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Helge Ruddat

foto Sep 2018 I started my Emmy Noether Junior Research Group Leadership
in June 2015 at the Institute of Mathematics in Mainz associated with
the chair for Algebraic Geometry Duco van Straten.

I am substituting the chair for complex geometry at Uni Hamburg from Sep 2018-Aug 2019

Institut für Mathematik
Raum 04-221
JGU Mainz
Staudingerweg 9
D-55128 Mainz

Tel. +49-6131-39-23606
ruddat ät uni-mainz.de



      My papers on the arXiv.
      1. Tropical quantum field theory, mirror polyvector fields, and multiplicities of tropical curves, preprint: arxiv:1902.07183 (with Travis Mandel)
      2. Local uniqueness of approximations and finite determinacy of log morphisms, preprint: arxiv:1812.02195
      3. The degeneration formula for stable log maps, preprint: arxiv:1803.04210 (with Bumsig Kim, Hyenho Lho)
      4. Local Gromov-Witten Invariants are Log Invariants, preprint: arxiv:1712.05210 (with Michel van Garrel, Tom Graber)
      5. Descendant log Gromov-Witten invariants for toric varieties and tropical curves, preprint: arxiv:1612.02402 (with Travis Mandel)
      6. Motivic Zeta Functions of the Quartic and its Mirror Dual, Proceedings of Symposia in Pure Mathematics 93, "Calabi-Yau Manifolds and their Moduli; and Quantum Curves and Quantum Knot Invariants", ed. Bouchard, Doran, Méndez-Diez, and Quigley, String-Math 2014, p. 204-215 (with Johannes Nicaise, Peter Overholser)
      7. Canonical Coordinates in Toric Degenerations, preprint: arxiv:1409.4750 (with Bernd Siebert)
      8. An Introduction to Hodge Structures, in "Calabi-Yau Varieties: Arithmetic, Geometry and Physics: Lecture Notes on Concentrated Graduate Courses", Fields Institute Monographs 34, ed. Laza, Schütt, Yui, p. 83-130;  arXiv:1412.8499v2 , (with Sara Filippini, Alan Thompson)
      9. Enumerative aspects of the Gross-Siebert program, in "Calabi-Yau Varieties: Arithmetic, Geometry and Physics: Lecture Notes on Concentrated Graduate Courses", Fields Institute Monographs 34, ed. Laza, Schütt, Yui, p. 337-420; arXiv:1410.4783, (with Peter Overholser, Michel van Garrel)
      10. Perverse Curves and Mirror Symmetry, J. Algebraic Geom. 26 (2017), p. 17-42; preprint: arxiv:1309.1803
      11. Skeleta of Affine Hypersurfaces, Geometry & Topology 18(3) (2014), p. 1343–1395; preprint: arXiv:1211.5263 (with Nicolò Sibilla, David Treumann, Eric Zaslow)
      12. Mirror Duality of Landau-Ginzburg models via Discrete Legrende Transforms, in "Homological Mirror Symmetry and Tropical Geometry", Lecture Notes of the Unione Matematica Italiana, Vol. 15 (2014), p. 377-406; preprint: arXiv:1204.5611
      13. Towards Mirror Symmetry for Varieties of General Type, Advances in Mathematics 308 (2017), p. 208–275, preprint: arXiv:1202.4042 (with Mark Gross, Ludmil Katzarkov)
      14. Log Hodge groups on a toric Calabi-Yau degeneration, in "Mirror Symmetry and Tropical Geometry", Contemporary Mathematics 527 (2010), Amer. Math. Soc., Providence, RI, p. 113-164. preprint paper1.ps preprint paper1.pdf (full dissertation: Freidok ALU Freiburg)
      15. Partielle Auflösung eines torischen log-Calabi-Yau-Raumes (German), Diplom thesis, ALU Freiburg, 2005, thesis



        1. "Calabi-Yau Degenerations and Related Geometries", presentation of my Emmy Noether research to a general science audience, presented on July 16, 2015 at the Emmy Noether annual meeting in Potsdam 



        1. "Logarithmic Enumerative Geometry and Mirror Symmetry", MFO Workshop Organizer, Jun 16-22, 2019, Oberwolfach
        2. Spring School: Enumerative Invariants from Differential Graded Lie Algebras and Categories, Mar 25-31, 2018, Tuscany, Italy
        3. Emmy Noether Kolloquium, I am organizing this colloquium in Mainz funded by my Emmy grant
        4. Intensive Course on Intersection TheoryJul 26-28, 2016, I organized this course in Mainz funded by my Emmy grant
        5. Irregular Hodge Structures and Stability Conditions, I am co-organizing this school in Mainz that is going to take place Feb 29-Mar 4, 2016
        6. "Hodge theoretic aspects of mirror symmetry", A workshop I co-organized in 2012


