E-mail: email

Research

I work on mirror symmetry, non-archimedean geometry and tropical geometry. I aim to build a theory of enumerative geometry in the setting of Berkovich spaces, which I call non-archimedean enumerative geometry. The theory will give us a new understanding of curve counting in Calabi-Yau manifolds, as well as the structure of their mirrors. It is also intimately related to the theory of cluster algebras and wall-crossing structures. I am awarded the Clay Research Fellowship in 2016.

Papers:

  1. Secondary fan, theta functions and moduli of Calabi-Yau pairs, joint with P. Hacking and S. Keel, (arXiv:2008.02299), 2020.
  2. Non-archimedean quantum K-invariants, joint with M. Porta, (arXiv:2001.05515), 2020.
  3. The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus, joint with S. Keel, (arXiv:1908.09861), 2019.
  4. The non-archimedean SYZ fibration, joint with J. Nicaise and Chenyang Xu, Compositio Mathematica, 155(5):953–972, 2019.
  5. 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.
  6. Representability theorem in derived analytic geometry, joint with M. Porta, (arXiv:1704.01683), To appear in Journal of the European Mathematical Society, 2017.
  7. Enumeration of holomorphic cylinders in log Calabi-Yau surfaces. II. Positivity, integrality and the gluing formula, (arXiv:1608.07651), To appear in Geometry & Topology, 2016.
  8. Derived non-archimedean analytic spaces, joint with M. Porta, Selecta Mathematica, 24(2):609–665, 2018.
  9. Enumeration of holomorphic cylinders in log Calabi-Yau surfaces. I, Mathematische Annalen, 366(3):1649-1675, 2016.
  10. Higher analytic stacks and GAGA theorems, joint with M. Porta, Advances in Mathematics, 302:351–409, 2016.
  11. Tropicalization of the moduli space of stable maps, Mathematische Zeitschrift, 281(3):1035–1059, 2015.
  12. Gromov compactness in non-archimedean analytic geometry, Journal für die reine und angewandte Mathematik (Crelle), 741:179–210, 2018.
  13. The number of vertices of a tropical curve is bounded by its area, L’Enseignement Mathématique, 60(3-4):257–271, 2014.
  14. Balancing conditions in global tropical geometry, Annales de l'Institut Fourier, 65(4):1647–1667, 2015.

Invited Talks

  • 2020.07 My online mini-course at IHES: Notes 1 2 3 4, Videos 1 2 3 4
  • 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

  • 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 (sujets), Université Paris Diderot