism groups. He has developed important connections between algebraic geometry and combinatorial methods, particularly in the context of toric varieties and group actions. His work on the pigeonhole principle demonstrates applications to geometric problems, bridging discrete mathematics with algebraic geometry. Arzhantsev's recent publications demonstrate a consistent focus on affine varieties, transformation groups, and geometric structures. His work shows a progression from foundational studies of homogeneous spaces to more complex structures involving flexible varieties and infinite transitivity. The research spans both theoretical developments and practical applications in algebraic geometry, with several papers exploring connections between different mathematical structures through group actions. Medal 'Recognition - 10 years of successful work' of HSE University (July 2025) Honorary Certificate of the Ministry of Science and Higher Education of the Russian Federation (December 2024) Honorary Certificate of HSE University (March 2024) Letter of Gratitude from the Rector of HSE University (February 2023) Best Teacher - 2019, 2015 Laureate of the All-Russian Prize 'Dean of the Year' in Physical and Mathematical Sciences (2024) Arzhantsev has supervised numerous PhD students, including Y. I. Zaitseva, I. S. Beldiev, and K. V. Shakhmatov, among others. He leads multiple research grants, including the Russian Science Foundation grant 'Demazure Roots and Root Subgroups' (2025-2027) and the Russian-Indian grant 'Study of Affine Spaces and Related Objects Using Algebraic Transformation Groups and Locally Nilpotent Derivations' (2022-2024). His research has been supported by various prestigious funding sources including the Russian Foundation for Basic Research and the 'Basis' Foundation. He directs the Research Laboratory of Algebraic Transformation Groups at HSE University, which organizes the annual 'Algebraic Groups: White Nights Season' conference in St. Petersburg. The laboratory focuses on advanced research in algebraic transformation groups, homogeneous spaces, and related geometric structures, fostering international collaboration and training the next generation of mathematicians.

Emanuele MacrìView profile

Professor

• Algebraic Geometry
• Derived Categories
• Moduli Spaces
• +3 more

Emanuele Macrì is a Professor at the Laboratoire de mathématiques d'Orsay, Université Paris-Saclay, specializing in algebraic geometry with a focus on derived categories, stability conditions, and moduli spaces. He holds editorial roles at Mathematische Zeitschrift, International Mathematics Research Notices, and Selecta Mathematica. His research explores hyperkähler manifolds, Fano varieties, and wall-crossing phenomena, contributing to foundational advancements in geometric stability theory. Education & Positions Current roles include: Professor, Université Paris-Saclay (since 2024) Member of the Orsay Mathematics Laboratory (LMO) Research Interests Key areas of study encompass: Derived categories of coherent sheaves and their stability conditions Moduli spaces of sheaves on K3 surfaces and hyperkähler varieties Applications of wall-crossing techniques to classical algebraic geometry problems Geometry of Fano varieties and hyperkähler manifolds Publications & Trends Recent work emphasizes: Advances in understanding hyperkähler manifolds via stability conditions (e.g., Mukai models of Fano varieties ) Classification of hyperkähler fourfolds using Riemann-Roch polynomials Investigations into antisymplectic involutions and their geometric implications Development of stability frameworks for Kuznetsov components in derived categories Awards & Recognition Plenary speaker at the 2025 Summer Research Institute in Algebraic Geometry Member of the Accademia dei Lincei (2024) Medaglia dei XL per la matematica (2023) Invited speaker at the International Congress of Mathematicians 2022 Advising & Grants Macrì has advised numerous PhD students and postdocs, including: Current students: Matteo Verni, Vanja Zuliani Notable past students: Luigi Martinelli, Benjamin Schmidt He leads the ERC Synergy Grant HyperK (2020–2026), exploring hyperkähler manifolds and related geometries. Labs & Collaborations Active in organizing workshops and seminars, including: HyperK workshop series (2020–2025) Reading seminars on hyperkähler geometry and moduli spaces Working groups on P=W conjecture and D-modules

