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:
• ✑ Algebraic Geometry & Number Theory Seminar with Tamas Hausel
• ✑ Browning group working seminar
• ✑ Women in math day
I used to organise the:
• ✑ Mathematics Colloquium

Teaching

• Topics in analytic number theory, Autumn 2024, IST Austria.

Preprints

• a. (With Sofos and Teräväinen) Bateman-Horn, polynomial Chowla and the Hasse principle with probability 1
• b. (With Bilu) A motivic circle method
• c. (With Lyczak and Smeets) Paucity of rational points on fibrations with multiple fibres
• d. (With Chan) Almost all quadratic twists of an elliptic curve have no integral points
• e. (With Glas and Wang) Sums of three cubes over a function field
• f. (With Vishe and Yamagishi) Rational curves on complete intersections and the circle method
• g. (With Wilsch) Integral points on cubic surfaces: heuristics and numerics
• h. (With Glas and Wang) Optimal sums of cubes in F_q[t]
• i. (With Verzobio) Counting integer points on affine surfaces with a side condition
• j. (With Sawin and Wang) Pairs of commuting integer matrices
• k. (With Lichtman and Teräväinen) Bounds on the exceptional set in the abc conjecture
• l. (With Chan) Solubility of a resultant equation and applications

Events

• Since 2022: Graz-ISTA Number Theory Number Theory Days, ISTA
• Jun 2-6, 2025: Statistics of class groups and number fields, ETH
• June 23-27, 2025: Diophantine equations, combinatorics, analysis in Number Theory, ICMS, Edinburgh
• July 7-11, 2025: Full circle: 100 years of the circle method, IML, Stockholm
• Sep 1-5, 2025: Annual ÖMV-DMG meeting, Linz.
• Sep 8-12, 2025: Geometric and analytic number theory, Bath.
• November 2-7, 2025: Analytic number theory, Oberwolfach
• November 9-14, 2025: Arithmetic statistics for algebraic objects, Oberwolfach
• April 2-6, 2026: Arithmetic statistics workshop, CRM, Montreal
• May 4-15, 2026: Universal statistics in number theory summer school, CRM, Montreal
• May 18-22, 2026: Discrete harmonic analysis and analytic number theory, Erdös Centre, Budapest

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; 2023-26)
• 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 Duke University
• Tal Horesh (2019-22)
• Julian Lyczak (2019-22); now at Universiteit Antwerpen
• Florian Wilsch (2019-22); now at Universität Göttingen
• Margaret Bilu (2020-22); now CNRS at Université de Bordeaux
• Zhizhong Huang (2021-22); now at Chinese Academy of Sciences
• Matteo Verzobio (2023-26)
• Victor Wang (2023-25)
• Stephanie Chan (2023-25)
• Loïs Faisant (2023-)

Links

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