          1. winter 2018/19: Das Buch der Beweise, Seminar fürs Lehramt, Univ. Hamburg
          2. winter 2018/19: Advanced Algebraic Geometry, MSc Vorlesung 4+2, Univ. Hamburg
          3. summer 2017: Elementare Algebraische Geometrie, Seminar 
          4. summer 2016: Enumerative Geometrie (in German), MSc Seminar
          5. winter 2015/16: Birational Geometry of Degenerations (in German), MSc Seminar
          6. winter 2014/15: Algebraische Geometrie II
          7. summer 2014: Algebraische Geometrie I
          8. summer 2012: Geometrie, Algebra und Zahlentheorie (Übungen betreut und unterrichtet)
          9. winter 2012/13: Riemannsche Flächen und Algebraische Kurven (Übungen betreut und unterrichtet)
          10. summer 2011: Geometrie, Algebra und Zahlentheorie (Übungen betreut und unterrichtet)

          Invited Talks

          • 2019
          1. "Tropical Geometry: new directions", MFO, Oberwolfach, Apr 28 - May 4
          2. "From tropical 1-cycles to period integrals and analyticity of smoothings", AMS Spring Central and Western Joint Sectional Meeting, Section "Special Session on SYZ Mirror Symmetry and Enumerative Geometry", University of Hawaii at Manoa, Honolulu, Mar 22-24
          3. "From algebraic curves to tropical curves to Lagrangian submanifolds", colloquium, Kansas State University, Manhattan, Mar 7.
          4. "Period integrals from wall structures", M-seminar, Kansas State University, Manhattan, Mar 7.
          5. "Introduction to toric degenerations and their smoothings", graduate minicourse, Kansas State University, Manhattan, Mar 4,6,8
          6. "A Tropical TQFT that computes multiplicities of tropical curves", Geometry seminar, UT Austin, Feb 28
          7. "Smoothing toroidal crossing varieties", geometry seminar, Cambridge, Feb 13
          8. "Smoothing toroidal crossing varieties", Oberseminar, Hannover, Jan 17
          • 2018 
          1. "From algebraic curves to tropical curves to Lagrangian submanifolds", Pure Math colloquium, Univ. Hamburg, Oct 30
          2. "Smoothing toroidal crossing varieties", Recent developments in Higgs theory, Moscow, Oct 22-27
          3. "Smoothing toroidal crossing varieties", seminar, Seattle, Oct 9.
          4. "Smoothing toroidal crossing varieties", Edinburgh Geometry (EDGE) seminar, Oct 2.
          5. "Constructing Lagrangian Submanifolds in Calabi-Yau threefolds from tropical curves", seminar, IC London, Sep 14
          6. "How tropical curves give a swift proof of the degeneration formula", "Degenerate contributions to enumerative invariants" workshop at IC London, July 30-Aug 03
          7. "Higher genus mirror symmetry for the elliptic curve, proof of Si Li", at school "Enumerative invariants from differential graded Lie algebras and categories", Montegufoni, Italy, Mar 29
          8. "An introduction to generalized theta functions", Singularities, Toric Geometry and Differential Equations, Chemnitz, Mar 19-23
          9. Mittag-Leffler from Feb 25-Mar 17
          10. "Local Gromov-Witten invariants are log invariants", Seminar, Univ. of Utah, Feb 3
          11. "Tropical Construction of Lagrangian Submanifolds", Univ. Heidelberg, Jan 15
          12. "Duality of polyhedral cones and mirror symmetry for algebraic curves", Univ. Münster, Jan 10
          • 2017 
          1. "Analyticity of Gross-Siebert Calabi-Yau families", Conference: Mirror Symmetry and Related Topics 2017, Kyoto, Dec 11-15
          2. "Factoring multiplicities of tropical curves via an L-infinity structure on polyvector fields", video, Workshop: A∞-structures in geometry and representation theory, HIM Bonn, Dec 04-08, 2017
          3. "Analyticity of Gross-Siebert Calabi-Yau families", Workshop: Young Researchers in String Mathematics, MPIM Bonn, Nov 27-30, 2017
          4. "Local Gromov-Witten invariants are log invariants", RTG seminar, Hamburg, Oct 30-Nov 3, 2017
          5. "Analyticity of Gross-Siebert Calabi-Yau families", Mirror Symmetry and Fano Manifolds, London, Oct 24-26, 2017
          6. "Local and Relative Gromov-Witten Invariants", Algebraic Geometry and Moduli Seminar at ETH Zürich, Sep 22, 2017
