(click here for less standard but outdated pic)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

Yale University

10 Hillhouse Avenue

New Haven, CT 06510

phone: (203)-432-4689

firstname.lastname@yale.edu

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.

curriculum vitae

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, arxiv
- 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). , accepted. - (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 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)