Research activities


Research papers


Submitted
  • Two-dimensional Weyl sums failing square-root cancellation along lines (with Igor E. Shparlinski). Submitted. ArXiv.

    Accepted
  • Optimal mean value estimates beyond Vinogradov's mean value theorem (with Trevor D. Wooley). Accepted for publication in Acta Arith. ArXiv.
  • The Hasse principle for diagonal forms restricted to lower-degree hypersurfaces (with Scott T. Parsell). Accepted for publication in Algebra and Number Theory. ArXiv.

    In print
  • Rational lines on cubic hypersurfaces (with Rainer Dietmann). Math. Proc. Camb. Philos. Soc. 171 (2021), No. 1, 99--112. ArXiv.
  • The density of rational lines on hypersurfaces: A bihomogeneous perspective. Monatsh. Math. 195 (2021), no. 2, 191-231. ArXiv.
  • On generating functions in additive number theory, II: Lower-order terms and applications to PDEs (with Scott T. Parsell, Konstantinos Poulias, George Shakan, Robert C. Vaughan). Math. Ann. 379 (2021), 347376. ArXiv.
  • On the number of linear spaces on hypersurfaces with a prescribed discriminant. Math. Z. 289 (2018), no. 34, 803827. pdf, ArXiv.
  • Vinogradov systems with a slice off (with Trevor D. Wooley). Mathematika 63, no. 3 (2017), 797-817. pdf, ArXiv.
  • Linear spaces on hypersurfaces over number fields. Michigan Math. J. 66 (2017), 769-784. ArXiv.
  • The Hasse principle for systems of quadratic and cubic diagonal equations. Q. J. Math. 68 (2017), 831-850. pdf, ArXiv.
  • Simultaneous additive equations: Repeated and differing degrees (with Scott T. Parsell). Canad. J. Math., 69 (2017), 258-283. pdf, ArXiv.
  • Forms representing forms: The definite case. J. London Math. Soc. 92 (2015), 393-410. ArXiv.
  • Sums and differences of power-free numbers. Acta Arith. 169 (2015), 169-180. pdf, ArXiv.
  • A note on p-adic solubility for forms in many variables. Bull. London Math. Soc. 47 (2015), 501-508. ArXiv.
  • Forms representing forms and linear spaces on hypersurfaces. Proc. London Math. Soc. 108 (2014), 809-835. ArXiv.
  • Qualification theses

  • Local-Global principles for linear spaces on hypersurfaces. PhD Thesis. Bristol, 2014.
  • Paare s-freier Zahlen (Twins of s-free numbers). Diplomarbeit. Stuttgart, 2009. Auf Deutsch, in English.
  • 2021

  • Two-dimensional Weyl sums failing square-root cancellation along lines. ℕ3-Days XIV, Uppsala, 29.05.2021.
  • Simultaneous diagonal and non-diagonal equations. Hausdorff Summer School "The Circle Method: Entering its Second Century", Bonn, 14.05.2021.
  • Two-dimensional Weyl sums failing square-root cancellation along lines. Browning group seminar, IST Vienna, 17.03.2021.
  • From mean values to asymptotic formulae: An introduction to the circle method. 4 lectures within the Discrete Analysis Working Group. The Internet, 02.02.-02.03.2021.

    2020

  • Diophantine systems containing both diagonal and non-diagonal equations. Seminar for Algebraic Geometry and Number Theory, Gothenburg, 15.12.2020.
  • Approximations of Weyl sums. Purdue Analytic Number Theory and Harmonic Analysis seminar, Purdue / The Internet, 11.11.2020.
  • Approximations of Weyl sums. Number Theory during Lockdown, The Internet, 10.07.2020.

    2019

  • Approximations of Weyl sums. CMS Winter meeting, Toronto, 08.12.2019.
  • Rational lines on cubic hypersurfaces. Rational points on Fano and similar varieties, Institut Henri Poincaré, Paris, 23.05.2019.
  • Diophantine problems via Fourier analysis. Colloquium, Linköping, 03.04.2019.
  • Rational lines on cubic hypersurfaces. Arithmétique en Plat Pays, Lille, 11.03.2019.

