Omer Bobrowski

I am a Visiting Assistant Professor in the Mathematics Department at Duke University.

Contact Information

Office: 222 Physics Building

Phone: (919) 660-2878

Email: olmlelrl@lmlaltlhl.ldlulklel.leldlu

Department of Mathematics

Duke University

Durham, NC 27708

Research Interests

• Stochastic topology. More specifically - algebraic topology of random fields and complexes.

• Statistical theory for topological data analysis (TDA).

• Statistical models and applications for TDA.

• Probability and stochastic processes.

Publications

• Maximally Persistent Cycles in Random Geometric Complexes
  O. Bobrowski, M. Kahle, and P. Skraba
  Submitted, arXiv:1509.04347, 2015.
  PDF

• On the Vanishing of Homology in Random Čech Complexes
  O. Bobrowski, and S. Weinberger
  Submitted, arXiv:1507.06945, 2015.
  PDF

• The Topology of Probability Distributions on Manifolds
  O. Bobrowski, and S. Mukherjee
  Probability Theory and Related Fields 161 (3-4): 651-686, 2015
  PDF

• Topology of Random Geometric Complexes: A Survey
  O. Bobrowski, M. Kahle
  To appear in: Topology in Statistical Inference, the Proceedings of Symposia in Applied Mathematics, arXiv:1409.4734, 2014.
  PDF

• Topological Consistency via Kernel Estimation
  O. Bobrowski, S. Mukherjee and J. Taylor
  To Appear in Bernoulli, arXiv:1407.5272, 2014.
  PDF

• Crackle: The Homology of Noise
  R.J. Adler, O. Bobrowski, and S. Weinberger
  Discrete and Computational Geometry 52 (4): 680-704, 2014
  PDF

• Distance Functions, Critical Points, and the Topology of Random Cech Complexes
  O. Bobrowski, R.J. Adler
  Homology, Homotopy and Applications 16 (2): 311-344, 2014
  PDF

• Euler Integration of Gaussian Random Fields and Persistent Homology
  O. Bobrowski, M.S. Borman
  Journal of Topology and Analysis, 4(1), 2012.
  PDF

• Persistent Homology for Random Fields and Complexes
  R.J. Adler, O. Bobrowski, M.S. Borman, E. Subag and S. Weinberger
  Borrowing Strength: Theory Powering Applications, A festschrift for Lawrence D. Brown. IMS Collections Vol. 6, 2010.
  PDF

• Bayesian Filtering in Spiking Neural Networks: Noise, Adaptation and Multisensory Integration
  O. Bobrowski, R. Meir and Y. C. Eldar
  Neural Computation 21(5), 2009.
  PDF, online appendix.

• A Neural Network Implementing Optimal State Estimation Based on Dynamic Spike Train Decoding
  O. Bobrowski, R. Meir, S. Shoham and Y. C. Eldar
  Neural Information Processing Systems (NIPS 2007).
  PDF

Theses

• PhD Thesis: Algebraic Topology of Random Fields and Complexes
  Advisor: Prof. Robert J. Adler
  PDF

• MSc Thesis: Real Time Spike Train Decoding by Neural Networks
  Advisors: Prof. Ron Meir and Prof. Yonina C. Eldar
  
  
  

Teaching

Fall 2015:
MATH/STAT 690 - Topics in Probability
STAT 130 - Probability and Statistics in Engineering

Fall 2014/2013/2013:
MATH 212 - Mutlivariate Calculus

A Neat (?) Simulation

Move your mouse to change angles, and you can click the following:

z/x - zoom in/out

left/right - change size

up/down - speed

f/g - fluctuations (more/less)

r - start over

p - pause (on/off)

s - show a slice (on/off)

0-9 - take a screenshot