(click here for less standard but outdated pic)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: Tuesday 2pm -3pm, Thursday 2pm -3pm, see here for DUS Business
Spring 2019: MATH 724 (The Heat Kernel), TTh 11:35-12:50
- (with Dmitry Kobak, George Linderman, Yuval Kluger, Philipp Berens) Heavy-tailed kernels reveal a finer cluster structure in t-SNE visualisations,
- Dynamically Defined Sequences with Small Discrepancy, arxiv
- A Nonlocal Functional Promoting Low-Discrepancy Point Sets, arxiv
- A forgotten Theorem of Schoenberg on one-sided integral averages, arxiv, American Mathematical Monthly, accepted.
- 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, SIAM J. Math. Data Science, accepted.
- (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.
University of Rochester (Jan 17)
University of Connecticut (Feb 21)
University of Michigan (Feb 28)
Wisconsin-Madison (Apr 2)
Duke (Apr 22 - 25)
UMass Amherst (May 1)
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)