Publications

Universal lower bounds for Dirichlet eigenvalues, arxiv

On differences of two harmonic numbers arxiv

(with Bandeira and Mixon) A lower bound for the Balan-Jiang matrix problem, arxiv

Randomly Pivoted Partial Cholesky: Random How? arxiv

On a problem involving unit fractions arxiv

A note on approximate Hadamard matrices arxiv, Designs, Code and Cryptography , accepted.

(with Thomas) Conformally rigid graphs, arxiv

Bad Science Matrices arxiv

Sums of square roots that are close to an integer arxiv, J. Number Theory, accepted.

Nonlinear recursions on the reals and a problem of Graham, arxiv

(with Raghav Venkatraman), Dirichlet eigenfunctions with nonzero mean value, arxiv

(with Mariana Smit Vega Garcia) An Almgren monotonicity formula for discrete harmonic functions, arxiv

Random Growth via Gradient Flow Aggregation, arxiv

(with Ovall, Quan, Reid) On localization of eigenfunctions of the magnetic Laplacian, arxiv

(with Bilyk, Mastrianni), Single radius spherical cap discrepancy via gegenbadly approximable numbers arxiv

(with Bilyk, Chang, Heinävaara, Matzke) A random line intersects S^2 in two probabilistically independent locations, arxiv

(with Ottolini) Greedy Matching in Optimal Transport with concave cost, arxiv

(with Babecki and Thomas) Spectrahedral Geometry of Graph Sparsifiers, arxiv

(with Faulhuber) Maximal polarization for periodic configurations on the real line, arxiv

(with Ottolini) Concentration of Hitting Times in Erdos-Renyi graphs, arxiv

(with Bilyk, Mastrianni, Matzke) Polarization and Greedy Energy on the Sphere, arxiv

(with Devriendt and Ottolini) Graph curvature via resistance distance, arxiv

Local sign changes of polynomials, arxiv

(with Shubham Gupta) Rearrangement Inequalities on the Lattice Graph, arxiv

(with Andrea Ottolini) Guessing cards with complete feedback, arxiv

Quadratic Crofton and sets that see themselves as little as possible, arxiv

(with Hoskins and Quan) Magnetic Schrodinger operators and landscape functions, arxiv

An Inequality Characterizing Convex Domains, arxiv

Discrete Rearrangements and the Polya-Szegő Inequality on Graphs, arxiv

(with Burdzy, Hoskins) From pinned billiard balls to partial differential equations, arxiv

Some Remarks on the Erdős Distinct Subset Sums Problem, arxiv, Int. J. Number Theory, accepted.

(with Anna Gilbert and Yulan Zhang) May the force be with you, arxiv

An elementary proof of a lower bound for the inverse of the star discrepancy, arxiv, J. Complexity, accepted.

On Combinatorial Properties of Greedy Wasserstein Minimization, arxiv

Approximate Solutions of Linear Systems at a Universal Rate, arxiv, SIAM J. Matrix Analysis and Applications, accepted.

An Agmon estimate for Schrodinger operators on Graphs, arxiv, Lett. Math. Phys., accepted.

(with Rekha Thomas) Random Walks, Equidistribution and Graphical Designs arxiv

The first eigenvector of a distance matrix is nearly constant arxiv, Discrete Math., accepted.

(with Alaifari, Bartolucci, Wellershoff) On the connection between uniqueness from samples and stability in Gabor phase retrieval arxiv, Sampling Theory, Signal Processing, and Data Analysis, accepted.

(with Bamdad Hosseini) Intrinsic Sparsity of Kantorovich Solutions arxiv, Comptes Rendus Mathematique, accepted.

Sums of Distances on Graphs and Embeddings into Euclidean Space arxiv, Mathematika, accepted.

Curvature on Graphs via Equilibrium Measures arxiv, J. Graph Theory, accepted.

The Boundary of a Graph and its Isoperimetric Inequality arxiv, J. Discrete Applied Mathematics, accepted.