    2018

  • Rational lines on cubic hypersurfaces. Number Theory and Function fields, Exeter, 18.12.2018.
  • Optimal mean value estimates beyond Vinogradov's mean value theorem. Number Theory Seminar, Royal Holloway University of London, 13.12.2018.
  • Vinogradov Systems missing the linear slice. Summer school on Number theory and coding theory: Contemporary applications in security, Åbo Akademi, Turku, 29.05.2018.
  • Exponential Sums, Diophantine Equations and Vinogradov's Mean Value Theorem. Mini-course, Trondheim, 02.-04.05.2018.
  • Optimal mean value estimates beyond Vinogradov's mean value theorem. ESTIA Seminar, Bristol, 20.03.2018.
  • Optimal mean value estimates beyond Vinogradov's mean value theorem. Seminar for Algebraic Geometry and Number Theory, Gothenburg, 09.03.2018.
  • Linear spaces on cubic hypersurfaces. Quebec-Vermont Number Theory Seminar, Montreal, 25.01.2018.
  • Diophantine equations and the Hardy-Littlewood circle method. Postdoctoral Seminar, Waterloo, 17.01.2018.

    2017

  • Vinogradov Systems missing the linear slice. CMS Winter Meeting 2017, Number Theory Session, Waterloo, 11.12.2017.
  • Optimal mean value estimates beyond Vinogradov's mean value theorem. Number Theory Seminar, Waterloo, 14.09.2017.
  • Systems of cubic and quadratic diagonal eqations. Workshop on Efficient Congruencing and Translation-Invariant Systems, Fields Institute, Toronto, 17.03.2017.
  • Lines on smooth cubic hypersurfaces. Seminar for Number Theory and Representation Theory, Toronto, 08.03.2017.
  • From points to lines and beyond: Higher-dimensional objects contained in hypersurfaces. Analytic Number Theory Postdoc Seminar, Programme in Analytic Number Theory, MSRI, Berkeley, 24.02.2017.
  • Systems of cubic and quadratic diagonal eqations. Connections for Women, Programme in Analytic Number Theory, MSRI, Berkeley, 03.02.2017.

    2016

  • Counting (and not counting) linear spaces on hypersurfaces by the circle method. Seminar in Algebraic Geometry and Number Theory, Göteborg, 04.10.2016.
  • A smoothness criterion for linear spaces on hypersurfaces. ELAZ, 06.09.2016.
  • On the number of linear spaces on hypersurfaces with a prescribed discriminant. Nordic Congress of Mathematicians, 18.03.2016.
  • On the number of linear spaces on hypersurfaces with a prescribed discriminant. Number Theory Seminar, Copenhagen, 19.02.2016.

    2015

  • Counting rational points on complete intersections via the Hardy-Littlewood circle method. Seminar in Algebraic Geometry and Number Theory, Göteborg, 13.10.2015.
  • Simultaneous additive equations: Repeated and differing degrees. Workshop Quantitative arithmetic geometry, Institut Mittag-Leffler, Stockholm, 25.06.2015.
  • Simultaneous additive equations: Repeated and differing degrees. Turku, 04.06.2015.
  • Simultaneous additive equations: Repeated and differing degrees. Algebra, Number Theory, and Applications Seminar, Aalto, 03.06.2015.
  • Simultaneous additive equations: Repeated and differing degrees. 3. Göttingen-Hannover Number Theory Workshop, Göttingen, 24.04.2015.
  • Simultaneous additive equations: Repeated and differing degrees. Séminaire de Théorie des Nombres, Nancy, 26.03.2015.
  • Forms in many variables and differing degrees. Oberseminar Analytic Number Theory, Göttingen, 19.01.2015.

    2014

  • Learning how to count. Junior Zahlentheorie Seminar, Göttingen, 04.11.2014.
  • p-adic solubility for Birch's theorem. Workshop Analytic Number Theory, Oxford, 29.09.2014.
  • Linear Spaces on hypersurfaces. DMV-PTM meeting, Poznań, 19.09.2014
  • Non-singular p-adic solubility for systems of forms. ENFANT workshop, Bonn, 11.07.2014.
  • Vinogradov's Mean Value Theorem II: Efficient Congruencing. Junior Zahlentheorie Seminar, Göttingen, 18.06.2014.
  • An introduction to Vinogradov's Mean Value Theorem. Junior Zahlentheorie Seminar, Göttingen, 04.06.2014.
  • Sums and differences of power-free numbers. Oberseminar Analytic Number Theory, Göttingen, 05.05.2014.
  • On generalised Möbius functions. Junior Zahlentheorie Seminar, Göttingen, 08.01.2014.

