Outline

• I run a research group at IST Austria, where I work at the interface of analytic number theory and Diophantine geometry. I organise the:
• ✑ Number theory seminar
• ✑ Discrete Analysis Days
• ✑ arXiv Verain
I used to organise the:
• ✑ Algebraic Geometry & Number Theory Seminar with Tamas Hausel
• ✑ Mathematics Colloquium
• ✑ Women in math day

Teaching

• Topics in analytic number theory, Autumn 2024, ISTA.
• Additive combinatorics, Autumn 2025, ISTA.

Preprints

• a. (With Sofos and Teräväinen) Bateman-Horn, polynomial Chowla and the Hasse principle with probability 1
• b. (With Chan) Almost all quadratic twists of an elliptic curve have no integral points
• c. (With Vishe and Yamagishi) Rational curves on complete intersections and the circle method
• d. (With Bernert, Lichtman and Teräväinen) Bounds on the exceptional set in the abc conjecture
• e. (With Yamagishi) Rational surfaces on low degree hypersurfaces
• f. (With Sawin) Random Diophantine equations of large degree
• g. (With Munshi and Wang) Beyond the square-root barrier: cubic forms of Perazzo type
• h. (With Verzobio) Sums of three powerful numbers
• i. (With Kalinin, Ostafe, Schindler and Wurzinger) The divisor function for matrices

Events

• Since 2022: Graz-ISTA Number Theory Days, ISTA
• Aug 31 - Sep 4, 2026: Fouvry73, Bernoulli Centre, Lausanne
• Sep 7-11, 2026: Arithmetic, L-functions, and pseudorandomness, Banff, Canada
• Sep 28-Oct 2, 2026: Analytic methods for rational points on varieties, Strobl am Wolfgansee
• June 21-26, 2027: Analytic number theory conference, Kraków, Poland
• July 26-30, 2027: Rational points on varieties, ICMS, Edinburgh

Editorial work

• ✑ Editor for Compositio Mathematica
• ✑ Editor for Commentarii Mathematici Helvetici
• ✑ Editor for Monatshefte für Mathematik

Ph.D. students

• Mike Harvey (2006-2010)
  Diophantine problems in many variables
• Dan Loughran (2007-2011)
  Manin's conjecture for del Pezzo surfaces
• Mike Swarbrick-Jones (2009-2013)
  Rational points on varieties over algebraic number fields
• Damaris Schindler (2010-13; with T. Wooley)
  On Diophantine equations involving norm forms and bihomogeneous forms
• Efthymios Sofos (2011-15; with A. Booker)
  Counting rational points on smooth cubic surfaces
• Vladimir Mitankin (2013-17)
  Integral points on affine surfaces
• Yuchao Wang (2013-2014; from Shandong University)
  On the saturation number for cubic surfaces
• Vinay Kumaraswamy (2014-18)
  Zeros of quadratic forms and the delta-method
• Raphael Steiner (2014-18; with A. Booker)
  The harmonic conjunction of automorphic forms and the Hardy-Littlewood circle method
• Adelina Manzateanu (2015-19)
  Rational points in function fields
• Nicholas Rome (2016-20)
  Local-global problems in Diophantine geometry
• Alec Shute (2018-22)
  Existence and density problems in Diophantine geometry: from norm forms to Campana points
• Jakob Glas (2020-24)
  Counting rational points over function fields
• Yijie Diao (2022-)
• Lena Wurzinger (2023-)
• Anna Zanoli (2024-)

Postdocs

• Stephan Baier (2009-11); now at Ramakrishna Mission Vivekananda University
• Lilian Matthiesen (2011-13); now at Universität Göttingen
• Sean Prendiville (2012-13 and 2014-15); now at Lancaster University
• Shuntaro Yamagishi (2017-18; 2023-25); now at University of Bonn
• Kevin Destagnol (2018-19); now at Université Paris-Saclay
• Francesca Balestrieri (2019-20); now at American University of Paris
• Dante Bonolis (2019-22); now at TU Graz
• Tal Horesh (2019-22); now at MAK Vienna
• Julian Lyczak (2019-22); now at Universiteit Antwerpen
• Florian Wilsch (2019-22); now at Universität Göttingen
• Margaret Bilu (2020-22); now CNRS at Ecole Polytechnique
• Zhizhong Huang (2021-22); now at Chinese Academy of Sciences
• Matteo Verzobio (2023-26); now at KU Leuven
• Victor Wang (2023-25); now at IoMAS in Taiwan
• Stephanie Chan (2023-25); now at UCL
• Loïs Faisant (2023-25); now at KU Leuven
• Christian Bernert (2025-26)

Links

• [ArXiv/AG]   [ArXiv/NT]   [EMS]   [JonB]   [LMS]   [MSciN]   [NTW]