(with Hau-tieng Wu) Fundamental component enhancement via adaptive nonlinear activation functions, arxiv, App. Comp. Harm. Anal. , accepted.

Quantum Entanglement and the Growth of Laplacian Eigenfunctions arxiv, Comm. PDE, accepted.

(with Betermin, Faulhuber), A variational principle for Gaussian lattice sums, arxiv

Effective Bounds for the Decay of Schrodinger Eigenfunctions and Agmon bubbles, arxiv, Israel J. Math, accepted.

(with Hau-tieng Wu) Eigenvector phase retrieval: recovering eigenvectors from the absolute value of their entries, arxiv, Linear Algebra and Applications, accepted.

(with George Linderman) Dimensionality Reduction via Dynamical Systems: the case of t-SNE, SIAM Review 64, p. 153-178 (2022).

(with Raphy Coifman and Nick Marshall) A common variable minimax theorem for graphs, arxiv, FoCM, accepted.

Quantile-Based Random Kaczmarz for corrupted linear systems of equations, arxiv, Information and Inference, accepted.

An upper bound on the Hot Spots constant, arxiv, Revista Matematica Iberoamericana, accepted.

The product of two high-frequency Graph Laplacian eigenfunctions is smooth, arxiv, Discrete Mathematics, accepted.

(with Beltran, Betermin, Grabner), How well-conditioned can the eigenvalue problem be?, arxiv, Math. Comp. 91, p. 1237-1245 (2022).

A Graph Decomposition motivated by the Geometry of Randomized Rounding, arxiv

On Concavity of Solutions of the nonlinear Poisson equation, arxiv, Archive for Rational Mechanics and Analysis 244, p. 209-224 (2021).

(with Ofir Lindenbaum) Refined Least Squares for Support Recovery, arxiv, Signal Processing 195, number: 108493 (2022).

(with Yulan Zhang), t-SNE, Forceful Colorings and Mean Field Limits, arxiv GitHub, Res. Math. Sci. 9, number: 42 (2022).

Max-Cut via Kuramoto-type Oscillators, arxiv, SIAM Journal on Applied Dynamical Systems, accepted.

A Pointwise Inequality for Derivatives of Solutions of the Heat Equation in Bounded Domains, arxiv

(with Jianfeng Lu), Neural Collapse under Cross-Entropy Loss, arxiv, Applied and Computational Harmonic Analysis 59, p. 224-251 (2022).

(with Korssjoen, Li, Tripathi, Zhang) Finding Structure in Sequences of Real Numbers via Graph Theory: a Problem List, arxiv, Involve 15, 251-270 (2022).

On the Logarithmic Energy of Points on S^2, arxiv, Journal d'Analyse Mathematique, accepted.

(with Murphey Lu), Fast localization of eigenfunctions via smoothed potentials, arxiv, Journal of Scientific Computing 90, number: 38 (2022).

On a Kantorovich-Rubinstein Inequality, arxiv, J. Math. Anal. Appl., 501, 125185 (2021).

(with Greengard, Liu, Tsyvinski) Factor Clustering with t-SNE, ssrn

Free Convolution Powers via Roots of Polynomials, arxiv, Experimental Math. , accepted.

Surrounding the solution of a Linear System of Equations from all sides, arxiv, Quart. Appl. Math. 79, p. 419-429 (2021).

Using Expander Graphs to test whether samples are iid, arxiv

(with Noah Kravitz) The Smoothest Average: Dirichlet, Fejer and Chebychev, arxiv, Bull. London Math. Soc. 53, p. 1801-1815 (2021).

On the Regularization Effect of Stochastic Gradient Descent applied to Least Squares, arxiv, ETNA 54, p. 610-619 (2021).

A Weighted Randomized Kaczmarz Method for Solving Linear Systems, arxiv, Math. Comp. 90, p. 2815-2826 (2021).

Randomized Kaczmarz converges along small singular vectors, arxiv, SIAM J. Matrix Anal. Appl. 42, p. 608-615 (2021).

Polynomials with Roots on the Unit Circle: Regularity of Leja sequences, arxiv, Mathematika 67, p. 553-268 (2021).

