The BBC Global News Podcast for June 3rd covers several international stories, including Ukrainian President Zelensky's strong condemnation after unsuccessful peace talks with Russia, where Russia presented demands deemed unacceptable by Ukraine, such as troop withdrawal from four regions and recognition of annexed territories. The podcast also reports on the Polish presidential election and the potential political crisis it poses for Prime Minister Tusk's government, as well as the UN Secretary General's call for an investigation into the deaths of Palestinians near a Gaza aid center, criticized by Israel. Additionally, the podcast discusses the charges against an Egyptian national in the US for a hate crime targeting a Jewish group, Sweden's investigation into irregularities in international adoptions, the search for missing American journalist Austin Tice in Syria, Islamist rebel attacks in Timbuktu, Mali, Paraguay's ambition to become a tech hub, and Dior's appointment of a new creative director.