@article{22406,
  abstract     = {It is known that for a uniform morphic sequence 𝒖 =⟨𝑢𝑛⟩∞
𝑛=0 and an algebraic number 𝛽 such that |𝛽| >1, the number [[𝒖]]𝛽 :=∑∞
𝑛=0(𝑢𝑛/𝛽𝑛) either lies in ℚ⁡(𝛽) or is transcendental. In this paper, we show a similar rational–transcendental dichotomy for sequences defined by irreducible Pisot morphisms on binary alphabets. Subject to the Pisot conjecture (an irreducible Pisot morphism has pure discrete spectrum), we generalise the latter result to arbitrary finite alphabets. In certain cases, we are able to show transcendence of [[𝒖]]𝛽 outright. In particular, for 𝑘 ≥2, if 𝒖 is the k-Bonacci word, then [[𝒖]]𝛽 is transcendental.},
  author       = {Kebis, Pavol and LUCA, FLORIAN and OUAKNINE, JOEL and SCOONES, ANDREW and WORRELL, JAMES},
  issn         = {1469-4417},
  journal      = {Ergodic Theory and Dynamical Systems},
  keywords     = {balanced-pair algorithm, Cobham’s conjecture, k-Bonacci words, Pisot conjecture, subspace theorem},
  pages        = {1--22},
  publisher    = {Cambridge University Press},
  title        = {{Transcendence for Pisot morphic words over an algebraic base}},
  doi          = {10.1017/etds.2026.10324},
  year         = {2026},
}

@article{22693,
  abstract     = {We study torus-equivariant algebraic K-theory of affine Schubert varieties in the perfect affine Grassmannians over Fp. We further compare it to the torus-equivariant Hochschild homology of perfect complexes, which has a geometric description in terms of global functions on certain fixed-point schemes. We prove that Fp-linearly, this comparison is an isomorphism. Our approach is quite constructive, resulting in new computations of these K-theory rings. We establish various structural results for equivariant perfect algebraic K-theory on the way; we believe these are of independent interest.},
  author       = {Löwit, Jakub},
  issn         = {1431-0643},
  journal      = {Documenta Mathematica},
  keywords     = {equivariant algebraic K-theory, perfection in positive characteristic, affine Grassmannian, affine Schubert varieties, Dennis trace map, equivariant Hochschild homology, fixed-point schemes, toric varieties},
  publisher    = {EMS Press},
  title        = {{Equivariant K-theory, affine Grassmannian and perfection}},
  doi          = {10.4171/dm/1064},
  year         = {2026},
}

@inproceedings{22373,
  abstract     = {Data dissemination is a fundamental task in distributed computing. This paper studies broadcast problems in various innovative models where the communication network connecting n processes is dynamic (e.g., due to mobility or failures) and controlled by an adversary. 
In the first model, the processes transitively communicate their ids in synchronous rounds along a rooted tree given in each round by the adversary whose goal is to maximize the number of rounds until at least one id is known by all processes. Previous research has shown a ⌈(3n-1)/2⌉-2 lower bound and an O(nlog log n) upper bound. We show the first linear upper bound for this problem, namely ⌈(1+√2) n-1⌉ ≈ 2.4n.
We extend these results to the setting where the adversary gives in each round k-disjoint forests and their goal is to maximize the number of rounds until there is a set of k ids such that each process knows of at least one of them. We give a ⌈3(n-k)/2⌉-1 lower bound and a (π²+6)/6 n+1 ≈ 2.6n upper bound for this problem.
Finally, we study the setting where the adversary gives in each round a directed graph with k roots and their goal is to maximize the number of rounds until there exist k ids that are known by all processes. We give a ⌈3(n-3k)/2⌉+2 lower bound and a ⌈(1+√2)n⌉+k-1 ≈ 2.4n+k upper bound for this problem.
For the two latter problems no upper or lower bounds were previously known.},
  author       = {El-Hayek, Antoine and Henzinger, Monika H and Schmid, Stefan},
  booktitle    = {14th Innovations in Theoretical Computer Science Conference},
  editor       = {Tauman Kalai, Yael},
  isbn         = {9783959772631},
  issn         = {1868-8969},
  keywords     = {broadcast, cover, k-broadcast, dynamic radius, dynamic graphs, oblivious message adversary, time complexity, Theory of computation → Distributed algorithms, Networks → Network algorithms},
  location     = {Cambridge, Massachusetts, USA},
  publisher    = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
  title        = {{Asymptotically tight bounds on the time complexity of broadcast and its variants in dynamic networks}},
  doi          = {10.4230/LIPICS.ITCS.2023.47},
  volume       = {251},
  year         = {2023},
}

@article{12151,
  abstract     = {The k-sample G(k,W) from a graphon W:[0,1]2→[0,1] is the random graph on {1,…,k}, where we sample x1,…,xk∈[0,1] uniformly at random and make each pair {i,j}⊆{1,…,k} an edge with probability W(xi,xj), with all these choices being mutually independent. Let the random variable Xk(W) be the number of edges in  G(k,W). Vera T. Sós asked in 2012 whether two graphons U, W are necessarily weakly isomorphic if the random variables Xk(U) and Xk(W) have the same distribution for every integer k≥2. This question when one of the graphons W is a constant function was answered positively by Endre Csóka and independently by Jacob Fox, Tomasz Łuczak and Vera T. Sós. Here we investigate the question when W is a 2-step graphon and prove that the answer is positive for a 3-dimensional family of such graphons. We also present some related results.},
  author       = {Cooley, Oliver and Kang, M. and Pikhurko, O.},
  issn         = {1588-2632},
  journal      = {Acta Mathematica Hungarica},
  keywords     = {graphon, k-sample, graphon forcing, graph container},
  pages        = {1--26},
  publisher    = {Springer Nature},
  title        = {{On a question of Vera T. Sós about size forcing of graphons}},
  doi          = {10.1007/s10474-022-01265-8},
  volume       = {168},
  year         = {2022},
}