(with Jeremy Hoskins) Semicircle Law for Derivatives of Random Polynomials, arxiv, IMRN 13,p. 9784-9809 (2022).

Fourier Uncertainty Principles, Scale Space Theory and the Smoothest Average, arxiv, Math. Res. Lett. 28,p. 1851-1874 (2021).

On the Stability of Fourier Phase Retrieval, arxiv, J. Fourier Anal. Appl. 28, no. 29 (2022)

(with Aleh Tsyvinski) On Vickreys Income Averaging, arxiv

A Spectral Approach to the Shortest Path Problem, arxiv, Linear Algebra and its Applications 620, p. 182-200 (2021).

(with Adela DePavia) Spectral Clustering Revisited: Information Hidden in the Fiedler Vector, arxiv, Foundations of Data Science 3, 225-249 (2021).

(with Ofir Lindenbaum) Randomly Aggregated Least Squares for Support Recovery, arxiv, Signal Processing, 180, 107858 (2021).

Regularized Potentials of Schrodinger Operators and a Local Landscape Function, arxiv, Comm. PDE 46,p. 1262-1279 (2021).

(with Jaffe, Kluger, Lindenbaum, Patsenker, Peterfreund), The Spectral Underpinning of word2vec, arxiv, Front. Appl. Math. Stat.

(with Jeremy Hoskins), Towards Optimal Gradient Bounds of the Torsion Function in the Plane, arxiv, Journal of Geometric Analysis 31, p. 7812-7841 (2021).

(with Roy Lederman), Extreme Values of the Fiedler Vector on Trees, arxiv

(with Jianfeng Lu), Synchronization of Kuramoto Oscillators in Dense Networks, arxiv, Nonlinearity, 33, 5905 (2020).

(with Sean O'Rourke) A Nonlocal Transport Equation Modeling Complex Roots of Polynomials under Differentiation arxiv, Proc. Amer. Math. Soc., 149, p. 1581-1592 (2021).

(with Louis Brown) On the Wasserstein Distance between Classical Sequences and the Lebesgue Measure arxiv, Trans. Amer. Math. Soc., 373, p. 8943-8962 (2020).

(with Louis Brown) Positive-definite Functions, Exponential Sums and the Greedy Algorithm: a curious Phenomenon arxiv, Journal of Complexity, 61, 101485 (2020).

(with Jianfeng Lu), Optimal Trapping of Brownian Motion: A Nonlinear Analogue of the Torsion Function, arxiv, Potential Analysis 54, p. 687-698 (2021)

Hot Spots in Convex Domains are in the Tips (up to an Inradius), arxiv, Comm. PDE, 45, p. 641-654 (2020).

A Wasserstein Inequality and Minimal Green Energy on Compact Manifolds, arxiv, J. Functional Analysis, 281 (2021).

(with Beck, Brandolini, Burdzy, Henrot, Langford, Larson, Smits), Improved Bounds for Hermite-Hadamard Inequalities in Higher Dimensions, arxiv, Journal of Geometric Analysis 31, p. 801-816 (2021).

On Sublevel Set Estimates and the Laplacian, arxiv, Potential Analysis 55, p. 11-28 (2021).

(with Amir Sagiv), Transport and Interface: an Uncertainty Principle for the Wasserstein distance, arxiv, SIAM J. Math. Anal., 52, p. 3039-3051 (2020).

(with Jianfeng Lu), A Dimension-Free Hermite-Hadamard Inequality via Gradient Estimates for the Torsion Function, arxiv, Proc. Amer. Math. Soc., 148, p. 673-679 (2020).

(with Aleh Tsyvinski) Tax Mechanisms and Gradient Flows arxiv

(with Rima Al-Aifari, Xiuyuan Cheng, Lillian Pierce), On Matrix Rearrangement Inequalities, arxiv, Proc. Amer. Math. Soc., 148, p. 1835-1848 (2020).

Roots of trigonometric polynomials and the Erdos-Turan theorem, arxiv, Mathematika, 66, p. 245-254 (2020).

