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publications: preprints

1. Convex Fujita numbers and the Kodaira-Enriques classification of surfaces
   with Jiaming Chen, Yusuf Mustopa and Alex Küronya
   preprint, October 2023.
   arXiv:2310.16987 [math.AG]
2. Convex Fujita numbers are not determined by the fundamental group
   with Jiaming Chen, Yusuf Mustopa and Alex Küronya
   preprint, January 2023.
   arXiv:2301.06367 [math.AG]
3. Galois sections and p-adic period mappings
   with L. Alexander Betts
   preprint, April 2022.
   arXiv:2204.13674 [math.NT]

publications: journals

1. Topological rigidity of maps in positive characteristic and anabelian geometry
   with Piotr Achinger
   preprint, October 2023
   to appear in Proceedings of the American Mathematical Society.
   arXiv:2310.11591 [math.AG]
2. Fundamental groups of proper varieties are finitely presented
   with Marcin Lara and Vasudevan Srinivas
   Comptes Rendus - Série Mathématique 362 (2024), 51-54.
   DOI: 10.5802/crmath.518
   arXiv:2303.11161 [math.AG]
3. Parametrized counting and Cayley graph expanders
   with Norbert Peyerimhoff, Marc Roth, Johannes Schmitt, Alina Vdodinva and Philip Wellnitz
   SIAM Journal on Discrete Mathematics 37 (2023), no. 2, 405-486.
   DOI: full/10.1137/22M1479804
   
4. An obstruction to lifting to characteristic 0
   with Hélène Esnault and Vasudevan Srinivas
   Algebraic Geometry 10 (2023), no. 3, 327-347.
   DOI: 10.14231/AG-2023-011
   arXiv:2106.08381 [math.AG]
5. Categories of abelian varieties over finite fields II: Abelian varieties over F_q and Morita equivalence
   with Tommaso Centeleghe
   Israel Journal of Mathematics 257 (2023), no.1, 103-170.
   DOI: 10.1007/s11856-023-2536-2
   arXiv:2112.14306 [math.NT]
6. Cubic twin prime polynomials are counted by a modular form
   with Lior Bary-Soroker
   Canadian Journal of Mathematics 71 (2019), no. 6, 1323-1350.
   DOI: 10.4153/CJM-2018-018-9
   arXiv:1711.05564 [math.NT]
7. Infinite series of quaternionic 1-vertex cube complexes, the doubling construction, and explicit cubical Ramanujan complexes
   with Nithi Rungtanapirom and Alina Vdovina
   International Journal of Algebra and Computation 29 (2019), no. 6, 951-1007.
   DOI: 10.1142/S0218196719500371
   arXiv:1808.03290 [math.GR]
8. Simply transitive quaternionic lattices of rank 2 over F_q(t) and a non-classical fake quadric
   with Alina Vdovina
   Math. Proc. of the Cambridge Philosophical Society 163 (2017), no. 3, 453-498.
   DOI: 10.1017/S0305004117000056
   arXiv:1304.5549 [math.GR]
9. Arithmetic in the fundamental group of a p-adic curve - On the p-adic section conjecture for curves -
   with Florian Pop
   Journal für die Reine und Angewandte Mathematik 725 (2017), 1-40.
   DOI: 10.1515/crelle-2014-0077
   arXiv:1111.1354 [math.AG]
10. Anabelian geometry with étale homotopy types
    with Alexander Schmidt
    Annals of Mathematics 184 (2016), no. 3, 817-868.
    DOI: 10.4007/annals.2016.184.3.5
    arXiv:1504.01068 [math.NT]
11. Series of p-groups with Beauville structure
    with Alina Vdovina
    Monatshefte der Mathematik 181 (2016), no. 1, 177-186.
    DOI: 10.1007/s00605-015-0805-9
    arXiv:1405.3872 [math.GR]
12. Categories of abelian varieties over finite fields I. Abelian varieties over F_p
    with Tommaso Centeleghe
    Algebra & Number Theory 9 (2015), no. 1, 225-265.
    DOI: 10.2140/ant.2015.9.225
    arXiv:1501.02446 [math.NT]
13. On the birational section conjecture with local conditions
    Inventiones mathematicae 199 (2015), no. 1, 239-265.
    DOI: 10.1007/s00222-014-0514-3
    arXiv:1203.3236 [math.AG]
14. Galois sections for abelian varieties over number fields
    with Mirela Çiperiani
    Journal de Théorie des Nombres de Bordeaux 27 (2015), no. 1, 47-52.
    Journal de Théorie des Nombres de Bordeaux
15. Weil-Châtelet divisible elements in Tate-Shafarevich groups II:
    On a question of Cassels
    with Mirela Çiperiani
    Journal für die Reine und Angewandte Mathematik 700 (2015), 175-207.
    DOI: 10.1515/crelle-2013-0013
    arXiv:1308.4528 [math.NT]
16. Lifting Galois sections along torsors
    with Niels Borne and Michel Emsalem
    Mathematische Nachrichten 288 (2015), no. 17-18, 1939-1951.
    DOI: 10.1002/mana.201400251
    arXiv:1301.4429 [math.AG]
17. Étale contractible varieties in positive characteristic
    with Armin Holschbach and Johannes Schmidt
    Algebra & Number Theory 8 (2014), no. 4, 1037-1044.
    DOI: 10.2140/ant.2014.8.1037
    arXiv:1310.2784 [math.AG]
18. Weil-Châtelet divisible elements in Tate-Shafarevich groups I:
    The Bashmakov problem for elliptic curves over Q
    with Mirela Çiperiani
    Compositio Mathematica 149 (2013), no. 5, 729-753.
    DOI: 10.1112/S0010437X12000747
    arXiv:1106.4255 [math.NT]
19. Birational p-adic Galois sections in higher dimensions
    Israel Journal of Mathematics 198 (2013), no. 1, 49-61.
    DOI: 10.1007/s11856-012-0189-7
    arXiv:1202.2781 [math.AG]
20. The Brauer-Manin obstruction for sections of the fundamental group
    Journal of Pure and Applied Algebra 215 (2011), no. 6, 1371-1397.
    DOI: 10.1016/j.jpaa.2010.08.017
    arXiv:0910.5009 [math.AG]
21. On the period-index problem in light of the section conjecture
    American Journal of Mathematics 132 (2010), no. 1, 157-180.
    DOI: 10.1353/ajm.0.0092
    arXiv:0802.4125 [math.AG]
22. Trading degree for dimension in the section conjecture: The non-abelian Shapiro Lemma
    Mathematical Journal of Okayama University 52 (2010), 29-43.
    arXiv:0902.1653 [math.AG]
    Mathematical Journal of Okayama University
    See also the following harmless correction.
23. A general Seifert-Van Kampen theorem for algebraic fundamental groups
    Publications of RIMS 42 (2006), no. 3, 763-786.
    DOI: 10.2977/prims/1166642159
24. A monodromy criterion for extending curves
    International Mathematics Research Notices (2005), no. 29, 1787-1802.
    DOI: 10.1155/IMRN.2005.1787
    arXiv:math/0408315 [math.AG]
25. A logarithmic view towards semistable reduction
    Journal of Algebraic Geometry 14 (2005), no. 1, 119-136.
    DOI: 10.1090/S1056-3911-04-00388-1
    arXiv:math/0305255 [math.AG]
26. Affine Anabelian Curves in Positive Characteristic
    Compositio Mathematica 134 (2002), no. 1, 75-85.
    DOI: 10.1023/A:1020290619656
    arXiv:math/0206188 [math.AG]

