(click here for less standard but outdated pic)
I am a Gibbs Assistant Professor 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, where I like questions combining PDEs, geometry, spectral theory and harmonic analysis.
Spring 2017: MATH 231 (Vector Calculus and Linear Algebra II)
Spring 2017: AMTH 160 (The Structure of Networks)
Office Hours: to be determined
All relevant information will be posted in the canvas system. In case of questions, send me an email.
Most of my recent work is on the arxiv:
- (with Bogdan Georgiev and Mayukh Mukherjee) The van den Berg conjecture in two dimensions, arxiv
- (with Jianfeng Lu) A Variation on the Donsker-Varadhan Inequality for the Principal Eigenvalue, arxiv
- (with Xiuyuan Cheng and Manas Rachh) On the Diffusion Geometry of Graph Laplacians and Applications, arxiv
- An amusing sequence of functions, arxiv
- Well-Distributed Great Circles on S^2, arxiv
- (with Raphy Coifman and Hau-tieng Wu) Carrier frequencies, holomorphy and unwinding, arxiv
- (with Roy Lederman) Stability Estimates for Truncated Fourier and Laplace Transforms, arxiv
- (with Alex Cloninger) On Suprema of Autoconvolutions with an Application to Sidon sets, arxiv
- Fast Escape in Incompressible Vector Fields, arxiv
- (with Alex Cloninger) Spectral Echolocation via the Wave Embedding, arxiv, Appl. Comp. Harm. Anal., accepted.
- (with Manas Rachh) On the location of maxima of solutions of Schroedinger's equation, arxiv, Comm. Pure. Appl. Math., accepted.
- Refined Heinz-Kato-Loewner inequalities, arxiv, Journal of Spectral Theory, accepted.
- (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., in revision.
- (with Yuke Li, Tianhao Wu and Nicholas Marshall) Extracting Geography from Trade Data, arxiv, Physica A, accepted.
- (with Jakob Kapeller) Emergent phenomena in scientific publishing: a simulation exercise, Research Policy, accepted.
- Localization of Quantum States and Landscape Functions, arxiv, Proc. Amer. Math. Soc., accepted.
- A Hidden Signal in the Ulam sequence, arxiv, Experimental Mathematics, accepted.
- (with Raphy Coifman) Nonlinear phase unwinding of functions arxiv, Journal of Fourier Analysis and Applications, accepted.
- (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 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, Proceedings of the Royal Society of 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.
Princeton, Ergodic Theory Seminar (11. Feb.)
Urbana-Champaign, Colloquium (18. Feb)
Indiana University, Analysis Seminar (9. Mar)
Harmonic Analysis, Graphs and Learning, Hausdorff Center for Mathematics, Bonn (14. - 18. Mar)
TU Munich, Geometry Seminar (23. Mar)
Brown, PDE Seminar (15. April)
Duke, Analysis Seminar (2. May)
Conference in Harmonic Analysis in Honor of Michael Christ, Wisconsin-Madison (16. May - 20. May)
University of Vienna (2. Jun)
Time-Frequency Analysis and Related Topics, Strobl (Austria) (6. Jun - 10. Jun)
Discrepancy Theory, Varenna (Italy) (12. Jun - 18. Jun)
Williams College, (5. Jul - 7. Jul)
Yale, Analysis Seminar (20. Sep.)
University of Wisconsin-Madison, Colloquium (25. Oct.)
Cornell, Analysis Seminar (14. Nov.)
Waterloo, Colloquium (24. Nov.)
Toronto, Analysis Seminar (25. Nov.)
Princeton, IDeAS Seminar (30. Nov.)
University of Minnesota, Analysis Seminar (1. Dec.)
IMA, Data Science Seminar (2. Dec.)
USC, Colloquium (5. Dec.)
Stony Brook, Colloquium (7.-8. Dec.)
JKU Linz, Austria (29. Dec.)
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)
Approximation Theory and Function Spaces, CRM Barcelona (26. - 30. Jun)
Oberwolfach: Real Analysis, Harmonic Analysis, and Applications (23 - 29 Jul.)
Tractability of High Dimensional Problems and Discrepancy, Erwin Schrodinger Institute, Vienna (25.Sep. - 29.Sep.)