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)
In Press
Publications
Ergodic Theory and Additive Combinatorics
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Glasner property for linear group actions and their products
with K. Bulinski. Mathematische Zeitschrift volume 303, Article number: 99 (2023)
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Reconstructing a minimal topological dynamical system from a set of return times
with K. Bulinski. Ergodic Theory Dynam. Systems 42 (2022), no. 9, 2723-2739.
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Patterns in sets of positive density in trees and affine buildings
with M. Björklund and J. Parkinson. Groups, Geometry, and Dynamics, 15 (2021), 1267-1295.
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Sets of transfer times with small densities
with M. Björklund and I. D. Shkredov. Journal de l'Ecole polytechnique -- Mathematiques, 8 (2021), 311-329.
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Approximate invariance for ergodic actions of amenable groups
with M. Björklund. Discrete Analysis, 2019:6, 56 pp.
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Extensions of Schreiber's theorem on discrete approximate subgroups in R^d
Journal de l'Ecole polytechnique -- Mathematiques, 6 (2019), 149-162.
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Ergodic theorems for coset spaces
with M. Björklund. Journal d'Analyse Mathematique 135 (2018), no. 1, 85-122.
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On product of difference sets for sets of positive density
Proc. Amer. Math. Soc. 146 (2018), no. 8, 3449-3453.
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On Bohr sets of integer valued traceless matrices
Proc. Amer. Math. Soc. 146 (2018), no. 2, 625-636.
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Plunnecke inequalities for measure graphs with applications
with K. Bulinski. Ergodic Theory Dynam. Systems 37 (2017), no. 2, 418-439.
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Plunnecke inequalities for countable abelian groups
with M. Björklund. Journal für die reine und angewandte Mathematik (2017), no. 730, 199-224.
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Characteristic polynomial patterns in difference sets of matrices
with M. Björklund. Bull. London Math. Soc. (2016) 48 (2): 300-308.
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Product set phenomena for countable groups
with M. Björklund. Advances in Mathematics 275 (2015) 47-113.
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Sumset Phenomenon in Countable Amenable Groups
with M. Beiglböck and V.Bergelson.
Advances in Mathematics 223 (2010) 416-432.
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Equidistribution of dilations of polynomial curves in nilmanifolds
with M. Björklund. Proc. Amer. Math. Soc. 137 (2009), 2111-2123.
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Continuous Measures on Homogeneous Spaces
with M. Björklund. Annales de l'institut Fourier, 59 no. 6 (2009), p. 2169-2174.
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Solvability of Rado systems in D-sets
with M. Beiglböck, V. Bergelson and T. Downarowicz. Topology Appl. 156 (2009), no. 16, 2565--2571.
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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.
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Polynomial largeness of sumsets and totally ergodic sets
Online Journal of Analytic Combinatorics, Issue 5, 2010.
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Solvability of linear equations within weak mixing sets
Israel Journal of Math. 184 (2011), 477-504.
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Liouville Random functions and normal sets
Acta Arith. 120 (2005), no. 2, 191--196.
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Geometry
Wireless Communication
Journal Publications
Proceedings of Conferences
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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.
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Almost linear complexity methods for delay-Doppler channel estimation
with S. Gurevich.
To appear in 2014 International Zurich Seminar on Communications.
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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.
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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.
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Preprints
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.
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