Research

 My research interests are: Harmonic Analysis, Number Theory, Discrete and Convex Geometry.

You can find preprints to my papers below at ArXiv. 

Publications

Published

• A linear programming approach to Fuglede's conjecture in $\mathbb{Z}_p^3$,  Sampling Theory, Signal Processing, and Data Analysis, Vol. 22, Issue 1, article no. 3, pp. 16 (2024). 

• Fuglede's conjecture holds for cyclic groups of order pqrs (joint with Gergely Kiss, Gábor Somlai, Máté Vizer), Journal of Fourier Analysis and Applications, Vol. 28, Issue 5, article no. 79, pp. 23 (2022).

• Computing the covering radius of a polytope with an application to lonely runners (joint with Jana Cslovjecsek, Márton Naszódi, Matthias Schymura), Combinatorica, Vol. 42, Issue 4, 463-490 (2022).

• On the structure of spectral and tiling subsets of cyclic groups, Forum of Mathematics, Sigma, Vol. 10, e23, 1-42 (2022).

• Full spark frames in the orbit of a representation (joint with Vignon Oussa), Applied and Computational Harmonic Analysis, Vol. 49, Issue 3, 791-814 (2020).

• On the discrete Fuglede and Pompeiu problems, (joint with Gergely Kiss, Gábor Somlai, Máté Vizer), Analysis & PDE, Vol. 13, Issue 3, 765-788 (2020).

• Formal duality in finite cyclic groups, Constructive Approximation, Vol. 49, Issue 3, 607-652 (2019).

• Spark deficient Gabor frames, Pacific Journal of Mathematics, Vol. 294, No.1, 159-180 (2018).

• Rotations by roots of unity and Diophantine approximation, The Ramanujan Journal, Vol. 44, Issue 1, 105-113 (2017).

• Fuglede's conjecture on cyclic groups of order pnq (joint with Mihail N. Kolountzakis), Discrete Analysis 2017:12, 16pp.

• On the covering radius of lattice zonotopes and its relation to view-obstructions and the lonely runner conjecture (joint with Matthias Schymura), Aequationes Mathematicae, Vol. 91, Issue 2, pp 331-352 (2017).

• Polyhedral Gauss sums, and polytopes with symmetry (joint with Sinai Robins and Yichi Zhang), Journal of Computational Geometry, Vol. 7, No. 1, 149-170 (2016).

• A note on Gabor frames in finite dimensions, Applied and Computational Harmonic Analysis 38 (2), 318-330 (2015).

• Lattice-point enumerators of ellipsoids, Combinatorica 33 (6), 733-744 (2013).

• A note on the pyjama problem (joint with Máté Matolcsi and Imre Ruzsa), European Journal of Combinatorics 34 (7), 1071-1077 (2013).

• A discrete analogue for Minkowski's second theorem on successive minima, Advances in Geometry 12 (2), 365-380 (2012).

• An optimization problem related to Minkowski's successive minima, Discrete and Computational Geometry 43 (4), 784-797 (2010).