Alexander Fish
Associate Professor
Contact
School of Mathematics and Statistics F07
University of Sydney NSW 2006
Australia
afish(you know what)maths.usyd.edu.au
Research interests
Ergodic theory, additive combinatorics, wireless communication.
Biography
I defended my thesis "Ramsey properties of subsets of N" in 2007, at Hebrew University of Jerusalem, Israel, under supervsion of Hillel Furstenberg.
Afterwards, for three years I was Zassenhaus
Assistant Professor at Ohio State University
and for the next three years I was Van Vleck Assistant
Professor at UWMadison .
Preprints (submitted)
In Press
Publications
Ergodic Theory and Additive Combinatorics

Glasner property for linear group actions and their products
with K. Bulinski. Mathematische Zeitschrift volume 303, Article number: 99 (2023)


Reconstructing a minimal topological dynamical system from a set of return times
with K. Bulinski. Ergodic Theory Dynam. Systems 42 (2022), no. 9, 27232739.


Patterns in sets of positive density in trees and affine buildings
with M. Björklund and J. Parkinson. Groups, Geometry, and Dynamics, 15 (2021), 12671295.


Sets of transfer times with small densities
with M. Björklund and I. D. Shkredov. Journal de l'Ecole polytechnique  Mathematiques, 8 (2021), 311329.


Approximate invariance for ergodic actions of amenable groups
with M. Björklund. Discrete Analysis, 2019:6, 56 pp.


Extensions of Schreiber's theorem on discrete approximate subgroups in R^d
Journal de l'Ecole polytechnique  Mathematiques, 6 (2019), 149162.


Ergodic theorems for coset spaces
with M. Björklund. Journal d'Analyse Mathematique 135 (2018), no. 1, 85122.


On product of difference sets for sets of positive density
Proc. Amer. Math. Soc. 146 (2018), no. 8, 34493453.


On Bohr sets of integer valued traceless matrices
Proc. Amer. Math. Soc. 146 (2018), no. 2, 625636.


Plunnecke inequalities for measure graphs with applications
with K. Bulinski. Ergodic Theory Dynam. Systems 37 (2017), no. 2, 418439.


Plunnecke inequalities for countable abelian groups
with M. Björklund. Journal für die reine und angewandte Mathematik (2017), no. 730, 199224.


Characteristic polynomial patterns in difference sets of matrices
with M. Björklund. Bull. London Math. Soc. (2016) 48 (2): 300308.


Product set phenomena for countable groups
with M. Björklund. Advances in Mathematics 275 (2015) 47113.


Sumset Phenomenon in Countable Amenable Groups
with M. Beiglböck and V.Bergelson.
Advances in Mathematics 223 (2010) 416432.


Equidistribution of dilations of polynomial curves in nilmanifolds
with M. Björklund. Proc. Amer. Math. Soc. 137 (2009), 21112123.


Continuous Measures on Homogeneous Spaces
with M. Björklund. Annales de l'institut Fourier, 59 no. 6 (2009), p. 21692174.


Solvability of Rado systems in Dsets
with M. Beiglböck, V. Bergelson and T. Downarowicz. Topology Appl. 156 (2009), no. 16, 25652571.


Rigidity of measures invariant under the action of a multiplicative semigroup of polynomial growth on T
with M. Einsiedler. Ergodic Theory and Dynamical Systems, 30 (2010), no. 1, 151157.


Polynomial largeness of sumsets and totally ergodic sets
Online Journal of Analytic Combinatorics, Issue 5, 2010.


Solvability of linear equations within weak mixing sets
Israel Journal of Math. 184 (2011), 477504.


Liouville Random functions and normal sets
Acta Arith. 120 (2005), no. 2, 191196.

Geometry
Wireless Communication
Journal Publications
Proceedings of Conferences

Performance Estimates of the PseudoRandom Method for Radar Detection
with S. Gurevich. To appear in Proceedings of ISIT 2014  IEEE
International Symposium on Information Theory, Honolulu.


Almost linear complexity methods for delayDoppler channel estimation
with S. Gurevich.
To appear in 2014 International Zurich Seminar on Communications.


The Incidence and Cross Methods for Efficient Radar Detection
with S. Gurevich.
To appear in Proceedings of 51st Annual Allerton Conference on Communication, Control, and Computing.


DelayDoppler Channel Estimation with Almost Linear Complexity
with S. Gurevich, R.Hadani, A.Sayeed, O.Schwartz.
Proceedings of ISIT 2012  IEEE International Symposium on Information Theory, Cambridge, MA, USA, July 16, 2012.

Preprints
Number Theory Down Under 09
I coorganize in September 2021 with
Dzmitry Badziahin an international conference in Number Theory at the University of Sydney.
Ergodic Theory, Diophantine Approximation and related topics
I coorganized in June 2019 with
Dzmitry Badziahin and
Mumtaz Hussain an international workshop in Ergodic Theory, Diophantine Approximation and related topics at MATRIX Institute.
Dynamics and Number Theory 2019
I coorganized in June 2019 with
Dzmitry Badziahin and
Mumtaz Hussain an international conference in Ergodic Theory at the University of Sydney.
Ergodic Theory and its Applications 2016
I coorganized in July 2016 with Mumtaz Hussain an international conference in Ergodic Theory at the University of Sydney.