    2013

  • Musings on Birch's Theorem. Pure Postgrad Seminar, Bristol, 06.12.2013.
  • A Multidimensional version of Birch's Theorem. Oberseminar Analytic Number Theory, Göttingen, 28.11.2013.
  • A Multidimensional Birch's Theorem. Oberwolfach, 24.10.2013.
  • Forms in many variables and p-adic solubility. Pure Maths Seminar, UEA, 25.02.2013.

    2012

  • Forms in many variables and p-adic solubility. Oberseminar Analytic Number Theory, Göttingen, 17.12.2012.
  • Learning how to count, or: On generalised Möbius functions. Pure postgrad seminar, Bristol, 09.11.2012.

    2011

  • An approach to Birch's theorem and its multidimensional generalisations. Junior Number Theory Seminar, Bristol, 26.10.2011.
  • A generalised version of the multi-dimensional Waring's problem. Pure Maths Seminar, RHUL, 11.10.2011.
  • A generalised version of the multi-dimensional Waring's problem. Paul Turán Memorial Conference, Budapest, 23.08.2011: Contributed talk.
  • 2009

  • Paare s-freier Zahlen. Die Diophanten, Stuttgart, 28.10.2009.
  • 2021

  • Arithmetic (and) Harmonic Analysis, 31.05.-04.06.2021, Institut Mittag-Leffler, Stockholm / The Internet. Member of the organising committee.
  • 3-Days XIV, 28.05.-29.05.2021, Uppsala / The Internet. Invited.
  • Hausdorff Summer School "The Circle Method: Entering its Second Century", Bonn / The Internet, 10.-21.05.2021. Invited.
  • Fourier Restriction Online, 04.03.-12.03.2021, The Internet.
  • Arithmetic Statistics, Discrete Restriction, And Fourier Analysis, 15.02.-19.02.2021, American Institute of Mathematics / The Internet. Invited.
  • 2020

  • 3-Days XIII, 26.11.-27.11.2020, Copenhagen / The Internet.
  • 3-Days XII, 28.05.-29.05.2020, Copenhagen / The Internet.
  • Öresund number theory day, 28.01.2020, Lund.
  • 2019

  • CMS Winter Meeting, 06.12.-09.12.2019, Toronto. Invited.
  • 3-Days XI, 15.11.-16.11.2019, Gothenburg. Member of the organising committee.
  • Analytic Number Theory, 04.11.-09.11.2019, Oberwolfach. Invited.
  • Second Symposium on Analytic Number Theory, 08.07.-12.07.2019, Cetraro.
  • Heilbronn Focused Research Group on Efficient Congruencing and l^2-decoupling, 17.06.-21.06.2019, Bristol. Invited.
  • Rational points on Fano and similar varieties, 20.05.-24.05.2019, Paris. Invited.
  • Arithmétique en plat pays, 11.03.2019, Lille. Invited.
  • 2018

  • Number Theory and Function Fields, 18.12.-20.12.2018, Exeter. Invited.
  • 3-Days IX, 30.11.-01.12.2018, Lund.
  • Rational Points on Schiermonnikoog, 02.07.-06.07.2018, Schiermonnikoog.
  • N-cube week, 25.06.-29.06.2018, Institut Mittag-Leffler, Stockholm.
  • Summer school on Number theory and coding theory: Contemporary applications in security, 28.05.-01.06.2018, Åbo Akademi, Turku. Invited.
  • 2017

  • CMS Winter Meeting 2017, 08.-11.12.2017, Waterloo. Invited.
  • Where Geometry meets Number Theory, Conference in honour of Per Salberger's 60th birthday. 17.07.-19.07.2017, Göteborg. Member of the organising committee.
  • Recent developments in Harmonic Analysis, 15.05.-19.05.2017, Programme Harmonic Analysis, MSRI, Berkeley.
  • Recent developments in Analytic Number Theory, 01.05.-05.05.2017, Programme Analytic Number Theory, MSRI, Berkeley.
  • Workshop on Efficient Congruencing and Translation-invariant Systems, 13.03.-17.03.2017, Thematic Programme on Unlikely Intersections, Heights, and Efficient Congruencing, Fields Institute, Toronto. Invited.
  • Introductory Workshop, 06.02.-10.02.2017, Programme Analytic Number Theory, MSRI, Berkeley.
  • Connections for Women, 02.02.-03.02.2017, Programme Analytic Number Theory, MSRI, Berkeley. Invited.
  • 2016

