## Omer Bobrowski 2010-2011

- Institution of PhD:
- Technion – Israel Institute of Technology
- Academic Discipline of PhD:
- Electrical Engineering
- PhD Advisor/s:
- Robert Adler
- Dissertation Topic:
- Algebraic Topology of Random Fields and Complexes
- Year Awarded PhD:
- 2012
- Institution of Postdoc:
- Duke University
- Present Institution:
- Duke University
- Present Academic Position:
- Assistant Research Professor
- Email:
- omer@math.duke.edu
- Phone:
- 1-919-937-4523
- CV
- Publications
- Homepage

Omer Bobrowski, an electrical engineer and mathematician, is currently an assistant research professor in the Mathematics Department at Duke University. He is primarily interested in random topology – specifically, the algebraic topology of random fields and complexes, probability and stochastic processes, and applied algebraic topology.

Omer completed his PhD in 2012 at the Technion – The Israel Institute of Technology. His dissertation, “Algebraic Topology of Random Fields and Complexes,” written under the supervision of Prof. Robert Adler, focused on theoretical mathematics in the field of probability and stochastic processes. As part of this research he studied the persistent homology of Gaussian random fields, and compute its expected Euler characteristic. The results we present also have surprising and interesting consequences related to the critical points of Gaussian fields. In the second part we focus on the limiting behavior of the Betti numbers of random geometric complexes, as the number of vertices goes to infinity. We study different ways to construct a geometric complex, each resulting in a completely different structure.

Omer has always been fascinated by mathematics and embarked on his academic studies at Bar-Ilan University while still in high school. He completed his BA in mathematics and computer science at the Open University of Israel during his military service. Omer received his MSc at the Technion, in the Department of Electrical Engineering. His work there explored the applications of mathematics to real-world problems. His MSc thesis, “Real Time Spike Train Decoding by Neural Networks,” was written under the supervision of Prof. Ron Meir and Prof. Yonina C. Eldar.

Omer has published his work in a variety of scientific journals including *Neural Computation, Probability Theory and Related Fields* and the *Journal of Topology and Analysis*