Dr. Erik Lundberg
Education
- Ph.D. in Mathematics, University of South Florida, 2011
Research Interests
- Complex Analysis and asymptotics
- Topology of random manifolds
- PDE, potential theory, and free boundaries
- harmonic mappings and gravitational lensing
- Analytic Combinatorics
Research Description
My core research areas are in Analysis (Complex Analysis, PDE, potential theory, asymptotics), but what I really love are well-motivated problems that are simple to state.
Recent Publications
- 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.
- Full list of publications: http://brain2.math.fau.edu/~elundber/publications.html
Scholarly Activities
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I work with Jason Mireles-James to organize the Analysis and Applications Seminar in the Department of Mathematical Sciences at FAU.
Here is a link to the seminar page: Hompage/Schedule
- I am the faculty advisor for FAU's Math Club
- I'm currently writing a book with Dmitry Khavinson, "Linear Holomorphic Partial Differential Equations and Classical Potential Theory," (under contract for publication by the AMS).
- I have published more than 30 papers, most appearing in journals rated as A or A* (according to the AustMS rating system).
- Refereed papers for over a dozen journals.
- I have delivered over sixty invited talks, including international conferences in over a dozen countries.
- I have given, and continue to give several presentations for students at various specific levels: grad students, undergraduates, high school students, and middle school students