By Koh Gui Qing NEW YORK (Reuters) – Stock markets surged across the world on Tuesday and oil prices dived more than $3, as investors celebrated signs of progress in negotiations between Russia and Ukraine that they hoped would lead to a settlement in a five-week conflict. U.S. stock indices jumped over 0.5%, Europe’s main bourses enjoyed 1% to 2.5% gains, and oil tumbled 4% as Russia’s deputy defence minister emerged saying Moscow has decided to drastically cut military activity around Ukraine’s capital Kyiv and also Chernihiv.[.EU][O/R] Even though the U.S. government warned that Russia’s la…