Research 
Research interests: number theory, analytic number theory, Diophantine geometry Here is a list of my recent preprints and publications.  Optimal quantitative weak approximation for projective quadrics (with Z. Huang and A. Shute), 52 pages, available on arXiv
 Points of bounded height on certain subvarieties of toric varieties (with M. Pieropan), arXiv:2403.19397, 22 pages
 Rational points near manifolds, homogeneous dynamics, and oscillatory integrals (with R. Srivastava and N. Technau), submitted
 Generalised quadratic forms over totally real number fields (with T. D. Browning and L. B. Pierce), J. Inst. Math. Jussieu, published online 2024: pp 1  54. doi:10.1017/S1474748024000161
 Hyperbola method on toric varieties (with M. Pieropan), Journal de l'École polytechnique  Mathématiques 11 (2024), 107 – 157
 Density of rational points near/on compact manifolds with certain curvature conditions (with S. Yamagishi), Adv. Math 403 (2022), Paper No. 108358, 36pp
 On prime values of binary quadratic forms with a thin variable (with P. Lam and S. Xiao), J. London Math. Soc. 102 (2) (2020), 749  772
 Diophantine inequalities for generic ternary diagonal forms, Int. Math. Res. Not., no.11 (2020), 3396–3416
 On the algebraic Brauer classes on open degree four del Pezzo surfaces (with J. Jahnel), J. Number Theory 203 (2019), 376  427
 On the frequency of algebraic Brauer classes (with J. Jahnel), Canad. Math. Bull. 62 (2019), 551  563
 Sarnak's saturation problem for complete intersections (with E. Sofos), Mathematika 65 (2019), no. 1, 1  56
 Strong approximation and a conjecture of Harpaz and Wittenberg (with T. D. Browning), Int. Math. Res. Not. 14 (2019), 4340  4369
 On integral points on degree four del Pezzo surfaces (with J. Jahnel), Israel J. Math. 222 (2017), no. 1, 21  62
 Counting rational points on hypersurfaces and higher order expansions, J. Number Theory 173 (2017), 332370
 Del Pezzo surfaces of degree four violating the Hasse principle are Zariski dense in the moduli scheme (with J. Jahnel), Annales de l'Institut Fourier 67, no.4 (2017), 17831807
 Representations of integers by systems of three quadratic forms (with L. B. Pierce and M. M. Wood), J. London Math. Soc. (3) 113, no.3 (2016), 289344
 On the number of certain Del Pezzo surfaces of degree four violating the Hasse principle (with J. Jahnel), Journal of Number Theory 162 (2016), 224254
 On the BrauerManin obstruction for degree four del Pezzo surfaces (with J. Jahnel), Acta Arithmetica 176 (2016), 301319
 Manin's conjecture for certain biprojective hypersurfaces, J. reine angew. Math. 714 (2016), 209250
 A variant of Weyl's inequality for systems of forms and applications, Advances in the theory of numbers, 207–218, Fields Inst. Commun. 77, Fields Inst. Res. Math. Sci., Toronto, ON, 2015
 Symmetries of rational functions arising in Ecalle's study of multiple zeta values (with A. Salerno and A. Tucker), in Women in Numbers Europe, Springer 2015, pp 153166.
 Bihomogeneous forms in many variables, J. Th. Nombres Bordeaux 26 (2014), 483506
 Norms as products of linear polynomials (with A. N. Skorobogatov), J. London Math. Soc. 89 (2014), 559580
Reports Field Arithmetic, Oberwolfach report 25/2018, 'The localglobal principle for rational points and a conjecture of Harpaz and Wittenberg' 

How to write a Bachelor's or Master's thesis with me 
If you would like to write a Bachelor's or Master's thesis with me, then please write me an email and we will start discussing. In this case it would be valuable for me to know which courses you have already attended, which courses you plan to take in the coming semester say, what your mathematical interests so far are and anything else that I should know and would be relevant in finding a topic. Normally, after first discussions about what your goals are and what your background is, we will then have a first meeting to discuss potential topics. If you already have something concrete in mind, that you would like to look at, then please let me know (though this is certainly not necessary, I'm very happy to suggest topics). Courses which would be ideal to take before starting a Bachelor thesis under my supervision: algebra and number theory, as well as a seminar in this direction Courses which would be ideal to take before starting a Master thesis under my supervision: 2 parts of a cycle and a seminar in the area of analytic number theory, number theory, diophantine geometry Here are a couple of examples of thesis that I supervised in the past Bachelor thesis:  A polynomial random walk in finite fields
 Werteverteilung multiplikativer Funktionen in Restklassen
 Gegenbeispiele zum Hasse Prinzip
 Progressionfree subsets and the polynomial method
 Prime generators
 The cap set problem
Master thesis:  Systems of Diophantine equations in many variables
 Two problems related to the circle method
 On Runge’s method
 Sieving and systems of quadratic equations
 Diophantine inequalities
 Prime lattice points in ovals
 Linear equations in dense sets of Sidon sets

