Helge Ruddat

foto Nov 2021 I started my Emmy Noether Junior Research Group Leadership
in June 2015 at the Institut für Mathematik in Mainz associated with
the chair for Algebraic Geometry Duco van Straten.

I am currently substituting the chair for complex geometry at Uni Hamburg

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. A homology theory for tropical cycles on integral affine manifolds and a perfect pairing,
        Geom. Topol. 25:6 2021, p.3079-3132.
      2. Smoothing toroidal crossing spaces,
        Forum Math. Pi 9, 2021, e7, p.1-36, published pdf (with Simon Felten, Matej Filip)
      3. Tailoring a pair of pants,
        Adv. Math. 381, 2021, preprint, published (with Ilia Zharkov)
      4. Tropically constructed Lagrangians in mirror quintic threefolds,
        Forum Math. Sigma 8, 2020, e58, p.1-55, published pdf (with Cheuk Yu Mak)
      5. Compactifying torus fibrations over integral affine manifolds with singularities,
        2019-20 MATRIX Annals, MATRIX Book Series 4, 2021, Pages 609-622, published version (with Ilia Zharkov)
      6. Period integrals from wall structures via tropical cycles, canonical coordinates in mirror symmetry and analyticity of toric degenerations,
        Publ. math. IHES 132, 2020, Pages 1-82, published version, preprint: arxiv:1907.03794, supercedes version from 2014 arxiv:1409.4750 (with Bernd Siebert)
      7. Local Gromov-Witten Invariants are Log Invariants,
        Adv. Math. 350, 9 July 2019, Pages 860-876. published (with Michel van Garrel, Tom Graber)
      8. Descendant log Gromov-Witten invariants for toric varieties and tropical curves,
        Trans. Amer. Math. Soc. 373, 2020, Pages 1109-1152. (with Travis Mandel)
      9. Motivic Zeta Functions of the Quartic and its Mirror Dual,
        Proc. Sympos. Pure Math. 93 String-Math 2014, published 2016, Pages 189-200. (with Johannes Nicaise, Peter Overholser)
      10. An Introduction to Hodge Structures,
        Fields Inst. Monogr. 34 Calabi-Yau varieties: arithmetic, geometry and physics, 2015, Pages 83-130, link. (with Sara Filippini, Alan Thompson)
      11. Enumerative aspects of the Gross-Siebert program,
        Fields Inst. Monogr. 34 Calabi-Yau varieties: arithmetic, geometry and physics, 2015, Pages 337-420. (with Peter Overholser, Michel van Garrel)
      12. Perverse Curves and Mirror Symmetry,
        J. Algebraic Geom. 26, 2017, Pages 17-42, link.
      13. Skeleta of Affine Hypersurfaces,
        Geom. Topol. 18(3), 2014, Pages 1343-1395, link. (with Nicolò Sibilla, David Treumann, Eric Zaslow)
      14. Mirror Duality of Landau-Ginzburg models via Discrete Legendre Transforms,
        Lect. Notes Unione Mat. Ital. 15, Homological mirror symmetry and tropical geometry, Springer, Cham, 2014, Pages 377-406, link.
      15. Towards Mirror Symmetry for Varieties of General Type,
        Adv. Math. 308, 2017, Pages 208-275, link. (with Mark Gross, Ludmil Katzarkov)
      16. Log Hodge groups on a toric Calabi-Yau degeneration,
        Contemp. Math. 527, Mirror symmetry and tropical geometry, 2010, Pages 113-164. (full dissertation: Freidok ALU Freiburg)
      17. Partielle Auflösung eines torischen log-Calabi-Yau-Raumes (German),
        Diplom thesis, ALU Freiburg, 2005, thesis
      1. Tropical quantum field theory, mirror polyvector fields, and multiplicities of tropical curves,  to appear in IMRN, 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, to appear in Manuscripta Math., preprint: arxiv:1803.04210 (with Bumsig Kim, Hyenho Lho)



      1. Instructions on finding the 2875 worth of tropical lines in a quintic threefold using GAP



      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. Kolloquium für Reine Mathematik, Organizer, Universität Hamburg, 2021-2022
      2. Emmy Noether Kolloquium, I organize this ongoing colloquium in Mainz funded by my Emmy grant
      3. Logarithmic Enumerative Geometry and Mirror Symmetry, MFO Workshop Organizer, Jun 16-22, 2019, Oberwolfach
      4. Spring School: Enumerative Invariants from Differential Graded Lie Algebras and Categories, Organizer, Mar 25-31, 2018, Tuscany, Italy
      5. Intensive Course on Intersection Theory, Jul 26-28, 2016, I organized this course in Mainz funded by my Emmy grant
      6. Irregular Hodge Structures and Stability Conditions, I organized this school in Mainz that took place Feb 29-Mar 4, 2016
      7. Hodge theoretic aspects of mirror symmetry, a workshop I organized in 2012


