A more complete publication list can be found on my CV.
Preprints of most of my papers can be found here on arXiv.
Linear Holomorphic PDE and Classical Potential Theory
(co-authored with Dmitry Khavinson),
AMS Mathematical Surveys and Monographs,
Vol. 232, 2018, 214 + x pp.
Recent Papers (since 2015):
- Limit cycle enumeration in random vector fields,
- A note on arclength null quadrature domains,
(with D. Khavinson) submitted.
- Homotopy types of random cubical complexes,
(with K.A. Dowling) submitted.
- Topologies of random geometric complexes on Riemannian manifolds in
the thermodynamic limit,
(with A. Auffinger and A. Lerario), IMRN, to appear.
- Asymptotic enumeration of lonesum matrices,
(with J. Khera and S. Melczer), Adv. Appl. Math, to appear.
- A note on the critical points of the localization landscape,
(with K. Ramachandran), Complex Analysis and its Synergies, to appear.
- The lemniscate tree of a random polynomial,
(with M. Epstein and B. Hanin), Annales de l'Institut Fourier, to appear.
- Random fields and the enumerative geometry of lines on real and complex hypersurfaces,
(with S. Basu, A. Lerario, and C. Peterson), Math. Ann., 374 (2019), 1773-1810.
- EGBTER: Capturing degree distribution, clustering coefficients, and
community structure in a single random graph model,
(with O. Eldaghar and R. Bridges), 2018 IEEE/ACM International Conference on Advances in Social
Networks Analysis and Mining (ASONAM), pages 282--289, 2018.
- The arclength and topology of a random lemniscate,
(with K. Ramachandran), J. Lond. Math. Soc., 96 (2017), 621-641.
- A four-dimensional Neumann ovaloid,
(with L. Karp), Ark. Mat., 55 (2017), 185-198.
- The Bergman analytic content of planar domains,
(with M. Fleeman), Comput. Methods Funct. Theory (2017) 17, 369-379.
- The Dirichlet problem for the slab with entire data and a difference equation for harmonic functions,
(with D. Khavinson and H. Render), Canadian Math. Bull., 60 (2017), 146-153.
- Dirichlet's problem with entire data posed on an ellipsoidal cylinder,
(with D. Khavinson and H. Render), Potential Analysis, 46 (2017), 55-62.
- On the geometry of random lemniscates,
(with A. Lerario), Proc. London Math. Soc., 113 (2016), 649-673.
- On the zeros of random harmonic polynomials: The truncated model, (with A. Lerario),
J. Math. Analysis Appl. 438 (2016), 1041-1054.
- Gap probabilities and Betti numbers of a random intersection of quadrics, (with A. Lerario),
Discrete Comput. Geom. 55 (2016), 462-496.
- A solution to Sheil-Small's harmonic mapping problem for polygons,
(with D. Bshouty and A. Weitsman), Proc. Amer. Math. Soc. 143 (2015), 5219-5225.
- On the growth of solutions to the minimal surface equation over domains containing a halfplane, (with A. Weitsman),
Calculus of Variations and PDE 54 (2015), 3385-3395.
- On the number of connected components of random algebraic hypersurfaces, (with Y. V. Fyodorov and A. Lerario),
Geometry and Physics, 95 (2015), 1-20.
- Statistics on Hilbert's sixteenth problem, (with A. Lerario), Internat. Math. Res. Not., 12 (2015), 4293-4321.
- Remarks on Wilmshurst's theorem, (with A. Lerario and S-Y. Lee), Indiana Univ. Math. J., 64 (2015), 1153-1167.
- Experiments on the zeros of harmonic polynomials using certified counting, (with J. Hauenstein, A. Lerario, and D. Mehta),
Exper. Math., 24 (2015), 133-141.
- Quasi-exceptional domains, (with A. Eremenko), Pacific J. Math., 276 (2015), 167-183.
- Electrostatic skeletons, (with K. Ramachandran), Annales Academiae Scientiarum Fennicae, 40 (2015), 397-401.
- Asymptotics of the extremal excedance set statistic, (with R. Ferraz de Andrade and B. Nagle), European J. Combin., 46 (2015), 75-88.