Associate Professor Alexander Fish
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Associate Professor Alexander Fish

Associate Professor in the School of Mathematics and Statistics
Phone
9351 2968
Fax
9351 4534
Address
F07 - Carslaw Building
The University of Sydney
Associate Professor Alexander Fish

Alexander Fish defended his Ph.D. thesis 'Ramsey properties of subsets of N' in 2007 under the supervision of Hillel Furstenberg, at Hebrew University of Jerusalem, Israel.

Before arriving to Sydney, he was Zassenhaus Assistant Professor at Ohio State University, and Van Vleck Assistant Professor at UW-Madison .

Alexander Fish is a member of the Geometry, Topology and Analysis Research Group, in which he works in ergodic theory, with particular emphasis on ergodic theoretical problems related to additive combinatorics of discrete groups. Dr Fish is also interested in information theory.

Publications

Journals

  • Fish, A., Jiang, L., Shkredov, I. (2024). Direct and inverse results for popular differences in trees of positive dimension. Ergodic Theory and Dynamical Systems, 44(2), 481-508. [More Information]
  • Bulinski, K., Fish, A. (2024). Quantitative twisted patterns in positive density subsets. Discrete Analysis, 2024, 1-17. [More Information]
  • Bjorklund, M., Fish, A. (2024). Simplices in large sets and directional expansion in ergodic actions. Forum of Mathematics, Sigma, 12(10 December 2024), Article e121-1-Article e121-20. [More Information]

Conferences

  • Fish, A., Gurevich, S. (2014). Almost linear complexity methods for delay-Doppler channel estimation. International Zurich Seminar on Communications 2014, Zurich: ETH-Zürich.
  • Fish, A., Gurevich, S. (2014). Performance Estimates of the Pseudo-Random Method for Radar Detection. 2014 IEEE International Symposium on Information Theory, Piscataway: Institute of Electrical and Electronics Engineers (IEEE). [More Information]
  • Fish, A., Gurevich, S. (2013). The Incidence and Cross Methods for Efficient Radar Detection. 2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton), Piscataway, NJ, USA: Institute of Electrical and Electronics Engineers (IEEE). [More Information]

2024

  • Fish, A., Jiang, L., Shkredov, I. (2024). Direct and inverse results for popular differences in trees of positive dimension. Ergodic Theory and Dynamical Systems, 44(2), 481-508. [More Information]
  • Bulinski, K., Fish, A. (2024). Quantitative twisted patterns in positive density subsets. Discrete Analysis, 2024, 1-17. [More Information]
  • Bjorklund, M., Fish, A. (2024). Simplices in large sets and directional expansion in ergodic actions. Forum of Mathematics, Sigma, 12(10 December 2024), Article e121-1-Article e121-20. [More Information]

2023

  • Bulinski, K., Fish, A. (2023). Arithmetic subtrees in large subsets of products of trees. Journal d'Analyse Mathematique, 150, 359-381. [More Information]
  • Bulinski, K., Fish, A. (2023). Glasner property for linear group actions and their products. Mathematische Zeitschrift, 303(4), Article 99 - 1-Article 99 - 12. [More Information]
  • Bulinski, K., Fish, A. (2023). Glasner Property for Unipotently Generated Group Actions on Tori. Israel Journal of Mathematics, 255, 109-122. [More Information]

2022

  • Bulinski, K., Fish, A. (2022). Reconstructing a minimal topological dynamical system from a set of return times. Ergodic Theory and Dynamical Systems, 42(9), 2723-2739. [More Information]

2021

  • Bjorklund, M., Fish, A., Parkinson, J. (2021). Patterns in sets of positive density in trees and affine buildings. Groups, Geometry, and Dynamics, 15 (Open Access)(4), 1267-1295. [More Information]
  • Bjorklund, M., Fish, A., Shkredov, I. (2021). Sets of transfer times with small densities. Journal de l'Ecole Polytechnique Mathematiques, 8, 311-329. [More Information]

2019

  • Bjorklund, M., Fish, A. (2019). Approximate invariance for ergodic actions of amenable groups. Discrete Analysis, 6, 1-56. [More Information]
  • Fish, A. (2019). Extensions of Schreiber's theorem on discrete approximate subgroups in R^d. Journal de l'Ecole Polytechnique Mathematiques, 6, 149-162. [More Information]

