Stefan Steinerberger


(click here for less standard but outdated pic)
  
I am an Assistant Professor 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, where I like questions combining PDEs, geometry, spectral theory and harmonic analysis.
curriculum vitae

Teaching  

Fall 2017: MATH 310 (Introduction to Complex Analysis)
Spring 2018: MATH 247 (Partial Differential Equations)
Office Hours: tbd
All relevant information will be posted in the canvas system. In case of questions, send me an email.

Research  

  1. Oscillatory functions vanish on a large set, arxiv
  2. Exponential Sums and Riesz energies, arxiv, Journal of Number Theory, accepted
  3. (with Nick Marshall) Triangles capturing many lattice points, arxiv
  4. (with George Linderman) Clustering with t-SNE, provably, arxiv
  5. (with Xiuyuan Cheng and Gal Mishne) The Geometry of Nodal Sets and Outlier Detection, arxiv
  6. Topological Bounds on Fourier Coefficients and Applications to Torsion, arxiv
  7. (with Noah Kravitz) Ulam Sequences and Ulam sets, arxiv
  8. (with Florian Pausinger and Manas Rachh) Optimal Jittered Sampling for Two Points in the Unit Square, arxiv
  9. (with Uri Shaham) Stochastic Neighbor Embedding separates well-separated clusters, arxiv
  10. (with Bogdan Georgiev and Mayukh Mukherjee) A Spectral Gap Estimate and Applications, arxiv
  11. (with Jianfeng Lu) A Variation on the Donsker-Varadhan Inequality for the Principal Eigenvalue, arxiv, Proc. Royal Soc. A, accepted.
  12. (with Xiuyuan Cheng and Manas Rachh) On the Diffusion Geometry of Graph Laplacians and Applications, arxiv
  13. Well-Distributed Great Circles on S^2, arxiv
  14. (with Jakob Kapeller) Stability, Fairness and Random Walks in the Bargaining Problem, arxiv, Physica A, accepted,
  15. Fast Escape in Incompressible Vector Fields, arxiv
  16. (with Jakob Kapeller and Matthias Aistleitner) The Power of Scientometrics and the Development of Economics, Journal of Economics Issues, accepted.
  17. Localized Quantitative Criteria for Equidistribution, arxiv, Acta Arithmetica, accepted.
  18. (with Manas Rachh) On the location of maxima of solutions of Schroedinger's equation, arxiv, Comm. Pure. Appl. Math., accepted.
  19. (with Raphy Coifman and Hau-tieng Wu) Carrier frequencies, holomorphy and unwinding, arxiv, SIAM J. Math. Anal., accepted.
  20. (with Roy Lederman) Stability Estimates for Truncated Fourier and Laplace Transforms, arxiv, Integral Equations and Operator Theory, accepted.
  21. An amusing sequence of functions, arxiv, Mathematics Magazine, accepted.
  22. (with Alex Cloninger) On Suprema of Autoconvolutions with an Application to Sidon sets, arxiv, Proc. Amer. Math. Soc., accepted.
  23. (with Alex Cloninger) Spectral Echolocation via the Wave Embedding, arxiv, Appl. Comp. Harm. Anal., accepted.
  24. Refined Heinz-Kato-Loewner inequalities, arxiv, Journal of Spectral Theory, accepted.
  25. Localization of Quantum States and Landscape Functions, arxiv, Proc. Amer. Math. Soc., accepted.
  26. A Hidden Signal in the Ulam sequence, arxiv, Experimental Mathematics, accepted.
  27. (with Raphy Coifman) Nonlinear phase unwinding of functions arxiv, Journal of Fourier Analysis and Applications, accepted.
  28. (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 p. 678-711 (2017).
  29. (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).
  30. (with Yuke Li, Tianhao Wu and Nicholas Marshall) Extracting Geography from Trade Data, arxiv, Physica A, 473 p. 205-212 (2017)
  31. (with Jakob Kapeller) Emergent phenomena in scientific publishing: a simulation exercise, Research Policy 45 , p. 1945-1952 (2016).
  32. (with Alberto Enciso and Daniel Peralta-Salas) Prescribing the nodal set of the first eigenfunction in each conformal class, arxiv, IMRN, 54 , 555-569.
  33. Directional Poincare Inequalities along Mixing Flows, Arkiv för Matematik 54 , 555-569, 2016 arxiv .
  34. A Filtering Technique for Markov Chains with Applications to Spectral Embedding, Applied and Computational Harmonic Analysis , 40 (2016), 575-587, arxiv.
  35. (with Florian Pausinger) On the Discrepancy of Jittered Sampling, Journal of Complexity, 33 (2016), 199-216, arxiv
