Johannes Nicaise
Johannes Nicaise (born February 24, 1981 in Leuven ) is a Belgian mathematician who deals with arithmetic and algebraic geometry , non-Archimedean geometry, singularity theory and their intersections.
Nicaise acquired in 2001 with a degree in mathematics at the Catholic University of Leuven and in 2004 was there in January Denef and François Loeser (where he attended the École normale supérieure studied) PhD (igusa zeta functions and motivic generating series). In 2006 he was appointed Chargé des Recherches of the CNRS at the University of Lille , where he completed his habilitation in 2008 (Formule des traces et fiber de Milnor analytique). Since 2009 he has been an assistant professor (lecturer) in Leuven.
He deals with zeta functions and the theory of motivic integration of Denef and Loeser and made progress in proving the motivic monodromy conjecture of Denef and Loeser. This generalizes Jun-Ichi Igusa's monodromic conjecture for p-adic zeta functions of a polynomial over the p-adic numbers according to Weil , which connects the poles of the zeta function with the structure of the singularities in the complex case, and contains the p-adic case as Special case. The conjecture combines number theory (the definition of the zeta function includes the number of solutions mod ) and the theory of singularities in the complex and, like its motivic generalization, is only proven in special cases. Nicaise developed a new interpretation of the conjecture based on non-Archimedean geometry (a geometric object they called the analytic Milnor fiber ) and proved it for one-parameter degeneracies of Abelian varieties . He is investigating the possibility of extending the evidence to degenerate Calabi-Yau varieties.
He is also concerned with Neron models of Abelian varieties.
From 2013 he has been a senior scientist in the Starting Grant of the European Research Council Motivic zeta functions and the monodromy conjecture . For 2017 he was awarded the Ferran Sunyer i Balaguer Prize .
Fonts
- with Ralf Cluckers, Julien Sebag : Motivic integration and its interactions with model theory and non-Archimedean geometry (ICMS Edinburgh conference). 2 volumes, Cambridge University Press, 2011
- therein with Sebag: The Grothendieck Ring of Varieties , Motivic Invariants of Rigid Varieties and applications to complex singularities
- with Antoine Chambert-Loir , J. Sebag: Motivic Integration. Progress in Mathematics, Birkhäuser 2014
- An introduction to p-adic and motivic zeta functions and the monodromy conjecture. In: Bhouwmik, Matsumoto, Tsumura (Eds.): Algebraic and analytic aspects of zeta functions and L-functions. In: Mathematical Society of Japan Memoirs. 2010, pp. 115-140, Arxiv
- with L. Halle: Motivic zeta functions for degenerations of abelian varieties and Calabi-Yau varieties. In: Recents trends on Zeta Functions in Algebra and Geometry. Contemporary Mathematics 566, AMS 2012, pp. 233-259
- with L. Halle: Néron Models and Base Change. Astérisque, SMF 2014
- with Julien Sebag: Motivic Serre invariants, ramification, and the analytic Milnor fiber. In: Inventiones Mathematicae. Volume 168, 2007, pp. 133-173, Arxiv
- with J. Sebag: Motivic Serre Invariants of Curves. In: Manuscripta Mathematica. Volume 128, 2007, pp. 105-182
- with J. Sebag: Rigid geometry and the Monodromy Conjecture. In: D. Chéniot Dutertre, Murolo (Ed.): Singularity Theory. Proc. of the 2005 Marseille Singularity School and Conference. World Scientific, 2007, pp. 819-886
- A trace formula for rigid varieties, and motivic Because generating series for formal schemes. In: Mathematical Annals. Volume 343, 2009, pp. 285-349
- with Lars Halvard Halle: Motivic zeta functions of abelian varieties, and the monodromy conjecture. In: Advances in Mathematics. Volume 227, 2011, pp. 610-653
- Formal and rigid geometry: an intuitive introduction and some applications , L´Enseignement Mathématique, Volume 54, 2008, Issue 3–4, pp. 213–249 Online
Web links
Individual evidence
| personal data | |
|---|---|
| SURNAME | Nicaise, Johannes |
| BRIEF DESCRIPTION | Belgian mathematician |
| DATE OF BIRTH | February 24, 1981 |
| PLACE OF BIRTH | Lions |