2018

  • Bjorklund, M., Fish, A. (2018). Ergodic theorems for coset spaces. Journal d'Analyse Mathematique, 135(1), 85-122. [More Information]
  • Fish, A. (2018). On Bohr sets of integer-valued traceless matrices. Proceedings of the American Mathematical Society, 146(2), 625-636. [More Information]
  • Fish, A. (2018). On product of difference sets for sets of positive density. Proceedings of the American Mathematical Society, 146(8), 3449-3453. [More Information]

2017

  • Bjorklund, M., Fish, A. (2017). Plunnecke inequalities for countable abelian groups. Journal fur die Reine und Angewandte Mathematik, 730, 199-224. [More Information]
  • Bulinski, K., Fish, A. (2017). Plunnecke inequalities for measure graphs with applications. Ergodic Theory and Dynamical Systems, 37(2), 418-439. [More Information]

2016

  • Bjorklund, M., Fish, A. (2016). Characteristic polynomial patterns in difference sets of matrices. Bulletin of the London Mathematical Society, 48(2), 300-308. [More Information]

2015

  • Bjorklund, M., Fish, A. (2015). Product set phenomena for countable groups. Advances in Mathematics, 275, 47-113. [More Information]

2014

  • Fish, A., Gurevich, S. (2014). Almost linear complexity methods for delay-Doppler channel estimation. International Zurich Seminar on Communications 2014, Zurich: ETH-Zürich.
  • Fish, A., Gurevich, S. (2014). Performance Estimates of the Pseudo-Random Method for Radar Detection. 2014 IEEE International Symposium on Information Theory, Piscataway: Institute of Electrical and Electronics Engineers (IEEE). [More Information]

2013

  • Fish, A., Gurevich, S., Hadani, R., Sayeed, A., Schwartz, O. (2013). Delay-Doppler Channel Estimation in Almost Linear Complexity. IEEE Transactions on Information Theory, 59(11), 7632-7644. [More Information]
  • Fish, A., Gurevich, S. (2013). The Incidence and Cross Methods for Efficient Radar Detection. 2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton), Piscataway, NJ, USA: Institute of Electrical and Electronics Engineers (IEEE). [More Information]

2012

  • Fish, A., Gurevich, S., Hadani, R., Sayeed, A., Schwartz, O. (2012). Delay-Doppler Channel Estimation with Almost Linear Complexity. 2012 IEEE International Symposium on Information Theory (ISIT 2012), Piscataway: Institute of Electrical and Electronics Engineers (IEEE). [More Information]

2011

  • Fish, A. (2011). Solvability of linear equations within weak mixing sets. Israel Journal of Mathematics, 184(1), 477-504. [More Information]
  • Fish, A., Nazarov, F., Ryabogin, D., Zvavitch, A. (2011). The unit ball is an attractor of the intersection body operator. Advances in Mathematics, 226(3), 2629-2642. [More Information]

2010

  • Fish, A. (2010). Polynomial Largeness of Sumsets and Totally Ergodic Sets. Online Journal of Analytic Combinatorics, 5, 1-17.
  • Einsiedler, M., Fish, A. (2010). Rigidity of measures invariant under the action of a multiplicative semigroup of polynomial growth on T. Ergodic Theory and Dynamical Systems, 30(1), 151-157. [More Information]
  • Beiglbock, M., Bergelson, V., Fish, A. (2010). Sumset phenomenon in countable amenable groups. Advances in Mathematics, 223(2), 416-432. [More Information]

2009

  • Bjorklund, M., Fish, A. (2009). Continuous Measures of Homogenous Spaces. Annales de l'Institut Fourier, 59(6), 2169-2174. [More Information]
  • Bjorklund, M., Fish, A. (2009). Equidistribution of dilations of polynomial curves in nilmanifolds. Proceedings of the American Mathematical Society, 137(6), 2111-2123. [More Information]
  • Beiglbock, M., Bergelson, V., Downarowicz, T., Fish, A. (2009). Solvability of Rado systems in D-sets. Topology and Its Applications: a journal devoted to general, geometric, set-theoretic and algebraic topology, 156(16), 2565-2571. [More Information]

Selected Grants

2023

  • Interplay between Ergodic Theory, Additive Combinatorics and Ramsey Theory, Fish A, Australian Research Council (ARC)/Discovery Projects (DP)

2020

  • Additive combinatorics of infinite sets via ergodic theoretic approach, Fish A, Australian Research Council (ARC)/Discovery Projects (DP)