(with Rick Barnard) Three Convolution Inequalities on the Real Line with Connections to Additive Combinatorics arxiv, Journal of Number Theory, 207, p. 42-55 (2020).

(with Markus Faulhuber) An Extremal Property of the Hexagonal Lattice arxiv, Journal of Statistical Physics, 177, p. 285-298 (2019). .

(with Felipe Goncalves and Diogo Oliveira e Silva) A Universality Law For Sign Correlations of Eigenfunctions of Differential Operators arxiv, Journal of Spectral Theory, 11, p. 661-676 (2021).

(with Dmitry Kobak, George Linderman, Yuval Kluger, Philipp Berens) Heavy-tailed kernels reveal a finer cluster structure in t-SNE visualisations, arxiv, ECML PKDD 2019

Dynamically Defined Sequences with Small Discrepancy, arxiv, Monatshefte Math., 191, p. 639-655 (2020).

A Nonlocal Functional Promoting Low-Discrepancy Point Sets, arxiv, Journal of Complexity, 54, 101410 (2019).

The best way to reconcile your past is exponentially, arxiv, American Mathematical Monthly, 127, p. 64-69 (2020).

Poissonian Pair Correlation in Higher Dimensions, arxiv, Journal of Number Theory, 208, p. 47-58 (2020).

(with Jianfeng Lu and Chris Sogge) Approximating Pointwise Products of Laplacian Eigenfunctions, arxiv, Journal of Functional Analysis, 373, p. 3271-3282 (2019).

A Nonlocal Transport Equation Describing Roots of Polynomials Under Differentiation, arxiv, Proc. Amer. Math. Soc., 147, p. 4733-4744 (2019).

Quantitative Homogenization and Convergence of Moving Averages, arxiv

(with Raphy Coifman) A Remark on the Arcsine Distribution and the Hilbert Transform arxiv, Journal of Fourier Analysis and Applications, 25 p. 2690-2696 (2019), see also.

(with Trevor Richards) Leaky Roots and Stable Gauss-Lucas Theorems, arxiv, Complex Variables and Elliptic Equations 64, p. 1898-1904 (2019).

(with Peter W. Jones) Localization of Neumann Eigenfunctions near Irregular Boundaries, arxiv, Nonlinearity 32, p. 768-776 (2019).

A metric Sturm-Liouville theory in two dimensions, arxiv, Calculus of Variations and Partial Differential Equations 59, article 12 (2020).

The Hermite-Hadamard inequality in higher dimensions, arxiv, Journal of Geometric Analysis, 30, p. 466-483 (2020).

(with Hau-tieng Wu) On Zeroes of Random Polynomials and Applications to Unwinding, arxiv, IMRN,13, p. 10100-10117 (2021).

(with Eric Chi) Recovering Trees with Convex Clustering, arxiv, SIAM J. Math. Data Science, 1, p. 383-407 (2019).

A Stability Version of the Gauss-Lucas Theorem and Applications, arxiv, J. Aust. Math. Soc. 109, p. 262-269 (2020).

A Compactness Principle for Maximizing Smooth Functions over Toroidal Geodesics, arxiv, Bull. Aust. Math. Soc. 100, p. 148-154 (2019).

(with Jakob Kapeller and Matthias Aistleitner) Citation Patterns in Economics and Beyond, Science in Context, 32, p. 361 - 380 (2019).

(with Alex Cloninger) On the Dual Geometry of Laplacian Eigenfunctions, arxiv, Experimental Mathematics, 30, p. 283-293, (2021).

Electrostatic Interpretation of Roots of Orthogonal Polynomials, arxiv, Proc. Amer. Math. Soc., 146, p. 5323-5331 (2018).

An Endpoint Alexandrov Bakelman Pucci Estimate in the Plane, arxiv, Canad. Math. Bull., 62, p. 643-651 (2019).

Quantitative Projections in the Sturm Oscillation Theorem, arxiv, J. Math. Pure Appl., 144, p. 1-16 (2020).

