Eisenbud–Green–Harris and lex-plus-powers
What the paper claims, in its own words
Proves the Eisenbud–Green–Harris and lex-plus-powers conjectures over every characteristic-zero field. Any homogeneous ideal containing a regular sequence, of arbitrary length and degrees at least two, admits a lex-plus-powers ideal with the same Hilbert function and no smaller graded Betti numbers.
The plain-language explainer for this entry is still coming.