publications: proceedings

1. Anabelian geometry with étale homotopy types II
   to appear in: Arithmetic Geometry and Symmetries around Galois and Fundamental Groups, Oberwolfach report 15 (2018), no. 2, 1059-1061.
2. On Galois sections for hyperbolic p-adic curves
   in: The Arithmetic of Fields, Oberwolfach report 10 (2013), no. 2, 1799-1804.
3. Birational Galois sections with local conditions for hyperbolic curves
   in: Arithmetic Geometry, Oberwolfach report 9 (2012), no. 3, 2339-2342.
4. On cuspidal sections of algebraic fundamental groups
   in: "Galois-Teichmüller Theory and Arithmetic Geometry", Proceedings for a Conferences in Kyoto (October 2010), H. Nakamura, F. Pop, L. Schneps, A. Tamagawa eds., Advanced Studies in Pure Mathematics 63, 2012, 519-563.
   arXiv:0809.0017 [math.AG]
5. Descent obstruction and fundamental exact sequence
   with David Harari
   in: J. Stix (editor): The Arithmetic of Fundamental Groups - PIA 2010
   Contributions in Mathematical and Computational Sciences, Vol. 2, Springer-Verlag Berlin Heidelberg, 2012.
   arXiv:1005.1302 [math.AG]
6. Nonabelian examples for the section conjecture in anabelian geometry
   in: Algebraic Number Theory, Oberwolfach report 6 (2009), no. 2, 1720-1722.
7. On the period-index problem in light of the section conjecture
   in: The Arithmetic of Fields, Oberwolfach report 6 (2009), no. 1, 293-295.
8. On the geometry of higher dimensional anabelian varieties
   in: Arithmetic and Differential Galois Groups, Oberwolfach report 4 (2007), no. 2, 1501-1504.
9. Anabelian properties of the moduli spaces of smooth projective curves
   in: The Arithmetic of Fields, Oberwolfach report 3 (2006), no. 1, 364-367.

publications: conferences

1. Parameterized (Modular) Counting and Cayley Graph Expanders
   arXiv:2104.14596 [cs.CC]
   with Norbert Peyerimhoff, Marc Roth, Johannes Schmitt, and Alina Vdovina
   46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021), Leibniz International Proceedings in Informatics 202 (2021), 84:1-15.
   DOI: 10.4230/LIPIcs.MFCS.2021.84

publications: thesis

1. Evidence for the section conjecture in the theory of arithmetic fundamental groups
   Habilitationsschrift, School of Mathematics and Computer Science at the Ruprecht-Karls-Universität Heidelberg, January 2011, x+190 pages, in print as:
   Rational Points and Arithmetic of Fundamental Groups
   Evidence for the Section Conjecture
   Springer Lecture Notes in Mathematics 2054, xx+pp.249, Springer, 2013.
   Erratum for curves that are space filling in their jacobian.
   recension (2022)
2. Projective Anabelian Curves in Positive Characteristic and Descent Theory for Log-Etale Covers
   Dissertation, 2002, Bonn, Bonner Mathematische Schriften, 354 (2002)
   with a short version in german (Oktober 2004).
   The thesis was awarded the Felix-Hausdorff-Gedächtnispreis of the academic year 2002/2003 by the department of mathematics of the Rheinischen Friedrich-Wilhelms-Universität Bonn.
3. Affine anabelsche Kurven in positiver Charakteristik
   diploma thesis, Bonn, 2000.

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Books

1. Rational Points and Arithmetic of Fundamental Groups
   Evidence for the Section Conjecture

   Springer Lecture Notes in Mathematics 2054, 2013.
   Erratum for curves that are space filling in their jacobian.

2. The Arithmetic of Fundamental Groups - PIA 2010

   editor J. Stix, Contributions in Mathematical and Computational Sciences, Vol. 2, Springer-Verlag Berlin Heidelberg, 2012.

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