        1. winter 21/22: "Difference Equations", lecture 2+1, Univ. Hamburg
        2. winter 21/22: "Elementary Algebraic Geometry", pro-seminar, Univ. Hamburg
        3. winter 21/22: "Knot theory", pro-seminar, Univ. Hamburg
        4. summer 2021: "Algebraic Curves", lecture 4+2, Univ. Hamburg
        5. summer 2021: "Analytische Geometrie und Stochastik", lecture 2+1, Univ. Hamburg
        6. winter 20/21: "Enumerative Geometry", lecture 4+2, Univ. Hamburg
        7. winter 20/21: "Das Buch der Beweise", LAPS seminar 2, Univ. Hamburg
        8. winter 20/21: "Elementare Algebraische Geometrie", BSc+BEd seminar 2, Univ. Hamburg
        9. summer 2020: "Curves and Surfaces" (elementary differential geometry), Lecture 2+1, Univ. Hamburg
        10. summer 2020: "Complex Geometry", Lecture 4+2, Univ. Hamburg
        11. 2018/19: Research seminar for complex and symplectic geometry
        12. summer 2019: "Homological Mirror Symmetry for the Elliptic Curve", Master Seminar, Univ. Hamburg (Mo 10-12, Geom 434)
        13. summer 2019: "Algebraic Geometry", Lecture 4+2, Skript, Univ. Hamburg, Di 12-14, Mi 8:30-10:00, H03
        14. winter 18/19: Das Buch der Beweise, Seminar fürs Lehramt, Univ. Hamburg
        15. winter 2018/19: Advanced Algebraic Geometry, MSc Vorlesung 4+2, Univ. Hamburg
        16. summer 2017: Elementare Algebraische Geometrie, Seminar, JGU Mainz
        17. summer 2016: Enumerative Geometrie (in German), MSc Seminar, JGU Mainz
        18. winter 2015/16: Birational Geometry of Degenerations (in German), MSc Seminar, JGU Mainz
        19. winter 2014/15: Algebraische Geometrie II, JGU Mainz
        20. summer 2014: Algebraische Geometrie I, JGU Mainz
        21. summer 2012: Geometrie, Algebra und Zahlentheorie (Übungen betreut und unterrichtet), JGU Mainz
        22. winter 2012/13: Riemannsche Flächen und Algebraische Kurven (Übungen betreut und unterrichtet), JGU Mainz
        23. summer 2011: Geometrie, Algebra und Zahlentheorie (Übungen betreut und unterrichtet), JGU Mainz

        Invited Talks

        1. "The proper Landau-Ginzburg potential is the open mirror map", conference "Online Workshop on Mirror symmetry and Related Topics", Kyoto, Dec 15
        2. "Fano manifolds from smoothing toroidal crossing varieties", Zoom Algebraic Geometry Seminar, Edinburgh, Dec 9
        3. "Muster in Geometrie und mathematischer Physik", UBW Munich, Dec 7
        4. "Global Smoothings of Toroidal Crossing Varieties", conference "Faces of Singularities" during the Jean Morlet Semester of Anne Pichon and Javier Fernandez de Bobadilla, CIRM, Luminy, Nov 22-26
        5. Research in pairs, Oberwolfach MFO, August
        6. "Periods and Degenerations", Cardiff, Oct 14
        7. "Smoothing Toroidal Crossing Fano Threefolds", MCCME Moscow, Sep 1
        8. "Polytopes, Periods, Degenerations", Nottingham, May 26
        9. "Periods and Degenerations", Sheffield, May 14
        10. "Integration and Degeneration", Amsterdam, Feb 4
        1. "Periodenintegrale und Torusfaserungen", LMU Munich, Oct 14
        2. "Advances in smoothing normal crossing varieties", 3CinG Workshop, video of lecture1, video of lecture2, link to talk notes, Sep 16-18
        3. "Toroidal crossing spaces, log structures and smoothings", FanoSearch group meeting, Imperial College London, online, Sep 3
        4. "Smoothing normal crossing spaces", Bristol, Mar 12
        5. "Topological Mirror Symmetry", Kansas State University, Mar 5
        6. "Finite order period integrals in normal crossing K3 degenerations", Lisbon, Feb 19
        7. "Smoothing toroidal crossing spaces", Sheffield seminar, Jan 28
        1. "Introduction to Strominger-Yau-Zaslow torus fibrations" on Dec 9 and "Recent progress on SYZ torus fibrations via the Gross-Siebert program" on Dec 16 at MATRIX program "Tropical Geometry and Mirror Symmetry", Creswick, Victoria, Dec 9 - 20
        2. "Smoothing toroidal crossing spaces I,II", lectures at 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