Dr. Erik Lundberg
Ph.D. in Mathematics, University of South Florida, 2011
- Complex Analysis and asymptotics
- Topology of random manifolds
- PDE, potential theory, and free boundaries
- harmonic mappings and gravitational lensing
- Analytic Combinatorics
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.
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.
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 number of connected components of random algebraic hypersurfaces
, (with Y. V. Fyodorov and A. Lerario), Geometry and Physics, 95 (2015), 1-20.
Remarks on Wilmshurst's theorem
, (with A. Lerario and S-Y. Lee), Indiana Univ. Math. J., 64 (2015), 1153-1167.
- Full list of publications: http://brain2.math.fau.edu/~elundber/publications.html
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:
- 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