More Like this

1. A proof of a conjecture of Shklyarov

   https://doi.org/10.4171/jncg/501  

   Brown, Michael K.; Walker, Mark E. (January 2022, Journal of Noncommutative Geometry)
2. A proof of a sumset conjecture of Erdős

   https://doi.org/10.4007/annals.2019.189.2.4  

   Moreira, Joel; Richter, Florian; Robertson, Donald (March 2019, Annals of Mathematics)
3. A noncommutative generalisation of a problem of Steinhaus

   https://doi.org/10.1016/j.jfa.2020.108782  

   Junge, Marius; Scheckter, Thomas Tzvi; Sukochev, Fedor (January 2021, Journal of Functional Analysis)

   null (Ed.)
4. A proof of a sumset conjecture of Erdős

   Moreira, Joel; Richter, Florian K; Robertson, Donald (March 2019, Annals of mathematics)

   In this paper we show that every set A⊂ℕ with positive density contains B+C for some pair B,C of infinite subsets of ℕ, settling a conjecture of Erd\H os. The proof features two different decompositions of an arbitrary bounded sequence into a structured component and a pseudo-random component. Our methods are quite general, allowing us to prove a version of this conjecture for countable amenable groups. 

   more » « less
5. A monotonicity version of a concavity theorem of Lieb

   https://doi.org/10.1007/s00013-022-01774-6  

   Carlen, Eric A. (November 2022, Archiv der Mathematik)