(with Jianfeng Lu and Matthias Sachs) Quadrature Points via Heat Kernel Repulsion, arxiv, Constructive Approximation, 51, p. 27-48 (2020).

Wasserstein Distance, Fourier Series and Applications, arxiv, Monatshefte Math. , 194, p. 305-338 (2021).

(with George Linderman) Numerical Integration on Graphs: where to sample and how to weigh, arxiv, Mathematics of Computation, 89, p. 1933-1952 (2020).

Generalized Designs on Graphs: Sampling, Spectra, Symmetries, arxiv, Journal of Graph Theory, 93, p. 253-267 (2020), Gallery of examples,

Refined Heinz-Kato-Loewner inequalities, arxiv, Journal of Spectral Theory, 9, p. 1-20. (2018).

(with Dmitriy Bilyk and Feng Dai) General and Refined Montgomery Lemmata, arxiv, Math. Annalen, 373, p. 1283-1297 (2019).

A Sharp Estimate for Probability Distributions, arxiv, Stat. Prob. Lett. 155 (2019), 108584. .

(with George Linderman, Manas Rachh, Jeremy Hoskins, Yuval Kluger) Efficient Algorithms for t-distributed Stochastic Neighborhood Embedding, arxiv, Nature Methods, 16, p. 243-245 (2019).

On the Spectral Resolution of Products of Laplacian Eigenfunctions, arxiv, Journal of Spectral Theory, 9, p. 1367-1384 (2019)

(with Sam Johnson) Intuitions about mathematical beauty: A case study in the aesthetic experience of ideas, Cognition, 189, 242-259 (2019).

(with Sam Johnson) The Aesthetic Psychology of Mathematics, arXiv, Math. Intelligencer, 41, 67-70 (2019)

(with Janna Lierl) A Local Faber-Krahn inequality and Applications to Schrodinger's Equation, arxiv, Comm. PDE, 43, 66-81 (2018).

Varadhan Asymptotics for the Heat Kernel on Finite Graphs, arxiv

(with George Linderman, Gal Mishne, Ariel Jaffe, Yuval Kluger) Randomized Near Neighbor Graphs, Giant Components, and Applications in Data Science, arxiv, Journal of Applied Probability, 57 (2020), p. 458 - 476.

Poissonian Pair Correlation and Discrepancy, arxiv, Indag. Math. 29, 1167-1178 (2018).

(with Jianfeng Lu) Detecting Localized Eigenstates of Linear Operators, arxiv, Res. Math. Sci. 5, no. 34 (2018)

Spectral Limitations of Quadrature Rules and Generalized Spherical Designs, arxiv, IMRN, 16, 12265-12280 (2021).

Oscillatory functions vanish on a large set, arxiv, Asian J. Math., 24, 177-190 (2020).

Exponential Sums and Riesz energies, arxiv, Journal of Number Theory, 182, 37-56 (2018).

(with Nick Marshall) Triangles capturing many lattice points, arxiv, Mathematika, 64, 551-582 (2018).

(with George Linderman) Clustering with t-SNE, provably, arxiv, SIAM J. Math. Data Science, 1, 313-332 (2019).

(with Xiuyuan Cheng and Gal Mishne) The Geometry of Nodal Sets and Outlier Detection, arxiv, Journal of Number Theory, 185 , 48-64 (2018).

Topological Bounds on Fourier Coefficients and Applications to Torsion, arxiv, Journal of Functional Analysis, 274, 1611-1630 (2018).

(with Noah Kravitz) Ulam Sequences and Ulam sets, arxiv, Integers, 18 , A80 (2018).

(with Florian Pausinger and Manas Rachh) Optimal Jittered Sampling for Two Points in the Unit Square, arxiv, Statist. Probab. Lett., 132, 55-61 (2018).

(with Uri Shaham) Stochastic Neighbor Embedding separates well-separated clusters, arxiv

(with Bogdan Georgiev and Mayukh Mukherjee) A Spectral Gap Estimate and Applications, arxiv, Potential Analysis, 49, 635-645 (2018).