Sofia TirabassiView profile

Professor

• Algebraic Geometry
• Derived Categories
• Birational Geometry
• +4 more

Dr. Sofia Tirabassi is a Full Professor in the Department of Mathematics at Stockholm University, where she has been affiliated since 2019. She leads the research group 'Algebra, Geometry, Topology, and Combinatorics' and directs projects funded by the Knut and Alice Wallenberg Foundation and the Swedish Research Council (VR). Her work bridges algebraic geometry, derived categories, and arithmetic geometry, with emphasis on positive characteristic and birational classification. She holds a Ph.D. from Università degli Studi Roma Tre (2012), an M.Sc. and B.Sc. from the University of Bologna. Previously, she held positions at the University of Bergen, University of Utah, and University of Warsaw as a Marie Curie Fellow. Her research explores two primary areas: (1) Derived categories in positive characteristic , investigating invariants of algebraic varieties, and (2) Birational characterization of semiabelian varieties , developing tools for effective classification. Her publications frequently address geometric structures like abelian surfaces, Enriques surfaces, and cohomological properties. Tirabassi's recent articles (2020-2024) demonstrate a focus on surfaces in positive characteristic, derived equivalences, and quasi-abelian varieties. Common themes include Fourier-Mukai transforms, Brauer groups, and log-canonical thresholds, reflecting interdisciplinary engagement with combinatorics and topology. Awards & Fellowships: Marie Curie Fellowship (European Commission) International Postdoctoral Scholarship (Knut and Alice Wallenberg Foundation) Young Research Talents Grant (Research Council of Norway) Grants & Projects: She currently leads 'Generic Vanishing and Characterization of Semiabelian Varieties' (VR-funded) and hosts a guest professorship for Rita Pardini. Past projects include 'Derived Categories in Positive Characteristic' (KAW Foundation) and 'The Arithmetic of Derived Categories' (Norway). Teaching: In 2024/2025, she instructs courses in Galois Theory, Combinatorics, Abstract Algebra, and Topology, and is developing a master's course in Algebraic Geometry.

Jesus Martinez-GarciaView profile

Senior Lecturer

• Algebraic Geometry
• Complex Geometry
• Birational Geometry
• +3 more

Dr Jesus Martinez-Garcia is a Senior Lecturer in the Department of Mathematical Sciences at the University of Essex, within the School of Mathematics, Statistics and Actuarial Science (SMSAS). His research focuses on algebraic and complex geometry, particularly birational geometry of Fano varieties, K-stability, moduli spaces, and computational algebraic geometry. He has held postdoctoral positions at the University of Bath, Max Planck Institute for Mathematics in Bonn, and Johns Hopkins University, and briefly served as an Adjunct Professor at Korea University. Dr Martinez-Garcia holds a PhD in Mathematics from the University of Edinburgh (2013), an MASt in Mathematics from the University of Cambridge (2009), and dual degrees from Universidad Autónoma de Madrid: MEng in Computer Engineering (2008) and MSci in Mathematics (2008). His research interests include Kähler-Einstein metrics, classification of Fano varieties, geometric invariant theory (GIT), and computational methods in algebraic geometry. He has contributed to foundational work on K-moduli spaces, asymptotic log Fano varieties, and moduli compactifications. Dr Martinez-Garcia’s publications span theoretical advancements and computational tools, including the Variations of GIT quotients package. His work bridges algebraic geometry with differential geometry, emphasizing connections between stability conditions and geometric structures. Grants and funding details are listed on his profile, though specific grants are not detailed here. He actively advises students in his field and contributes to teaching at Essex, with academic support hours coordinated via Moodle. He is affiliated with STEM 5.9 on the Colchester Campus and can be reached via email at jesus.martinez-garcia@essex.ac.uk .

Maria Chiara BrambillaView profile

Associate Professor

• Algebraic Geometry
• Commutative Algebra
• Moduli Spaces
• +3 more

Maria Chiara Brambilla is an Associate Professor in the Department of Industrial Engineering and Mathematical Sciences (DIISM) at Università Politecnica delle Marche, Faculty of Engineering. Her research specializes in algebraic geometry, with emphasis on moduli spaces, vector bundles, and secant varieties. She investigates fundamental structures in birational geometry and interpolation theory, contributing to advancements in the classification of geometric objects and their deformations. Research Focus: Her work explores: Birational properties of Mori dream spaces and blowups Defectivity and non-defectivity in Segre-Veronese varieties Terracini loci and their minimality conditions Geometric invariants of flag manifolds and hypersurfaces Algebraic boundaries in tensor rank theory Publication Trends: Recent articles (2021-2025) demonstrate deepening work on Terracini loci, twistor geometry, and movable divisors, frequently employing combinatorial and deformation-theoretic methods to resolve problems in higher-dimensional algebraic geometry.

