Tony Yue YU

Professor of Mathematics, California Institute of Technology

E-mail: Due to the high volume of incoming emails, I may occasionally forget to reply. Please do not hesitate to send me a reminder if it is something important. email

Research

I work on algebraic geometry, including problems in enumerative geometry, mirror symmetry, birational geometry, non-archimedean geometry, tropical geometry and derived geometry. I am also advising student projects related to AI and mathematics.

I was awarded the Clay Research Fellowship in 2016, an ERC starting grant in 2020, and multiple NSF grants.

For students interested in undergraudate research projects, and prospective graduate students, please send me an email with your CV and research interests.

Papers:

Unfolding of equivariant F-bundles and application to the mirror symmetry of flag varieties, joint with T. Hinault, C. Li, C. Zhang, S. Zhang, (arXiv:2505.09950), 2025.
Log Calabi-Yau mirror symmetry and non-archimedean disks, joint with S. Keel, (arXiv:2411.04067), 2024.
Decomposition and framing of F-bundles and applications to quantum cohomology, joint with T. Hinault, C. Zhang, S. Zhang, (arXiv:2411.02266), 2024.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus, joint with S. Keel, Annals of Mathematics, (2), 198(2):419–536, 2023.
Topological Laplace Transform and Decomposition of nc-Hodge Structures, joint with S. Zhang, (arXiv:2405.19549), 2024.
Gromov-Witten invariants with naive tangency conditions, joint with F. Janda, (arXiv:2310.13059), 2023.
Non-archimedean quantum K-invariants, joint with M. Porta, (arXiv:2001.05515), Annales scientifiques de l'École normale supérieure,(4), 57(3):713–786, 2024..
Non-archimedean Gromov-Witten invariants, joint with M. Porta, (arXiv:2209.13176), 2022.
Secondary fan, theta functions and moduli of Calabi-Yau pairs, joint with P. Hacking and S. Keel, (arXiv:2008.02299), 2020.
Representability theorem in derived analytic geometry, joint with M. Porta, Journal of the European Mathematical Society (JEMS), 22(12):3867–3951, 2020.
The non-archimedean SYZ fibration, joint with J. Nicaise and Chenyang Xu, Compositio Mathematica, 155(5):953–972, 2019.
Derived Hom spaces in rigid analytic geometry, joint with M. Porta, (arXiv:1801.07730), To appear in Publications of the Research Institute for Mathematical Sciences, Special issue dedicated to Professor Masaki Kashiwara on his seventieth birthday, 2018.
Enumeration of holomorphic cylinders in log Calabi-Yau surfaces. II. Positivity, integrality and the gluing formula, (arXiv:1608.07651), To appear in Geometry & Topology.
Derived non-archimedean analytic spaces, joint with M. Porta, Selecta Mathematica, 24(2):609–665, 2018.
Enumeration of holomorphic cylinders in log Calabi-Yau surfaces. I, Mathematische Annalen, 366(3):1649-1675, 2016.
Higher analytic stacks and GAGA theorems, joint with M. Porta, Advances in Mathematics, 302:351–409, 2016.
Tropicalization of the moduli space of stable maps, Mathematische Zeitschrift, 281(3):1035–1059, 2015.
Gromov compactness in non-archimedean analytic geometry, Journal für die reine und angewandte Mathematik (Crelle), 741:179–210, 2018.
The number of vertices of a tropical curve is bounded by its area, L’Enseignement Mathématique, 60(3-4):257–271, 2014.
Balancing conditions in global tropical geometry, Annales de l'Institut Fourier, 65(4):1647–1667, 2015.

