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 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.