(with Xiuyuan Cheng and Manas Rachh) On the Diffusion Geometry of Graph Laplacians and Applications, arxiv, Appl. Comp. Harm. Anal., 46, p. 674-688 (2019).

(with SMALL 2016) On algorithms to calculate integer complexity, arxiv, Integers 19, A12, (2019).

Well-Distributed Great Circles on S^2, arxiv, Discrete & Computational Geometry, 60, 40-56 (2018).

Fast Escape in Incompressible Vector Fields, arxiv, Monatshefte Math., 186, 525-537 (2018).

(with Jakob Kapeller and Matthias Aistleitner) The Power of Scientometrics and the Development of Economics, Journal of Economics Issues, 52, 816-834 (2018).

(with Jianfeng Lu) A Variation on the Donsker-Varadhan Inequality for the Principal Eigenvalue, arxiv, Proc. Royal Soc. A, 473 (2017).

(with Jakob Kapeller) Stability, Fairness and Random Walks in the Bargaining Problem, arxiv, Physica A, 488, 60-71 (2017).

Localized Quantitative Criteria for Equidistribution, arxiv, Acta Arithmetica, 180, 183-199 (2017).

(with Manas Rachh) On the location of maxima of solutions of Schroedinger's equation, arxiv, Comm. Pure. Appl. Math., 71, 1109-1122 (2018).

(with Raphy Coifman and Hau-tieng Wu) Carrier frequencies, holomorphy and unwinding, arxiv, SIAM J. Math. Anal., 49 , 4838-4864 (2017).

(with Roy Lederman) Stability Estimates for Truncated Fourier and Laplace Transforms, arxiv, Integral Equations and Operator Theory, 87, 529-543 (2017).

An amusing sequence of functions, arxiv, Mathematics Magazine, 91, 262-266 (2018). pictures more fun

(with Alex Cloninger) On Suprema of Autoconvolutions with an Application to Sidon sets, arxiv, Proc. Amer. Math. Soc.,145, 3191-3200 (2017).

(with Alex Cloninger) Spectral Echolocation via the Wave Embedding, arxiv, Appl. Comp. Harm. Anal., 43, 577-590 (2017).

(with Florian Pausinger, Heating a Room with Number Theory Math. Mag., 92, 99-106 (2019).

Localization of Quantum States and Landscape Functions, arxiv, Proc. Amer. Math. Soc., 145, 2895-2907 (2017).

A Hidden Signal in the Ulam sequence, arxiv, Experimental Mathematics, 23, 460-467 (2017).

(with Raphy Coifman) Nonlinear phase unwinding of functions arxiv, Journal of Fourier Analysis and Applications, 23, 778-809 (2017).

(with Felipe Goncalves and Diogo Oliveira e Silva) Hermite polynomials, linear flows on the torus, and an uncertainty principle for roots, arxiv, J. Math. Anal. Appl.,451, 678-711 (2017).

(with Markus Faulhuber) Optimal Gabor frame bounds for separable lattices and estimates for Jacobi theta functions, arxiv, J. Math. Anal. Appl., 445 , 407-422 (2017).

(with Yuke Li, Tianhao Wu and Nicholas Marshall) Extracting Geography from Trade Data, arxiv, Physica A, 473 205-212 (2017)

(with Jakob Kapeller) Emergent phenomena in scientific publishing: a simulation exercise, Research Policy 45, 1945-1952 (2016).

(with Alberto Enciso and Daniel Peralta-Salas) Prescribing the nodal set of the first eigenfunction in each conformal class, arxiv, IMRN, 54, 555-569.

Directional Poincare Inequalities along Mixing Flows, Arkiv för Matematik 54 , 555-569, 2016 arxiv .

A Filtering Technique for Markov Chains with Applications to Spectral Embedding, Applied and Computational Harmonic Analysis , 40 (2016), 575-587, arxiv.

(with Florian Pausinger) On the Discrepancy of Jittered Sampling, Journal of Complexity, 33 (2016), 199-216, arxiv

(with Rima Al-Aifari and Lillian Pierce) Lower bounds for the truncated Hilbert transform, Revista Matematica Iberoamericana, 32 (2016), 23-56, arxiv.