Invited Talks

2021.11 Interdisciplinary applications of cluster algebras, Isaac Newton Institute for Mathematical Sciences, University of Cambridge, United Kingdom
2021.02 Utah Algebraic Geometry Seminar, online, University of Utah, Salt Lake City, UT, USA
2021.01 Homological Mirror Symmetry and Applications, online, University of Miami, USA
2020.11 Algebraic Geometry Seminar, online, Cornell University, Ithaca, NY, USA
2020.11 Séminaire d’Algèbre et Géométrie, Laboratoire de Mathématiques de Versailles, Université Versailles Saint-Quentin-en-Yvelines, Versailles, France
2020.10 M-Seminar, online, Kansas State University, Manhattan, KS, USA
2020.10 Enumerative geometry seminar, Institut de mathématiques de Jussieu -- Paris Rive Gauche, Paris-Sorbonne University, Paris, France
2020.10 Algebra and Algebraic Geometry seminar, online, University of British Columbia, Vancouver, Canada
2020.10 Geometric representation theory seminar, online, University of Toronto, Ontario, Canada
2020.09 Séminaire Arithmétique et Géométrie Algébrique, Université Paris-Sud, Orsay, France
2020.08 Novosibirsk summer school, Joint IMSA & ICMS & HSE Event, notes
2020.08 Cluster algebra 2020, online conference, notes
2020.07 Online mini-course at IHES, notes: lecture 1, lecture 2, lecture 3, lecture 4, videos playlist
2020.07 Rencontre de lancement du projet ANR CHARMS, online conference
2020.07 BPS states, mirror symmetry, and exact WKB, University of Sheffield, United Kingdom
2020.06 Non-archimedean geometry techniques in mirror symmetry, University of Copenhagen, Denmark
2020.03 New Perspectives on SYZ Mirror Symmetry, Imperial College, London, United Kingdom
2020.03 Non-archimedean geometry and related fields, Kyoto University, Japan
2019.09 Regensburg days on non-archimedean and tropical geometry, Universität Regensburg, Germany
2019.06 Mirror Symmetry and Cluster Algebras, Cambridge University, United Kingdom
2019.06 Mini-course, Summer school: New Perspectives in Gromov-Witten Theory, Institut de mathématiques de Jussieu - Paris Rive Gauche, France
2018.11 Algebraic geometry and number theory seminar, Institute of Science and Technology Austria, Klosterneuburg, Austria
2018.10 Cohomology of Algebraic Varieties, Centre International de Rencontres Mathématiques - Luminy, Marseille, France
2018.10 Conference CATS5: categories and stacks in algebraic geometry and algebraic topology, Museum of Natural History and Science, Lisbon, Portugal
2018.09 Lecture series, Mini school/workshop on p-adic and motivic integration, University of Geneva, Switzerland
2018.06 Séminaire de Géométrie Tropicale, Institut Mathématiques de Jussieu, Université Pierre et Marie Curie, Paris, France
2018.05 Workshop on degenerations of Calabi-Yau manifolds, Institut Henri Poincaré, Paris, France
2018.04 Sino-French conference in Algebraic and Complex Geometry, Institut Camille Jordan, Université Claude Bernard Lyon 1, Lyon, France
2018.03 Moduli spaces of curves and mirror symmetry, Institut Mittag-Leffler, Sweden
2018.02 Mathematics - String Theory seminar, Kavli Institute for the Physics and Mathematics of the Universe, Kashiwa, Japan
2018.02 The 3rd KTGU Mathematics Workshop for Young Researchers, Kyoto University, Kyoto, Japan
2018.01 Séminaire de géométrie, Université Savoie Mont Blanc, Chambéry, France
2017.12 The first annual meeting of International Consortium of Chinese Mathematicians, Sun Yat-Sen University, Guangzhou, China
2017.12 Conference: Mirror symmetry and applications, Higher School of Economics, Steklov Mathematical Institute, Moscow, Russia
2017.11 Séminaire de Géométrie Tropicale, Université Pierre et Marie Curie, Paris, France
2017.07 String-Math conference, Universität Hamburg, Germany
2017.07 Hausdorff Kolloquium, Hausdorff Center for Mathematics, Universität Bonn, Germany
2017.06 Non-Archimedean geometry, motives and vanishing cycles, Institut Mittag-Leffler, Sweden
2017.06 Algebraic Analysis in honor of Masaki Kashiwara’s 70th birthday, Institut des Hautes Études Scientifiques, France
2017.05 Simons Symposium on Non-Archimedean and Tropical Geometry, Krün, Germany
2017.05 Biannual Algebraic and Tropical Meetings of Brown and Yale, Brown University, USA
2017.03 The Mathematics Colloquium, Rutgers University, USA
2017.03 Homological mirror symmetry: emerging developments and applications, Institute for Advanced Study, Princeton, USA
2017.03 Brandeis-Harvard-MIT-Northeastern Colloquium, Harvard University, USA
2017.03 Geometric Representation Theory Seminar, Massachusetts Institute of Technology, USA
2017.02 Mini-course, Special program on Homological Mirror Symmetry, Institute for Advanced Study, Princeton, USA
2017.02 Member's Seminar, Institute for Advanced Study, Princeton, USA
2016.11 Séminaire Arithmétique et Géométrie Algébrique, Université Paris-Sud, Orsay, France
2016.11 Seminar Algebraic Geometry, Max Planck Institute for Mathematics, Bonn, Germany
2016.10 Lecture series, Berkovich spaces and degenerations of Calabi-Yau varieties, Mathematical Research Institute of Oberwolfach, Germany
2016.08 The 7th International Congress of Chinese Mathematicians, Beijing, China