• Algebraic Geometry
• Birational Geometry
• Calabi-Yau Manifolds
• +5 more

Prof. Dr. Isabel Stenger is an Assistant Professor at the Institute of Algebraic Geometry, Faculty of Mathematics and Physics, Leibniz University Hannover. She holds a Junior Professorship and is a member of the Riemann Center for Geometry and Physics. Her research focuses on advanced topics in algebraic geometry, including birational geometry, Calabi-Yau manifolds, and the Morrison-Kawamata cone conjecture. She also explores experimental methods in algebraic geometry and commutative algebra, construction and moduli of surfaces, and syzygy-related constructions of algebraic varieties. Her work integrates theoretical and computational approaches to address foundational questions in geometry. Recent publications (2020–2024) reflect her contributions to understanding Godeaux surfaces, Calabi-Yau 3-folds, and divisor cones in algebraic varieties. She maintains an active research agenda with a focus on geometric structures and their numerical properties. Stenger’s academic profile includes affiliations with the Institute of Algebraic Geometry and Riemann Center, where she collaborates on interdisciplinary projects at the intersection of geometry and physics. Her contact details are available on her homepage .

Marco AndreattaView profile

Professor

• Algebraic Geometry
• Projective Geometry
• Minimal Model Theory
• +5 more

Marco Andreatta is a Full Professor of Geometry at the University of Trento's Department of Mathematics, Faculty of Science. He earned his Ph.D. in Mathematics from the University of Trento in 1981 with highest honors. His academic career includes positions as Researcher (1983-1987), Associate Professor (1987-2000), and Full Professor (since 2000). He has held visiting professorships globally, including at the University of Notre Dame, Max-Planck Institute, and MSRI Berkeley. Research Interests: Andreatta specializes in algebraic geometry, focusing on classification of projective varieties, minimal models, Mori theory, and adjunction theory. His work extends to complex differential geometry, topology, and the philosophy of space. Since the 2000s, he has actively researched science communication, exploring mathematics' societal role through books and public engagement. Publications & Research: His 60+ publications emphasize birational geometry and higher-dimensional varieties. Recent works analyze Fano varieties, geometric contractions, and historical/theoretical intersections in mathematics. He frequently contributes to interdisciplinary topics linking geometry with art, history, and education. Awards & Leadership: Corresponding Member, Accademia delle Scienze di Torino (2014) Ordinary Member, Accademia Roveretana degli Agiati (2014) Finalist, Premio Nazionale di Divulgazione Scientifica (2022) Andreatta directs the Centro Internazionale di Ricerche Matematiche (CIRM) and has led the Department of Mathematics (2018-2021), the Faculty of Science (2004-2008), and the Trento Science Museum. He coordinates national research projects (PRIN) and advises doctoral students. Outreach: He authors popular science books (e.g., La Forma delle Cose , Archimede, l’arte della misura ) and lectures at festivals globally on mathematics' cultural and practical impact.

Gavin BrownView profile

Professor

• Algebraic Geometry
• Computer-Assisted Mathematics
• Birational Classification
• +1 more

Gavin Brown is Professor of Mathematics at the University of Warwick's Mathematics Institute. His research focuses on birational classification in algebraic geometry using computer-assisted constructions and databases. He investigates complex geometric structures including Fano varieties and Calabi-Yau manifolds through both theoretical frameworks and computational approaches. Research interests center on developing mathematical models for noncommutative functions, deformation theory of algebraic curves, and singularity classifications. This work bridges pure mathematics with computational applications to solve geometric classification problems. Recent publications demonstrate consistent themes in computational algebraic geometry, particularly in developing databases for geometric structures and advancing theoretical understanding of deformation spaces. The research integrates computational methods with deep geometric insights.