### Research

My research interests include Arakelov geometry and related questions.
This means I work in algebraic geometry with input from complex geometry,
and that I'm inspired by questions coming from number theory. In
particular, I have been working on refinements of Riemann-Roch theorems
and applications.

### Publications:

Spaces of norms, determinant
of cohomology and Fekete points in non-Archimedean geometry, to
appear in Advances in Mathematics (joint with Sébastien Boucksom).

BCOV
invariants of Calabi-Yau manifolds and degenerations of Hodge
structures, to appear in Duke Mathematical Journal (joint with
Gerard Freixas and Christophe Mourougane)

Global
representation of Segre numbers by Monge-Ampère products,
Mathematische Annalen (2020), (joint with Mats Andersson, Håkan
Samuelsson, Elizabeth Wulcan, Alain Yger)

Kähler
quantisation of vortex moduli, Letters in Mathematical Physics
110, pp. 659-693 (2020) (joint with Nuno Ramao)

Singularities
of metrics on Hodge bundles and their topological invariants,
Algebraic Geometry 5 (6) (2018) 742-775 (joint
with Gerard Freixas and Christophe Mourougane)

A logarithmic interpretation of
Edixhoven's jumps for Jacobians Advances in Mathematics 2016, (joint
with Lars-Halvard Halle and Johannes Nicaise)

Discriminants
and Artin conductors, Crelle 2016

earlier version on arXiv
Galois
theory of covers Normat 2012, (joint with Ulf Persson)

Degenerating
Riemann surfaces and the Quillen metric Int Math Res Notices (2012)
doi: 10.1093/imrn/rnr234 First published online: January 13, 2012

earlier version on Arxiv
Un
isomorphisme de type Deligne–Riemann–Roch Comptes Rendus
Mathematique, Volume 347, Issues 19-20, October 2009, Pages 1115-1118

On the
Brauer-Manin obstruction for zero-cycles on curves (w. Victor
Scharaschkin) Acta Arithmetica, vol. 135, no. 2, pp. 99-110, 2008

earlier version on arXiv
### Preprints and preliminary versions:

On genus one mirror symmetry in
higher dimensions and the BCOV conjectures (submitted, joint with
Gerard Freixas and Christophe Mourougane)

Nonproper intersection products
and generalized cycles (submitted, joint with Mats Andersson, Håkan
Samuelsson, Elizabeth Wulcan, Alain Yger)

Base
change conductor for Jacobians (preprint, joint with Lars-Halvard
Halle and Johannes Nicaise)

A
metrized Deligne-Riemann-Roch theorem (preprint, preliminary
version, only the Adams operations are considered in detail)

A
Deligne-Riemann-Roch theorem (preprint, preliminary version,
results on functorial Grothendieck-Riemann-Roch are only sketched)

The excess formula
in functorial form arXiv
Refined operations
on K-theory by lifting to the virtual category (submitted, current
version is a revision in progress)

earlier version on arXiv
### Mathematical education:

COMMUNICATING TO LEARN MULTIVARIABLE CALCULUS –
STUDENTS’ BLACKBOARD PRESENTATIONS AS A MEANS FOR
ENHANCING MATHEMATICS LEARNING, to appear in PRIMUS (joint with Hans
Malmström)

Last updated: April, 2018