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You are here: FRIAS Fellows Fellows 2019/20 Prof. Dr. Johannes Nicaise

Prof. Dr. Johannes Nicaise

Imperial College London
Mathematics
External Senior Fellow
Marie S. Curie FCFP Fellow
October – December 2017 & April 2018

Room 01 008
Phone +49 (0)761 203-97352
Fax +49 (0)761 203-97451

CV

Johannes Nicaise (born 1981) works on algebraic and non-archimedean geometry. He obtained his PhD in 2004 under the supervision of Jan Denef and Francois Loeser. He was Chargé de Recherche at the University of Lille (2005-2009), Assistant and Associate professor at the KU Leuven (2009-2015) and Reader at Imperial College London (2015-today), keeping a part-time position at the KU Leuven. Nicaise was awarded with a Starting Grant of the European Research Council (project MOTZETA 2013-2018) to work on the interactions between non-archimedean geometry, mirror symmetry and the theory of motivic zeta functions. Recent results of this project include a proof of Veys's conjecture on poles of maximal order of Igusa zeta functions (joint work with Chenyang Xu), and a proof of the Davison-Meinhardt conjecture on motivic nearby fibers of weighted homogeneous polynomials (joint work with Sam Payne).

Selected Publications

  • "Motivic Serre invariants, ramification, and the analytic Milnor fiber” (with J. Sebag). Inventiones Mathematicae 168:1, pages 133-173 (2007)
  • “A trace formula for varieties over a discretely valued field”. Journal für die Reine und Angewandte Mathematik 650, pages 193-238 (2011)
  • “Motivic zeta functions of abelian varieties, and the monodromy conjecture” (with L.H. Halle). Advances in Mathematics 227, pages 610-653 (2011)
  • “A logarithmic interpretation of Edixhoven's jumps for Jacobians”(with D. Eriksson and L.H. Halle). Advances in Mathematics 279, pages 532–574 (2015)
  • “Poles of maximal order of motivic zeta functions” (with C. Xu). Duke Mathematical Journal 165:2, pages 217-243 (2016)

FRIAS Research Project

Non‐archimedean Morse theory, mirror symmetry and the minimal model program

The aim of this project is to develop a notion of Morse theory on Berkovich spaces. This problem is motivated by recent work of the PI with Mircea Mustaţă and Chenyang Xu on the relations between the minimal model program (MMP) and the non-archimedean approach to the SYZ conjecture in mirror symmetry by Kontsevich and Soibelman. In particular, we want to obtain an intrinsic geometric explanation for the fact that the non-archimedean SYZ fibration is a strong deformation retract. These results would open new perspectives on the interactions between Berkovich spaces, mirror symmetry and the MMP.