Overview: Shows recent development in.geometry and topology.Gives access to sophisticated.techniques in geometric analysis.Leads to future directions ofresearch in geometry and topology.Includes supplementary mSince the year 2000, we have witnessed several outstanding results in geometry that have solved long-standing problems such as the Poincaré conjecture, the Yau–Tian–Donaldson conjecture, and the Willmore conjecture. There are still many important and challenging unsolved problems including, among others, the Strominger–Yau–Zaslow conjecture on mirror symmetry, the relative Yau–Tian–Donal
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