Joachim König

Visiting assistant professor

Korea Advanced Institute of Science and Technology

Contact

Teaching

• Spring 2019
  • Calculus I (MAS101)
  • Calculus II (MAS102)
• Fall 2018
  • Calculus I (MAS101)
  • Introduction to Linear Algebra (MAS109)
• Spring 2018
  • Calculus I (MAS101)
  • Introduction to Linear Algebra (MAS109)

Research interests

Current projects

• On Hilbert's irreducibility theorem.
• Arithmetic and geometric monodromy groups of rational functions
• Weak approximation and local conditions in Inverse Galois theory (NRF project 2019002665).
• Rank gain of elliptic curves over non-Galois extensions.

Career information

Previous positions

• 2014-16 and 2017-18: Universität Würzburg (Germany): Post-doc
• 2016-17: Technion, Haifa (Israel): Post-doc

CV

Publications

Submitted

• Reducible specializations of polynomials: The nonsolvable case. Preprint (2020).
  Joint with D. Neftin.
• On Galois extensions with prescribed decomposition groups. Preprint (2019).
  Joint with K.-S. Kim.
• Rational pullbacks of Galois covers. Preprint (2018).
  Joint with P. Debes, F. Legrand and D. Neftin.

Accepted

• Unramified extensions over low degree number fields. Joint with D. Neftin and J. Sonn.
  To appear in J. Number Theory.
• An approach for computing families of multi-branch-point covers and applications for symplectic Galois groups. Joint with D. Barth and A. Wenz
  To appear in J. Symb. Comp.
• Density results for specialization sets of Galois covers Joint with F. Legrand.
  To appear in J. Inst. Math. Jussieu.
• On the mod-p distribution of discriminants of G-extensions.
  To appear in Int. J. of Number Theory.
• The Grunwald problem and specialization of families of regular Galois extensions.
  To appear in Annali della Scuola Normale Superiore di Pisa, Classe di Scienze.

Published

• On number fields with power-free discriminant.
  Isr. J. Math. 235 (2020), 413-437.
• Some examples of quadratic fields with finite nonsolvable maximal unramified extensions II. Joint with K.-S. Kim.
  Ramanujan J. 51 (2020), 205-228.
• On the local behaviour of specializations of function field extensions .
  Joint with F. Legrand and D. Neftin. Int.Math.Res.Not. IMRN, Volume 2019, Issue 9 (2019), 2951-2980.
  Preprint.
• Almost-regular Dessins d'Enfant on a sphere and torus.
  Joint with A. Leitner and D. Neftin. Topology and its Applications 243 (2018), 78-99.
• Galois realizations with inertia groups of order two.
  Joint with D. Rabayev and J. Sonn. Int. J. Number Theory 14(7) (2018), 1983-1994.
  Preprint.
• A note on families of monogenic number fields.
  Kodai J. Math. 41 (2018), p.456-464.
• The admissibility of M11 over number fields.
  Joint with D. Neftin. J. Pure Appl. Algebra 222(9) (2018), 2456-2464.
  Preprint.
• On intersective polynomials with non-solvable Galois group.
  Communications in Algebra 46(6) (2018), 2405-2416.
  Preprint (2017).
  Supplementary data file for computations.
• Non-parametric sets of regular realizations over number fields.
  Joint with F. Legrand. J. Algebra 497 (2018), 302-336.
  Preprint.
• Non-parametricity of rational translates of regular Galois extensions.
  Acta Arithmetica 179 (2017), p.267-275.
  Preprint.
• On the reducibility behavior of Thue polynomials.
  J. Number Theory 176 (2017), 37-45.
  Preprint (2016).
• On rational functions with monodromy group M11.
  J.Symb.Comp. 79 (2) (2017), 372-383.
  Preprint (2015).
• Computation of Hurwitz spaces and new explicit polynomials for almost simple Galois groups.
  Math. Comp. 86 (2017), 1473-1498.
  Preprint (2015).
• A note on the product of two permutations of prescribed orders.
  J.Europ.Combin. 57 (2016), 50-56.
  Preprint (2016)
  
• Septic equations are solvable by 2-fold origami.
  Joint with D. Nedrenco. Forum Geometricorum, Vol. 16 (2016), 193-205.
  Preprint (2015).
• The inverse Galois problem and explicit computation of families of covers of P^1(C) with prescribed ramification.
  PhD Thesis (2014).
  Data files referenced in the thesis.
• Solvability of generalized monomial groups.
  Journal of Group Theory. Volume 13 (2010), 207-220.

Selected talks

• On the set of specializations of a Galois cover. Algebra Seminar, Bar Ilan University (2019).
• Density of specialization sets and Hasse principle in families of twisted Galois covers. Number Theory Days, Lille (2019).
• The inverse Galois problem with local restrictions. Algebra Seminar, Guangdong Technion I.I.T (2019).
• Methods for computing Galois groups. Summer School on Galois Theory and Number Theory, Dresden (2019).