  • 3 Days V, 25.11.-26.11.2016, Göteborg. Member of the organising committee.
  • ELAZ, 05.09.-09.09.2016, Strobl am Wolfgangsee.
  • Workshop in Number Theory and Dynamics, 18.08.-19.08.2016, Göteborg.
  • 3 Days IV, 03.06.-04.06.2016, Copenhagen.
  • British Mathematical Colloquium, 21.-24.03.2016, Bristol.
  • 27. Nordic Congress of Mathematicians, 16.-20.03.2016, Stockholm. Invited.
  • 2015

  • 3 Days III, 04.12.-05.12.2015, Göteborg.
  • LMS-CMI Summer School on Diophantine Equations, 15.09.-19.09.2015, Baskerville Hall, Hay-on-Wye.
  • Analytic Number Theory and Diophantine Geometry, 07.09.-11.09.2015, Hannover.
  • 4. Göttingen-Hannover Number Theory Workshop, 09.07.2015, Hannover.
  • Quantitative arithmetic geometry, 22.06.-26.06.2015, Institut Mittag-Leffler, Stockholm. Invited.
  • 3. Göttingen-Hannover Number Theory Workshop, 24.04.2015, Göttingen.
  • 2. Göttingen-Hannover Number Theory Workshop, 06.02.2015, Göttingen.
  • 2014

  • 1. Göttingen-Hannover Number Theory Workshop, 21.11.2014, Hannover.
  • Analytic Number Theory, 29.09.-03.10.2014, Oxford.
  • Bounded Gaps Between Primes, LMS-CMI Research School. 22.-26.09.2014, Oxford.
  • PTM-DMV Joint Meeting. 17.-20.09.2014, Poznań. Invited.
  • ENFANT-ELEFANT workshop on analytic number theory. 11.-18.07.2014, Bonn. Invited.
  • Automorphic Forms and Arithmetic. 10.-14.02.2014, Göttingen.
  • 2013

  • Analytic Number Theory. 20.-26.10.2013, Oberwolfach. Invited.
  • Wolfgang M. Schmidt 80th Birthday Conference. 08.-11.10.2013, Wien.
  • Etienne Fouvry 60th Birthday Conference. 17.-21.06.2013, Marseille.
  • Rational Points - Geometric, Analytic and Explicit Approaches. 26.-31.05.2013, Warwick.
  • TCC Number Theory Day. 21.05.2013, Bristol.
  • 2012

  • Synergies And Vistas in Analytic Number Theory. 03.-07.09.2012, Oxford.
  • Analytic methods for diophantine problems. 04.-08.06.2012, Göttingen. Invited.
  • Langlands Day. 13.09.2011, Warwick.
  • Young Researchers in Mathematics 2012. 02.-04.04.2012, Bristol. Member of the organising committee.
  • 2011

  • Paul Turán Memorial Conference. 22.-26.08.2011, Budapest.
  • TCC Number Theory Day. 28.02.2011, London (Imperial College).
  • 2010

  • Analytic Number Theory. 06.-10.04.2010, Göttingen.
  • Conferences

  • Arithmetic (and) Harmonic Analysis. Institut Mittag-Leffler, 31.05.-04.06.2021.
  • 3 Days XI. Göteborg, 15.11.-16.11.2019.
  • Where Geometry meets Number Theory, Conference in honour of Per Salberger's 60th birthday. Göteborg, 17.07.-19.07.2017.
  • 3 Days V. Göteborg, 25.11.-26.11.2016.
  • Young Researchers in Mathematics 2012. Bristol 02.-04.04.2012.
  • Seminars

  • Seminar for Algebraic Geometry and Number Theory, Gothenburg, Autumn 2016.
  • Junior Number Theory, Göttingen, Winter 2013 - Summer 2015.
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