Alexander Fish

Senior Lecturer


School of Mathematics and Statistics F07
University of Sydney NSW 2006

afish(you know what)

Teaching website

This semester I teach the course Introduction to Linear Algebra, and Honours Functional Analysis .

Research interests

Ergodic theory, additive combinatorics, wireless communication.


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 UW-Madison .

Preprints (submitted)

Delocalisation of one-dimensional marginals of product measures and the capacity of LTI discrete channels
with M. Bombar

Twisted recurrence via polynomial walks
with K. Bulinski

Approximate Invariance for Ergodic Actions of Amenable Groups
with M. Björklund

In Press

Extensions of Schreiber's theorem on discrete approximate subgroups in R^d
to appear in Journal de l'Ecole polytechnique -- Mathematiques.

Unwinding spirals I
with L. Paunescu. To appear in Methods and Applications of Analysis, the memorial volume dedicated to John Mather.


Ergodic Theory

Ergodic theorems for coset spaces
with M. Björklund. Journal d'Analyse Mathematique 135 (2018), no. 1, 85-122.

On product of difference sets for sets of positive density
Proc.Amer. Math. Soc. 146 (2018), no. 8, 3449-3453.

On Bohr sets of integer valued traceless matrices
Proc. Amer. Math. Soc. 146 (2018), no. 2, 625-636.

Characteristic polynomial patterns in difference sets of matrices
with M. Björklund. Bull. London Math. Soc. (2016) 48 (2): 300-308.

Plunnecke inequalities for measure graphs with applications
with K. Bulinski. Ergodic Theory Dynam. Systems 37 (2017), no. 2, 418-439.

Plunnecke inequalities for countable abelian groups
with M. Björklund. Journal für die reine und angewandte Mathematik (2017), no. 730, 199-224.

Product set phenomena for countable groups
with M. Björklund. Advances in Mathematics 275 (2015) 47-113.

Sumset Phenomenon in Countable Amenable Groups
with M. Beiglböck and V.Bergelson. Advances in Mathematics 223 (2010) 416-432.

Equidistribution of dilations of polynomial curves in nilmanifolds
with M. Björklund. Proc. Amer. Math. Soc. 137 (2009), 2111-2123.

Continuous Measures on Homogeneous Spaces
with M. Björklund. Annales de l'institut Fourier, 59 no. 6 (2009), p. 2169-2174.

Solvability of Rado systems in D-sets
with M. Beiglböck, V. Bergelson and T. Downarowicz. Topology Appl. 156 (2009), no. 16, 2565--2571.

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, 151--157.

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), 477-504.

Liouville Random functions and normal sets
Acta Arith. 120 (2005), no. 2, 191--196.

Convex Geometry

The unit ball is an attractor of the intersection body operator
with F. Nazarov, D. Ryabogin and A. Zvavitch. Advances in Mathematics 226 (2011) 2629-2642.

Wireless Communication

Journal Publications

Delay-Doppler Channel Estimation with Almost Linear Complexity
with S. Gurevich, R. Hadani, A. Sayeed, O. Schwartz. IEEE Transactions on Information Theory (2013), Vol. 59, Issue 11, 7632-7644.

Proceedings of Conferences

Performance Estimates of the Pseudo-Random 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 delay-Doppler 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.

Delay-Doppler 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 1--6, 2012.

Ergodic Theory and its Applications 2016

I co-organized in July 2016 with Mumtaz Hussain an international conference in Ergodic Theory at the University of Sydney.