23 citations · 63 across the 15 of their papers we have counts for
18 papers
The local dynamical structure of sets via a new Furstenberg family algebra
Angelina Blahodatna, Lauren Detmold, Daniel Glasscock +1
In this paper, we strengthen the connection between the combinatorics of difference sets and the dynamics of group rotations. Our main result shows that sets which have non-empty i…
The regionally proximal relation for commutative semigroup actions
Angelina Blahodatna, Lauren Detmold, Daniel Glasscock +1
The regionally proximal and equicontinuous structure relations are fundamental relations in topological dynamics that capture the equicontinuous behavior in a topological dynamical…
On sets of pointwise recurrence and dynamically thick sets
Daniel Glasscock, Anh N. Le
A set is a set of pointwise recurrence if for all minimal dynamical systems , all , and all open neighborhoods of , the…
A structure theorem for polynomial return-time sets in minimal systems
Daniel Glasscock, Andreas Koutsogiannis, Anh N. Le +3
We investigate the structure of return-time sets determined by orbits along polynomial tuples in minimal topological dynamical systems. Building on the topological characteristic f…
Dynamically syndetic sets and the combinatorics of syndetic, idempotent filters
Daniel Glasscock, Anh N. Le
A subset of the positive integers is dynamically central syndetic if it contains the times that a point returns to a neighborhood of itself in a minimal topological dynamical syste…
Simultaneous approximation in nilsystems and the multiplicative thickness of return-time sets
Daniel Glasscock
In the topological dynamical system , a point simultaneously approximates a point if there exists a sequence , , ... of natural numbers for which $T^{n_i}…
A combinatorial proof of a sumset conjecture of Furstenberg
Daniel Glasscock, Joel Moreira, Florian K. Richter
We give a new proof of a sumset conjecture of Furstenberg that was first proved by Hochman and Shmerkin in 2012: if is irrational and and are -…
On Katznelson's Question for skew product systems
Daniel Glasscock, Andreas Koutsogiannis, Florian K. Richter
Katznelson's Question is a long-standing open question concerning recurrence in topological dynamics with strong historical and mathematical ties to open problems in combinatorics…
Additive and geometric transversality of fractal sets in the integers
Daniel Glasscock, Joel Moreira, Florian K. Richter
By juxtaposing ideas from fractal geometry and dynamical systems, Furstenberg proposed a series of conjectures in the late 1960's that explore the relationship between digit expans…
A Khintchine-type theorem and solutions to linear equations in Piatetski-Shapiro sequences
Daniel Glasscock
Our main result concerns a perturbation of a classic theorem of Khintchine in Diophantine approximation. We give sufficient conditions on a sequence of positive real numbers $(ψ_n)…
Multiplicative combinatorial properties of return time sets in minimal dynamical systems
Daniel Glasscock, Andreas Koutsogiannis, Florian K. Richter
We investigate the relationship between the dynamical properties of minimal topological dynamical systems and the multiplicative combinatorial properties of return time sets arisin…
Norm forms represent few integers but relatively many primes
Daniel Glasscock
Norm forms, examples of which include , , and , are integral forms arising from norms on number fields. We prove that…
Shift equivalence in the generalized factor order
Jennifer Fidler, Daniel Glasscock, Brian Miceli +2
We provide a geometric condition that guarantees strong Wilf equivalence in the generalized factor order. This provides a powerful tool for proving specific and general Wilf equiva…
What is a graphon?
Daniel Glasscock
Graphons, short for graph functions, are limiting objects for sequences of large, finite graphs with respect to the so-called cut metric. In this expository piece, we define grapho…
Multiplicative richness of additively large sets in
Vitaly Bergelson, Daniel Glasscock
In their proof of the IP Szemerédi theorem, a far reaching extension of the classic theorem of Szemerédi on arithmetic progressions, Furstenberg and Katznelson introduced an import…
On the interplay between notions of additive and multiplicative largeness and its combinatorial applications
Vitaly Bergelson, Daniel Glasscock
Many natural notions of additive and multiplicative largeness arise from results in Ramsey theory. In this paper, we explain the relationships between these notions for subsets of…
Solutions to certain linear equations in Piatetski-Shapiro sequences
Daniel Glasscock
Denote by the image of the Piatetski-Shapiro sequence where is non-integral and is the integer part of $x…
Marstrand-type theorems for the counting and mass dimensions in
D. Glasscock
The counting and (upper) mass dimensions are notions of dimension for subsets of . We develop their basic properties and give a characterization of the counting dimen…