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 UW-Madison .

Preprints (submitted)

Arithmetic subtrees in large subsets of products of trees
with K. Bulinski

On almost Cap sets in three variables and the multivariable Cap set problem
with D. Roy

Quantitative twisted patterns in positive density subsets
with K. Bulinski

Direct and inverse results for popular differences in trees of positive dimension
with L. Jiang; with a joint appendix with I.D. Shkredov

In Press

Glasner property for unipotently generated group actions on tori
with K. Bulinski. To appear in Israel Journal of Mathematics.

Reconstructing a minimal topological dynamical system from a set of return times
with K. Bulinski. To appear in Ergodic Theory and Dynamical Systems.

Patterns in sets of positive density in trees and affine buildings
with M. Björklund and J. Parkinson. To appear in Groups, Geometry, and Dynamics.

Publications

Ergodic Theory and Additive Combinatorics

Sets of transfer times with small densities
with M. Björklund and I. D. Shkredov. Journal de l'Ecole polytechnique -- Mathematiques, 8 (2021), 311-329.

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), 149-162.

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.

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.

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

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.

Geometry

Unwinding spirals I
with L. Paunescu. Methods and Applications of Analysis (the memorial volume dedicated to John Mather), 25 (2018), no. 3, 225-232.

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.

Preprints

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

Number Theory Down Under 09

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