2016.07 Regensburg days on non-archimedean geometry, Universität Regensburg, Germany
2016.06 Calabi-Yau varieties: Arithmetic, geometry and physics, Herstmonceux Castle, Queen's University, East Sussex, UK
2016.06 The London Geometry and Topology Seminar, Imperial College London, UK
2016.03 Tropical Geometry and Related Topics, Kyoto University, Japan
2016.03 Mathematics and string theory seminar, Kavli Institute for the Physics and Mathematics of the Universe, Tokyo, Japan
2016.03 Séminaire de topologie, Institut Fourier, Université Joseph Fourier, Grenoble, France
2016.03 Séminaire de Géométrie Algébrique, Institut Montpelliérain Alexander Grothendieck, Université de Montpellier, France
2016.03 Séminaire de Mathématique Physique, Institut de mathématiques de Bourgogne, Université de Bourgogne, Dijon, France
2016.02 Winter School on Tropical Geometry, Berkovich Spaces and Mirror Symmetry, KIAS, Seoul, South Korea
2016.02 Séminaire de Géométrie et Singularités, Université de Rennes 1, Rennes, France
2016.02 Séminaire de Théorie des Nombres, Université de Caen Normandie, France
2016.01 Lecture series, University of Texas at Austin, Texas, USA
2016.01 Séminaire de géométrie algébrique, champs et homotopie, Université Toulouse III, France
2016.01 Séminaire de géométrie algébrique, Université d’Angers, France
2015.12 Non-Archimedean Geometry and Applications, Oberwolfach, Germany
2015.11 Algebraic Geometry and Complex Geometry, CIRM Luminy, Marseille, France
2015.11 Séminaire Géométrie, Dynamique et Topologie, Aix-Marseille Université, France
2015.11 Séminaire d'algèbre, topologie et géométrie, Université Nice Sophia Antipolis, Nice, France
2015.10 Séminaire de géométrie algébrique, École normale supérieure, Paris, France
2015.10 Séminaire Théorie des Nombres, Université de Bordeaux, France
2015.08 Students' Workshop on Tropical and Non-Archimedean Geometry, Universität Regensburg, Germany
2015.07 AMS Summer Institute in Algebraic Geometry, University of Utah, Salt Lake City, USA
2015.06 Singular Landscapes 2015, conférence en l'honneur de Bernard Teissier, Centre Paul-Langevin, Aussois, France
2015.06 Non-Archimedean Geometry and its Applications, University of Michigan, Ann Arbor, USA
2015.05 Séminaire de géométrie algébrique, Université de Rennes 1, Rennes, France
2015.04 Séminaire Mathjeune, École normale supérieure, Paris, France
2015.03 Séminaire de Géométrie et Quantification, Institut Henri Poincaré, Paris, France
2015.02 Geometry Seminar, Cinvestav, Gustavo A. Madero, Mexico
2015.01 Séminaire Géométries, Institut Camille Jordan, Université Claude Bernard Lyon 1, Lyon, France
2014.12 Current Developments of Mirror Symmetry, TSIMF, Sanya, China
2014.12 Seminar on Mirror Symmetry, Institut Henri Poincaré, Paris, France
2014.11 TROPGEO conference, Saas Fee, Switzerland
2014.11 Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel
2014.11 Weizmann Institute of Science, Rehovot, Israel
2014.11 Barcelona Mathematical Days, Institut d'Estudis Catalans, Barcelona, Spain
2014.11 Tropical Geometry in Europe, Itinerant Seminar, Université Paul Sabatier, Toulouse, France
2014.09 Séminaire des thésards, University Pierre et Marie Curie, Paris, France
2014.07 Workshop on tropical geometry and related topics, Swansea University, Wales, UK
2014.06 Lecture series, Nordfjordeid summer school 2014: Toric degenerations and mirror symmetry, Sophus Lie Conference Center, Nordfjordeid, Norway
2014.05 Oberseminar: Algebraische Geometrie, Universität Zürich, Switzerland
2014.05 Lecture series, Forschungsseminar Komplexe Geometrie, Universität Hamburg, Germany
2014.05 Oberseminar über Arakelov-Theorie, Universität Regensburg, Germany
2014.03 Complex-algebraic aspects of tropical geometry, École polytechnique fédérale de Lausanne, Switzerland
2014.03 Journée géométrie tropicale, École Polytechnique, France
2014.01 Conference on homological mirror symmetry, University of Miami, USA
2013.10 Séminaire de géométrie tropicale, University Pierre et Marie Curie, Paris, France
2013.06 Cluster algebras and tropical geometry (Dedicated to the memory of Andrei Zelevinsky), Institut de Recherche Mathématique Avancée, Université de Strasbourg, France
2013.05 Séminaire de géométrie tropicale, University Pierre et Marie Curie, Paris, France
2013.05 Séminaire Bourbakette, Université Paris Diderot, Paris, France
2013.02 Séminaire Mathjeune, École normale supérieure, Paris, France

Teaching

2021/2022 Math1CA Multivariable Calculus, Lecture notes, Caltech
2020/2021 Introduction to Derived Geometry, Peking University
2019/2020 Introduction à la géométrie non-archimédienne et application à la géométrie énumérative, Cours M2, Université Paris-Sud
2018/2019 Cours d’Alègbre de L3, Travaux Dirigés, Université Paris-Sud
2017/2018 Introduction à la géométrie analytique non-archimédienne, Cours M2, Université Paris-Sud
2015/2016 LBIOS1 Mathématiques pour biologistes, Travaux Dirigés, Université Paris Diderot
2014/2015 LBIOS1 Mathématiques pour biologistes, Travaux Dirigés, Université Paris Diderot
2013/2014 L1/S2 52U3MT12 Mathématiques, Travaux Dirigés, Université Paris Diderot

Last updated: 2021.08.01