          7. "Tropical Geometry and Mirror Symmetry" (slides), Annual meeting of the Austrian and German mathematical society, Salzburg, Sep 11-15, 2017
          8. "Descendant log Gromov-Witten invariants for toric varieties and tropical curves", Tropical curve counts, motivic integration and nonarchimedean geometry, workshop supported by this SPP, Tübingen, Mar 27-31, 2017.
          9. "Three applications of log Gromov-Witten invariants", conference and winter school Mirror Symmetry, Tropical Geometry, Gelfand-Kapranov-Zelevinsky A-Philosophy and Beyond, KIAS, Seoul, Feb 27-Mar 3, 2017
          10. Three lectures at School on Cluster Algebras and Log GW Invariants, Feb 20-22, 2017
          11. "Tropical descendant Gromov-Witten invariants", Utrecht, Feb 7, 2017
          1. "One-dimensional K3 mirror families", Reading Course at IAS Princeton, Nov 23, Nov 30, 2016
          2. "Introduction to Logarithmic Gromov-Witten invariants", Homological Mirror Symmetry (minicourse), IAS Princeton, Oct 26, Oct 28, 2016 
          3. "Tropical geometry via logarithmic geometry", "Convexity in Algebraic Geometry" workshop, Fields Institute, Toronto, Oct 3-7, 2016
          4. "Logarithmic Gromov-Witten invariants", lecture series, Workshop on moduli and mirror symmetry, Alpensia Resort, Korea, Aug 8-12, 2016
          5. "Two applications of Logarithmic Gromov-Witten invariants", ECM satellite conference, Hannover, July 13-16, 2016
          6. "Counting real and complex curves in toric varieties - a tropical view", Manin's Seminar, Bonn, Jun 28, 2016
          7. "Tropical descendent log Gromov-Witten invariants", "Calabi-Yau varieties: Arithmetic, geometry and physics" workshop, Herstmonceux Castle in East Sussex, UK, June 20-26, 2016
          8. "Block-Göttsche type invariants in higher dimensions", Seminar Algebraische Geometrie, FU Berlin, May 30, 2016
          9. "Canonical coordinates of canonical Calabi-Yau families", UT Austin Backporch seminar @ Sean Keel, Apr. 13, 2016
          10. "Tropical descendent Gromov-Witten invariants" (video), "Homological Mirror Geometry" workshop, Banff, Alberta, Mar 6-11, 2016
          11. "Tropical descendent Gromov-Witten invariants", Number theory seminar, Copenhagen university, Feb 26, 2016
          12. "Tropical descendent Gromov-Witten invariants", conference "Algebraic and Tropical Geometry", Bar Ilan University, Ramat Gan, Israel, Jan 10-16, 2016
          • 2015 
          1. "Counting curves - complex and tropical", colloquium talk, UBC Vanouver, Dec 4, 2015
          2. "Analycity and Versality of Gross-Siebert families", Workshop at the Simons Center on Collapsing Calabi-Yau manifolds", Aug 31-Sep 4, 2015
          3. "Mini-lectures on the Gross-Siebert program" (videos), Simons Center program on "Moduli spaces and singularities in algebraic and Riemannian geometry", Aug 26-Aug 28, 2015
          4. "Periods for canonical coordinates", Workshop for the Hodge theory FRG, University of Maryland, 22 August, 2015
          5. "Canonical Calabi-Yau families" (slides), AMS Summer Research Institute on Algebraic Geometry, University of Utah, Salt Lake City, 23 July, 2015
          6. "A proof of Morrison's Conjecture", Oberseminar Arithmetische und Algebraische Geometrie, LMU Munich, July 8, 2015
          7. "Reconstructing Calabi-Yau manifolds, periods and cycles" (videos), plenary lecture series at the KIAS school Introduction to the Gross-Siebert program, KIAS, Seoul, 7-10th May, 2015
          8. "A proof of Morrison's Conjecture", University of Zürich, May 4, 2015
          9. "Canonical Calabi-Yau families", Oberseminar "Algebra, Geometrie und Zahlentheorie", Universität Essen, April 31, 2015
          10. "Canonical Coordinates in Toric Degenerations", MFO workshop on "Mirror Symmetry, Hodge Theory and Differential Equations", Oberwolfach, April 2015
          11. "Canonical Calabi-Yau families", University of Alberta, April 10, 2015
          12. "A proof of Morrison's Conjecture", MFO workshop on "Complex Algebraic Geometry", Oberwolfach, March 2015
          13. "Canonical Calabi-Yau families", KU Leuven, Feb 20, 2015