(click here for less standard but outdated pic)
I am an Assistant Professor and the Director of Undergraduate Studies in the Math Department at Yale. I can be reached via
Office: 456 DL
Department of Mathematics
10 Hillhouse Avenue
New Haven, CT 06510
My main field of research is Analysis. I like questions combining PDEs, Spectral Theory, Harmonic Analysis
and all sorts of applications. My research is supported by NSF DMS-1763179 and the Sloan Foundation.
Office Hours: see for Office Hours
Spring 2019: MATH 724 (The Heat Kernel), TTh 11:35-12:50
All relevant information will be posted in the canvas system. In case of questions, send me an email.
- A forgotten Theorem of Schoenberg on one-sided integral averages, arxiv
- Poissonian Pair Correlation in Higher Dimensions, arxiv
- (with Jianfeng Lu and Chris Sogge) Approximating Pointwise Products of Laplacian Eigenfunctions, arxiv
- A Nonlocal Transport Equation Describing Roots of Polynomials Under Differentiation, arxiv
- Quantitative Homogenization and Convergence of Moving Averages, arxiv
- (with Raphy Coifman) A Remark on the Arcsine Distribution and the Hilbert Transform arxiv
- (with Trevor Richards) Leaky Roots and Stable Gauss-Lucas Theorems, arxiv, Complex Variables and Elliptic Equations, accepted.
- (with Peter W. Jones) Localization of Neumann Eigenfunctions near Irregular Boundaries, arxiv, Nonlinearity, accepted.
- A metric Sturm-Liouville theory in two dimensions, arxiv
- The Hermite-Hadamard inequality in higher dimensions, arxiv, Journal of Geometric Analysis, accepted.
- (with Hau-tieng Wu) On Zeroes of Random Polynomials and Applications to Unwinding, arxiv.
- (with Eric Chi) Recovering Trees with Convex Clustering, arxiv
- A Stability Version of the Gauss-Lucas Theorem and Applications, arxiv, J. Aust. Math. Soc., accepted.
- A Compactness Principle for Maximizing Smooth Functions over Toroidal Geodesics, arxiv, Bull. Aust. Math. Soc., accepted.
- (with Jakob Kapeller and Matthias Aistleitner) Citation Patterns in Economics and Beyond, Science in Context, accepted.
- (with Alex Cloninger) On the Dual Geometry of Laplacian Eigenfunctions, arxiv, Experimental Mathematics, accepted.
- Electrostatic Interpretation of Roots of Orthogonal Polynomials, arxiv, Proc. Amer. Math. Soc., 146, 5323–5331 (2018).
- An Endpoint Alexandrov Bakelman Pucci Estimate in the Plane, arxiv, Canad. Math. Bull., accepted.
- Quantitative Projections in the Sturm Oscillation Theorem, arxiv
- (with Jianfeng Lu and Matthias Sachs) Quadrature Points via Heat Kernel Repulsion, arxiv
- Wasserstein Distance, Fourier Series and Applications, arxiv
- (with George Linderman) Numerical Integration on Graphs: where to sample and how to weigh, arxiv
- Generalized Designs on Graphs: Sampling, Spectra, Symmetries, arxiv
- (with Dmitriy Bilyk and Feng Dai) General and Refined Montgomery Lemmata, arxiv, Math. Annalen, accepted.
- A Sharp Estimate for Probability Distributions, arxiv
- (with George Linderman, Manas Rachh, Jeremy Hoskins, Yuval Kluger) Efficient Algorithms for t-distributed Stochastic Neighborhood Embedding, arxiv, Nature Methods, accepted.
- On the Spectral Resolution of Products of Laplacian Eigenfunctions, arxiv, Journal of Spectral Theory, accepted.
- (with Sam Johnson) The Aesthetic Psychology of Mathematics, SSRN (long) and
arXiv (abridged), Math. Intelligencer, to appear.
- (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, Yuval Kluger) Randomized Near Neighbor Graphs, Giant Components, and Applications in Data Science, arxiv
- 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
- Oscillatory functions vanish on a large set, arxiv
- 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
- (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, accepted.
- (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., accepted.
- (with SUMRY 2016) On algorithms to calculate integer complexity, arxiv, Integers, accepted.
- 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 Mathematics Magazine, accepted.
- Refined Heinz-Kato-Loewner inequalities, arxiv, Journal of Spectral Theory, accepted.
- 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.
- A Short Note on Integer Complexity, Contributions to Discrete Mathematics 9 (2014), 63 - 69
- (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.
Bristol (10.-12. Jan)
Meeting on Sampling, Uncertainty Principles, and Combinatorial Methods in Harmonic Analysis, BCAM (Bilbao), (15.-17. Jan)
Memorial Conference in Honor of Alan McIntosh, ANU (Canberra) (10.-17. Feb.)
Optimal and Random Point Configurations (26. Feb - 2. Mar), ICERM
Analysis Seminar, UC San Diego (11. Mar - 14. Mar)
Colloquium, University of Oregon (30. April)
Analysis seminar, University of Oregon (1. May)
NTNU Trondheim, Norway (31. May - 1. June)
Harmonic Analysis and Applications (3. Jun - 9. Jun), Strobl (Austria)
Harmonic Analysis, IAS/Park City, Utah (July)
Norbert Wiener Center, U Maryland (Nov. 6)
Harmonic Analysis and PDE Seminar, CUNY (Nov. 9)
Western Washington University (Nov. 19)
University of Rochester (Jan 17)
University of Connecticut (Feb 21)
University of Michigan (Feb 28)
Wisconsin-Madison (Apr 2)
Duke (Apr 22 - 25)
Vietnam-USA Joint Mathematical Meeting, Quy Nhon, Vietnam (Jun 10-13)
Shape Optimization with Surface Interactions, American Institute of Mathematics (Jun 17 - 21)
Algorithms and Complexity for Continuous Problems, Dagstuhl (Aug. 18 -23)
Computational Harmonic Analysis and Data Science, BIRS (Oaxaca) (Oct. 27 - Nov. 1)