Daniel Glasscock Research

✢ Simultaneous approximation in nilsystems and the multiplicative thickness of return-time sets. Submitted.

✢ Additive and geometric transversality of fractal sets in the integers, with J. Moreira and F. K. Richter. Submitted.

✢ A combinatorial proof of a sumset conjecture of Furstenberg, with J. Moreira and F. K. Richter. To appear in Combinatorica.

✢ On Katznelson’s Question for skew product systems, with A. Koutsogiannis and F. K. Richter. To appear in the Bulletin of the AMS.

✢ A Khintchine-type theorem and solutions to linear equations in Piatetski-Shapiro sequences. Acta Arith. 192 (2020), no. 3, 267–288.

✢ On the interplay between notions of additive and multiplicative largeness and its combinatorial applications, with V. Bergelson. J. Combin. Theory Ser. A 172 (2020), 105203, 60 pp.

✢ Multiplicative combinatorial properties of return time sets in minimal dynamical systems, with A. Koutsogiannis and F. K. Richter. Discrete Contin. Dyn. Syst. 39 (2019), no. 10, 5891–5921.

✢ Multiplicative richness of additively large sets in Z^{d}, with V. Bergelson. J. Algebra 503 (2018), 67-103.

✢ Shift equivalence in the generalized factor order, with J. Fidler, J. Pantone, B. K. Miceli, and M. Xu. Arch. Math. (Basel) 110 (2018), no. 6, 539-547. (poster)

✢ Algebraic, analytic, and geometric notions of largeness for subsets of Z^{d} and their applications. PhD Dissertation.

✢ Solutions to certain linear equations in Piatetski-Shapiro sequences. Acta Arith. 177 (2017), no. 1, 39-52.

✢ Marstrand-type theorems for the counting and mass dimensions in Z^{d}. Combin. Probab. Comput. 25 (2016), no. 5, 700-743.

✢ Sumset estimates in abelian groups. MS Thesis.

✢ Organizing a short online math program successfully, with C. Merriman, D. Robertson, and C. Smyth. Notices Amer. Math. Soc. 68 (2021), no. 6, 935-936. (appendix)

✢ CP processes. Oberwolfach Reports, Arbeitsgemeinschaft: Additive Combinatorics, Entropy, and Fractal Geometry.

✢ What is … a graphon? Notices Amer. Math. Soc. 62 (2015), no. 1, 46-48.

✢ Norm forms represent few integers but relatively many primes.

✢ Partition regularity for linear equations over N.

✢ Euler’s … elliptic integral addition theorem, repeated exponentiation, cotangent series and the Herglotz trick

✢ What is … the crank of a partition?, a braid group?, the Kakeya needle problem?

✢ Density Hales-Jewett in a measure-preserving framework.

✢ Imre Z. Ruzsa: Difference sets and the Bohr topology. Unpublished manuscript, 1985. (Posted here with permission from Imre Z. Ruzsa.)