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 2020

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 and on Google Scholar.
    1. Smoothing toroidal crossing spaces, preprint: arxiv:1908.11235 (with Simon Felten, Matej Filip)
    2. Period integrals from wall structures via tropical cycles, canonical coordinates in mirror symmetry and analyticity of toric degenerations, preprint: arxiv:1907.03794, supercedes version from 2014 arxiv:1409.4750 (with Bernd Siebert)
    3. Tropically constructed Lagrangians in mirror quintic threefolds arxiv:1904.11780 (with Cheuk Yu Mak)
    4. Tropical quantum field theory, mirror polyvector fields, and multiplicities of tropical curves, preprint: arxiv:1902.07183 (with Travis Mandel)
    5. Local uniqueness of approximations and finite determinacy of log morphisms, preprint: arxiv:1812.02195
    6. The degeneration formula for stable log maps, preprint: arxiv:1803.04210 (with Bumsig Kim, Hyenho Lho)
    7. Local Gromov-Witten Invariants are Log Invariants, Adv. Math. 350, 9 July 2019, Pages 860-876. (with Michel van Garrel, Tom Graber)
    8. Descendant log Gromov-Witten invariants for toric varieties and tropical curves, to appear in Trans. Amer. Math. Soc. (with Travis Mandel)
    9. Motivic Zeta Functions of the Quartic and its Mirror Dual, String-Math 2014, Proc. Sympos. Pure Math. 93 (Amer. Math. Soc., Providence, RI), 2016, 189-200. (with Johannes Nicaise, Peter Overholser)
    10. An Introduction to Hodge Structures, Calabi-Yau varieties: arithmetic, geometry and physics, Fields Inst. Monogr. 34 (Fields Inst. Res. Math. Sci., Toronto, ON), 2015, 83-130. (with Sara Filippini, Alan Thompson)
    11. Enumerative aspects of the Gross-Siebert program, Calabi-Yau varieties: arithmetic, geometry and physics, Fields Inst. Monogr. 34 (Fields Inst. Res. Math. Sci., Toronto, ON), 2015, 337-420. (with Peter Overholser, Michel van Garrel)
    12. Perverse Curves and Mirror Symmetry, J. Algebraic Geom. 26, 2017, p. 17-42.
    13. Skeleta of Affine Hypersurfaces, Geom. Topol. 18(3), 2014, 1343-1395. (with Nicolò Sibilla, David Treumann, Eric Zaslow)
    14. Mirror Duality of Landau-Ginzburg models via Discrete Legrende Transforms, Homological mirror symmetry and tropical geometry, Lect. Notes Unione Mat. Ital. 15, Springer, Cham, 2014, 377-406.
    15. Towards Mirror Symmetry for Varieties of General Type, Adv. Math. 308, 2017, p. 208-275. (with Mark Gross, Ludmil Katzarkov)
    16. Log Hodge groups on a toric Calabi-Yau degeneration, Mirror symmetry and tropical geometry, Contemp. Math. 527 (Amer. Math. Soc., Providence, RI), 2010, 113-164. (full dissertation: Freidok ALU Freiburg)
    17. 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 organized this colloquium in Mainz funded by my Emmy grant
    4. Intensive Course on Intersection Theory, Jul 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 2019/20: "Mirror Symmetry", Master Seminar, Univ. Hamburg
      2. winter 2019/20: "Complex Geometry", Lecture 4+2, Univ. Hamburg
      3. winter 2019/20: "Buch der Beweise", Bachelor of Education Seminar, Univ. Hamburg
      4. winter 2019/20: Research seminar for complex and symplectic geometry
      5. summer 2019: "Homological Mirror Symmetry for the Elliptic Curve", Master Seminar, Univ. Hamburg (Mo 10-12, Geom 434)
      6. summer 2019: "Algebraische Geometrie", Lecture 4+2, Skript, Univ. Hamburg, Di 12-14, Mi 8:30-10:00, H03
      7. winter 2018/19: Das Buch der Beweise, Seminar fürs Lehramt, Univ. Hamburg
      8. winter 2018/19: Advanced Algebraic Geometry, MSc Vorlesung 4+2, Univ. Hamburg
      9. summer 2017: Elementare Algebraische Geometrie, Seminar 
      10. summer 2016: Enumerative Geometrie (in German), MSc Seminar
      11. winter 2015/16: Birational Geometry of Degenerations (in German), MSc Seminar
      12. winter 2014/15: Algebraische Geometrie II
      13. summer 2014: Algebraische Geometrie I
      14. summer 2012: Geometrie, Algebra und Zahlentheorie (Übungen betreut und unterrichtet)
      15. winter 2012/13: Riemannsche Flächen und Algebraische Kurven (Übungen betreut und unterrichtet)
      16. summer 2011: Geometrie, Algebra und Zahlentheorie (Übungen betreut und unterrichtet)

      Invited Talks

      1. MATRIX program "Tropical Geometry and Mirror Symmetry", Creswick, Victoria, Dec 9 - 20
      2. TBD, Workshop on Mirror Symmetry and Fano Manifolds II, Chicheley UK, Sep 25-27
      3. "Smoothing toroidal crossing spaces", conference "Homological Mirror Symmetry and Self Organized Criticalities", Inauguration of the Institute of the Mathematical Sciences of the Americas, Miami, Sep 9-13
      4. "Periods and Degenerations", HU Berlin, May 22
      5. "From algebraic curves to tropical curves to Lagrangian submanifolds", MFO workshop "Tropical Geometry: new directions", Oberwolfach, Apr 28 - May 4
      6. "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
      7. "From algebraic curves to tropical curves to Lagrangian submanifolds", colloquium, Kansas State University, Manhattan, Mar 7.
      8. "Period integrals from wall structures", M-seminar, Kansas State University, Manhattan, Mar 7.
      9. "Introduction to toric degenerations and their smoothings", graduate minicourse, Kansas State University, Manhattan, Mar 4,6,8
      10. "A Tropical TQFT that computes multiplicities of tropical curves", Geometry seminar, UT Austin, Feb 28
      11. "Smoothing toroidal crossing varieties", geometry seminar, Cambridge, Feb 13
      12. "Smoothing toroidal crossing varieties", Oberseminar, Hannover, Jan 17
      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
      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
      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


      Piano improvisation, November 29, 2018