Julia Brandes

Associate Professor at Algebra and geometry

My research interests lie in the area of analytic number theory, especially applications of the Hardy-Littlewood circle method. This is a Fourier-analytic method for estimating the number of solutions of diophantine equations which has been developed in the 1920s. But although the basic method is quite classical, its versatility makes it a strong tool that continues to yield new and exciting results. Furthermore, since polynomial equations occupy a central position in many fields of mathematics, results obtained by the circle method find applications in a wide range of problems.

Source: chalmers.se
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Showing 10 publications

2022

ON THE INHOMOGENEOUS VINOGRADOV SYSTEM

Julia Brandes, Kevin Hughes
Bulletin of the Australian Mathematical Society. Vol. In Press
Journal article
2021

On generating functions in additive number theory, II: lower-order terms and applications to PDEs

Julia Brandes, S. T. Parsell, C. Poulias et al
Mathematische Annalen. Vol. 379 (1-2), p. 347-376
Journal article
2021

Rational lines on cubic hypersurfaces

Julia Brandes, Rainer Dietmann
Mathematical Proceedings of the Cambridge Philosophical Society. Vol. 171 (1), p. 99-112
Journal article
2021

The density of rational lines on hypersurfaces: a bihomogeneous perspective

Julia Brandes
Monatshefte für Mathematik. Vol. 195 (2), p. 191-231
Journal article
2021

Optimal mean value estimates beyond Vinogradov's mean value theorem

Julia Brandes, Trevor D. Wooley
Acta Arithmetica. Vol. 200 (2), p. 149-182
Journal article
2018

On the number of linear spaces on hypersurfaces with a prescribed discriminant

Julia Brandes
Mathematische Zeitschrift. Vol. 289 (3-4), p. 803-827
Journal article
2017

Vinogradov systems with a slice off

Julia Brandes, Trevor D. Wooley
Mathematika. Vol. 63 (3), p. 797-817
Journal article
2017

Simultaneous Additive Equations: Repeated and Differing Degrees

Julia Brandes, S. T. Parsell
Canadian Journal of Mathematics. Vol. 69 (2), p. 258-283
Journal article
2017

Linear spaces on hypersurfaces over number fields

Julia Brandes
Michigan Mathematical Journal. Vol. 66 (4), p. 769-784
Journal article
2017

The Hasse Principle for Systems of Quadratic and Cubic Diagonal Equations

Julia Brandes
Quarterly Journal of Mathematics. Vol. 68 (3), p. 831-850
Journal article

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Showing 1 research projects

2018–2021

Higher-dimensional structures on hypersurfaces

Julia Brandes Algebra and geometry
Swedish Research Council (VR)

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