Â鶹ŮÀÉ

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

• I work with Jason Mireles-James to organize the Analysis and Applications Seminar in the Department of Mathematical Sciences at Â鶹ŮÀÉ.

• I am the faculty advisor for Â鶹ŮÀÉ'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