  36. (with Rima Al-Aifari and Lillian Pierce) Lower bounds for the truncated Hilbert transform, Revista Matematica Iberoamericana, 32 (2016), 23-56, arxiv.
  37. A Rigidity Phenomenon for the Hardy-Littlewood maximal function, Studia Mathematica, 229 , 263-278 (2015), arxiv
  38. An Uncertainty Principle on compact manifolds, Journal of Fourier Analysis and Applications, 21 (2015), 575-599 arxiv.
  39. (with Herbert Koch) Convolution Estimates for Singular Measures and Some Global Nonlinear Brascamp-Lieb Inequalities, arxiv, Proc. Roy. Soc. Edinburgh, 145 (2015), 1223–1237.
  40. Sharp L^1 Poincare inequalities correspond to optimal hypersurface cuts, Archiv der Mathematik, 105 (2015), 179-188 arxiv.
  41. On the Number of Positions in Chess without Promotion, International Journal of Game Theory 44, 761-767 (2015).
  42. (with Florian Pausinger) Local Extrema in Quantum Chaos, Physics Letters A, 379 (2015), 535-541 arxiv.
  43. Lower bounds on nodal sets of eigenfunctions via the heat flow, Communications in Partial Differential Equations, 39 (2014), arxiv.
  44. New Bounds for the Traveling Salesman Constant, Advances in Applied Probability, 47 (2015), arxiv.
  45. A Remark on Disk Packings and Numerical Integration of Harmonic Functions, Journal of Complexity: Oberwolfach Special Issue 31 (2015), 486-493, arxiv.
  46. Dispersion dynamics for the generalized Korteweg-de Vries equation, Proceedings of the American Mathematical Society 143 (2015), 789-800, arxiv.
  47. A Geometric Uncertainty Principle with an Application to Pleijel's Estimate, Annales Henri Poincare, 15 (2014), 2299 - 2319, arxiv.
  48. A Short Note on Integer Complexity, Contributions to Discrete Mathematics 9 (2014), 63 - 69
  49. (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.
  50. (with Jakob Kapeller) Modeling the Evolution of Preferences: An Answer to Schubert and Cordes, Journal of Institutional Economics 10 (2014), 337- 347 pdf.
  51. (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.
  52. (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.
  53. Random restricted matching and lower bounds for combinatorial optimization. Journal of Combinatorial Optimization 24 (2012) no.3, 280 - 298, link.
  54. (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.
  55. On the optimal interpoint distance sum inequality, Archiv der Mathematik 97 (2011) no.3, 289-298., link.
  56. Extremal uniform distribution and random chord lengths, Acta Mathematica Hungarica 130 (2011) no.4, 321-339, link.
  57. A note on implicitly defined sets in uniform distribution theory, Uniform Distribution Theory 6 (2011) no.2, 85-94, link.
  58. The asymptotic behavior of the average $L^p-$discrepancies and a randomized discrepancy, The Electronic Journal of Combinatorics 17 (2010) R106, link.
  59. A New Lower Bound for the Geometric Traveling Salesman Problem in Terms of Discrepancy, Operations Research Letters 38 (2010) no. 4, 318-319, link.
  60. 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.
  61. Uniform distribution preserving mappings and variational problems Uniform Distribution Theory 4 (2009) no. 1, 117-145, link.
  62. (with Friedrich Pillichshammer) Average distance between consecutive points of uniformly distributed sequences, Uniform Distribution Theory 4 (2009) no. 1, 51-67, link.

Travel/Events 2017  

Stanford (19.-20. Jan.)
AMS Sectional Meeting in Bloomington, Indiana (1.-2. Apr.)
Geometry, Analysis and Probability, Conference in Honor of P. Jones 65th birthday, KIAS (Seoul) (8.-12. May)
Combinatorial and Additive Number Theory (CANT 2017), New York (23.-26. May)
Oberwolfach: Real Analysis, Harmonic Analysis, and Applications (23 - 29 Jul.)
Duke (9.-11. Aug.)
Tractability of High Dimensional Problems and Discrepancy, Erwin Schrodinger Institute, Vienna (25.Sep. - 29.Sep.)
Colloquium, Binghamton (19. Oct.)
SIAM PDE 2017, Baltimore (9.-12.Dec.)
2018
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
Harmonic Analysis and Applications (3. Jun - 9. Jun), Strobl (Austria)
Harmonic Analysis, IAS/Park City, Utah (July)