In this talk, wediscuss the existence of rainbow 3-term arithmetic progressions within3-colorings of various ground sets, including finite intervals, cyclic groups,and general abelian groups. This foundational question -how rainbow structuresemerge under specific density conditions on color classes- has inspired awealth of insights, problems, and generalizations within Rainbow Ramsey Theory.

Amanda Montejanois a tenured professor and researcher at the National Autonomous University ofMexico (UNAM), with a Ph.D. in Applied Mathematics from the UniversitatPolitècnica de Catalunya, and over 15 years of experience as a full-timeresearcher, working primarily in Combinatorics, Extremal Graph Theory, andAdditive Number Theory. In the past five years, she has led several nationalresearch projects funded by PAPIIT and CONACYT. Currently, she coordinates theproject Variants in Ramsey Theory and Extremal Theory (PAPIIT IG100822,2022–2024). She is a member of the Mexican Academy of Sciences and holds aLevel II distinction in Mexico’s National Research System. In 2010, she wasawarded the Sofia Kovalevskaya Prize. Throughout her academic career, she hasserved as advisor for several undergraduate, master’s, and doctoral theses. Herwork includes more than 30 research papers.