Alexander Fish
Senior Lecturer
Contact
School of Mathematics and Statistics F07
University of Sydney NSW 2006
Australia
afish(you know what)maths.usyd.edu.au
Teaching website
This semester I teach the course Introduction to Linear Algebra, and Honours Functional Analysis .
Research interests
Ergodic theory, additive combinatorics, wireless communication.
Biography
My supervisor was Hillel Furstenberg. My thesis "Ramsey properties of subsets of N" was defended in 2007, at Hebrew University of Jerusalem, Israel.
Afterwards, for three years I was Zassenhaus
Assistant Professor at Ohio State University
and for another three years I was Van Vleck Assistant
Professor at UWMadison .
Preprints (submitted)
In Press
Unwinding spirals I
with L. Paunescu. To appear in Methods and Applications of Analysis, the memorial volume dedicated to John Mather.

Publications
Ergodic Theory

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.


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


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.


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.

Convex 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.

Dynamics and Number Theory 2019
I coorganize 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.
