Alexander Gamburd

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All published works

Action	Title	Year	Authors
+	Arithmetic and dynamics on varieties of Markoff type	2023	Alexander Gamburd
+	On the Origins, Nature, and Impact of Bourgain’s Discretized Sum-Product Theorem	2022	Alexander Gamburd
+	Singular Adventures of Baron Bourgain in the Labyrinth of the Continuum	2020	Alexander Gamburd
+ PDF	An asymptotic formula for integer points on Markoff-Hurwitz varieties	2019	Alexander Gamburd Michael Magee Ryan Ronan
+	Markoff triples and strong approximation	2016	Jean Bourgain Alexander Gamburd Peter Sarnak
+	Markoff Surfaces and Strong Approximation: 1	2016	Jean Bourgain Alexander Gamburd Peter Sarnak
+	Spectral gaps in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi mathvariant="italic">SU</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>d</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>	2010	Jean Bourgain Alexander Gamburd
+	Expansion Of Product Replacement Graphs	2006	Alexander Gamburd Igor Pak
+	Expansion of product replacement graphs	2002	Alexander Gamburd Igor Pak
+ PDF Chat	On the genus of a random Riemann surface	2002	Alexander Gamburd Eran Makover
+	On the Genus of a Random Riemann Surface	2001	Alexander Gamburd Eran Makover

Common Coauthors

Coauthor	Papers Together
Jean Bourgain	3
Eran Makover	2
Igor Pak	2
Peter Sarnak	2
Michael Magee	1
Ryan Ronan	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF	Uniform expansion bounds for Cayley graphs of SL<sub>2</sub>(𝔽<sub>p</sub>)	2008	Jean Bourgain Alex Gamburd	3
+	Continued fractions and the Markoff tree	2006	Enrico Bombieri	2
+ PDF	Finite Quotients of the Automorphism Group of a Free Group	1977	Robert H. Gilman	2
+	On the Erdős-Volkmann and Katz-Tao ring conjectures	2003	Jean Bourgain	2
+	Congruence Properties of Zariski-Dense Subgroups I	1984	Christopher R. Matthews L. N. Vaserstein Boris Weisfeiler	2
+	On the average genus of the random graph	1995	Saul Stahl	2
+	Algebraic solutions of the sixth Painlevé equation	2014	O. Lisovyy Yuriy Tykhyy	2
+ PDF	A modular Szemerédi–Trotter theorem for hyperbolas	2012	Jean Bourgain	2
+	Counting Mapping Class group orbits on hyperbolic surfaces	2016	Maryam Mirzakhani	2
+	On the spectral gap for finitely-generated subgroups of SU(2)	2007	Jean Bourgain Alex Gamburd	2
+ PDF	Affine linear sieve, expanders, and sum-product	2009	Jean Bourgain Alex Gamburd Peter Sarnak	2
+ PDF	Spectra of elements in the group ring of $\mathrm{SU}(2)$	1999	Alex Gamburd Dmitry Jakobson Peter Sarnak	2
+	The Isoperimetric Number of Random Regular Graphs	1988	Béla Bollobás	2
+	Groups and expanders	1993	Alexander Lubotzky Benjamin Weiss	2
+ PDF	New bounds for Gauss sums derived from KTH powers, and for Heilbronn's exponential sum	2000	D. R. Heath‐Brown	2
+ PDF	On the theorem of Jarník and Besicovitch	1981	Robert Kaufman	1
+	A remarkable identity for lengths of curves	1991	Greg McShane	1
+	Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations	1966	Wilhelm Magnus A. Karrass D. Solitar	1
+	Applications of sieve methods to the theory of numbers	1976	C. Hooley	1
+	Maximal operators related to the Radon transform and the Calderon-Zygmund method of rotations	1986	Michael Christ Javier Duoandikoetxea José L. Rubio de Francia	1
+ PDF	A group theoretic criterion for property FA	1996	Marc Culler Karen Vogtmann	1
+	Numerical investigation of the spectrum for certain families of Cayley graphs	1993	John Lafferty Daniel N. Rockmore	1
+	Zeta functions and the periodic orbit structure of hyperbolic dynamics	1990	William Parry Mark Pollicott	1
+ PDF	$L^{p}$ estimates for the $X$-ray transform	1983	S.W. Drury	1
+	Remarks on Montgomery's conjectures on dirichlet sums	1991	Jean Bourgain	1
+	A norm on homology of surfaces and counting simple geodesics	2000	Greg McShane Igor Rivin	1
+	Simple curves on hyperbolic tori	2000	Greg McShane Igor Rivin	1
+	Mordell’s exponential sum estimate revisited	2005	Jean Bourgain	1
+	The product replacement algorithm and Kazhdan’s property (T)	2000	Alexander Lubotzky Igor Pak	1
+ PDF	The nonlinear Schrödinger equation on tori: Integrating harmonic analysis, geometry, and probability	2015	Andrea R. Nahmod	1
+	Rational Quadratic Forms	1982	J. W. S. Cassels	1
+	Group representations in probability and statistics	1988	Persi Diaconis	1
+	Some Applications of Modular Forms	1990	Peter Sarnak	1
+ PDF	On the number of sums and products	1997	György Elekes	1
+ PDF	On sums and products of integers	1983	Péter L. Erdős Endre Szemerédi	1
+	Elementary Number Theory, Group Theory and Ramanujan Graphs	2001	Giuliana P. Davidoff Peter Sarnak Alain Valette	1
+	Sums of Finite Sets	1996	Imre Z. Ruzsa	1
+	ON THE NUMBER OF POINTS OF A HYPERELLIPTIC CURVE OVER A FINITE PRIME FIELD	1969	S. A. Stepanov	1
+	On the spectral gap for infinite index “congruence” subgroups of SL2(Z)	2002	Alex Gamburd	1
+	Hecke operators and distributing points on <i>S</i><sup>2</sup>. II	1987	Alexander Lubotzky Ralph S. Phillips Peter Sarnak	1
+ PDF	Growth of the number of simple closed geodesics on hyperbolic surfaces	2008	Maryam Mirzakhani	1
+	On dense free subgroups of Lie groups	2003	Emmanuel Breuillard Tsachik Gelander	1
+ PDF	Exponential Diophantine equations	1982	J. L. Brenner Lorraine L. Foster	1
+	Integral points on surfaces	2016	Pietro Corvaja Umberto Zannier	1
+ PDF Chat	A sum-product estimate in finite fields, and applications	2004	Jean Bourgain Nets Hawk Katz Terence Tao	1
+	Walks on generating sets of groups	1998	Persi Diaconis Laurent Saloff‐Coste	1
+	A polynomial bound in Freiman's theorem	2002	Mei-Chu Chang	1
+	Simple Groups, Probabilistic Methods, and a Conjecture of Kantor and Lubotzky	1996	Martin W. Liebeck Aner Shalev	1
+	A faithful polynomial representation of Out <i>F</i><sub>3</sub>	1989	James McCool	1
+	Expanding graphs and invariant means	1997	Yehuda Shalom	1