A Rigidity Phenomenon for the Hardy-Littlewood maximal function, Studia Mathematica, 229 , 263-278 (2015), arxiv

An Uncertainty Principle on compact manifolds, Journal of Fourier Analysis and Applications, 21 (2015), 575-599 arxiv.

(with Herbert Koch) Convolution Estimates for Singular Measures and Some Global Nonlinear Brascamp-Lieb Inequalities, arxiv, Proc. Roy. Soc. Edinburgh, 145 (2015), 1223-1237.

Sharp L^1 Poincare inequalities correspond to optimal hypersurface cuts, Archiv der Mathematik, 105 (2015), 179-188 arxiv.

On the Number of Positions in Chess without Promotion, International Journal of Game Theory 44, 761-767 (2015).

(with Florian Pausinger) Local Extrema in Quantum Chaos, Physics Letters A, 379 (2015), 535-541 arxiv.

Lower bounds on nodal sets of eigenfunctions via the heat flow, Communications in Partial Differential Equations, 39 (2014), arxiv.

New Bounds for the Traveling Salesman Constant, Advances in Applied Probability, 47 (2015), arxiv.

A Remark on Disk Packings and Numerical Integration of Harmonic Functions, Journal of Complexity: Oberwolfach Special Issue 31 (2015), 486-493, arxiv.

Dispersion dynamics for the generalized Korteweg-de Vries equation, Proceedings of the American Mathematical Society 143 (2015), 789-800, arxiv.

A Geometric Uncertainty Principle with an Application to Pleijel's Estimate, Annales Henri Poincare, 15 (2014), 2299 - 2319, arxiv.

(with Michaela Nieuwenhuis and James Robinson ), Minimal Periods for Ordinary Differential Equations in Strictly Convex Banach Spaces and Explicit Bounds for some L^p-Spaces, Journal of Differential Equations 256 (2014), 2846 - 2857, arxiv.

(with Jakob Kapeller) Modeling the Evolution of Preferences: An Answer to Schubert and Cordes, Journal of Institutional Economics 10 (2014), 337- 347 pdf.

(with Jakob Kapeller and Bernhard Schuetz ) The Impossibility of Rational Consumer Choice - A Problem and its Solution. Journal of Evolutionary Economics 23 (2013) 29 - 60, link.

(with Jakob Kapeller) How Formalism shapes Perception: An Experiment on Mathematics as a Language, International Journal of Pluralism and Economics Education 4 (2013): 138 - 156.

Random restricted matching and lower bounds for combinatorial optimization. Journal of Combinatorial Optimization 24 (2012) no.3, 280 - 298, link.

(with Erhard Aichinger) A proof of a Theorem by Fried and MacRae and applications to the composition of polynomial functions, Archiv der Mathematik 97 (2011) no.2, 115-124, link.

On the optimal interpoint distance sum inequality, Archiv der Mathematik 97 (2011) no.3, 289-298., link.

Extremal uniform distribution and random chord lengths, Acta Mathematica Hungarica 130 (2011) no.4, 321-339, link.

A note on implicitly defined sets in uniform distribution theory, Uniform Distribution Theory 6 (2011) no.2, 85-94, link.

The asymptotic behavior of the average $L^p-$discrepancies and a randomized discrepancy, The Electronic Journal of Combinatorics 17 (2010) R106, link.

A New Lower Bound for the Geometric Traveling Salesman Problem in Terms of Discrepancy, Operations Research Letters 38 (2010) no. 4, 318-319, link.

A note on the number of different inner products generated by a finite set of vectors, Discrete Mathematics 310 (2010) no. 5, 1112-1117, link.

Uniform distribution preserving mappings and variational problems Uniform Distribution Theory 4 (2009) no. 1, 117-145, link.

(with Friedrich Pillichshammer) Average distance between consecutive points of uniformly distributed sequences, Uniform Distribution Theory 4 (2009) no. 1, 51-67, link.