On singularity properties of word maps and applications to probabilistic Waring type problems

Singularities in algebraic geometry (14B05) Asymptotic properties of groups (20F69) Lie algebras of linear algebraic groups (17B45) Linear algebraic groups over local fields and their integers (20G25) Applications of model theory (03C98) Deformations of singularities (14B07)

Cites Work

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Representation growth and rational singularities of the moduli space of local systems
Fibers of word maps and some applications.
On the length of the shortest non-trivial element in the derived and the lower central series.
On the self-intersections of curves deep in the lower central series of a surface group
The Waring problem for finite simple groups.
Words and mixing times in finite simple groups.
Products of powers in finite simple groups
Equations in simple Lie algebras
On free subgroups of semi-simple groups
A right normed basis for free Lie algebras and Lyndon-Shirshov words
The Waring problem for Lie groups and Chevalley groups
Constructible motivic functions and motivic integration
On the verbal width of finitely generated pro-\(p\) groups.
Word maps, conjugacy classes, and a noncommutative Waring-type theorem.
A family of Calabi-Yau varieties and potential automorphy
Constructible exponential functions, motivic Fourier transform and transfer principle
The Ore conjecture.
Automorphy for some \(l\)-adic lifts of automorphic mod \(l\) Galois representations. With Appendix A, summarizing unpublished work of Russ Mann, and Appendix B by Marie-France Vignéras.
Automorphy for some \(l\)-adic lifts of automorphic mod \(l\) Galois representations. II
Characters of symmetric groups: sharp bounds and applications.
Adèles and algebraic groups. (Appendix 1: The case of the group \(G_2\), by M. Demazure. Appendix 2: A short survey of subsequent research on Tamagawa numbers, by T. Ono)
Low dimensional actions of semisimple groups
Singularités rationnelles et déformations
The space of surface group representations
Beweis für die Darstellbarkeit der ganzen Zahlen durch eine feste Anzahl \(n\)-ter Potenzen (Waringsches Problem).
Character bounds for finite groups of Lie type
Counting points of schemes over finite rings and counting representations of arithmetic lattices
Algebraic actions of discrete groups: the \(p\)-adic method
Fibers of automorphic word maps and an application to composition factors
On singularity properties of convolutions of algebraic morphisms
On rational singularities and counting points of schemes over finite rings
Motivic integration
Word maps have large image.
Integrability of oscillatory functions on local fields: transfer principles
Probabilistic Waring problems for finite simple groups
Resolution of singularities of an algebraic variety over a field of characteristic zero. II
Universal lattices and unbounded rank expanders.
Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas (Quatrième partie). Rédigé avec la colloboration de J. Dieudonné
Word values in p -adic and adelic groups
Transfer Principles for Bounds of Motivic Exponential Functions
Word maps and Waring type problems
Commutator maps, measure preservation, and 𝑇-systems
On the Degree of Igusa's Local Zeta Function
Singularities of pairs via jet schemes
A note on powers in simple groups
Presburger sets and p-minimal fields
Inversion of adjunction for local complete intersection varieties
Uniform analysis on local fields and applications to orbital integrals
IMPANGA lecture notes on log canonical thresholds<br>Notes by Tomasz Szemberg
On singularity properties of convolutions of algebraic morphisms ‐ the general case
Thom–Sebastiani Theorems for Filtered 𝒟-Modules and for Multiplier Ideals
Rational Singularities, Quiver Moment Maps, and Representations of Surface Groups
CHARACTER LEVELS AND CHARACTER BOUNDS
Words have bounded width in
Minimal Identities for Algebras
Number of Points of Varieties in Finite Fields
Jet schemes of locally complete intersection canonical singularities.
Diameters of finite simple groups: sharp bounds and applications
Character levels and character bounds for finite classical groups
A number theoretic characterization of \(E\)-smooth and (FRS) morphisms: estimates on the number of \(\mathbb{Z}/p^k\mathbb{Z}\)-points