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All my works on minimal surfaces has been motivated or inspired by natural sciences, including material sciences, bio-membranes, fluid dynamics, etc. I will give an informal talk (since I’m not natural scientist) about how minimal surface theory could benefit from interdisciplinary interactions.
Traizet’s node opening technique has been very powerful to construct minimal surfaces. In fact, it was first applied to glue saddle towers into minimal surfaces. But for technical reasons, the construction has much room to improve. I will talk about the ongoing project that addresses to various technical problems in the gluing construction. In particular, careful treatment of Dehn twist has revealed very subtle interactions between saddle towers.
Triply periodic minimal surfaces (TPMSs) are minimal surfaces in flat 3-tori. I will review recent discoveries of new examples of TPMSs and outline future steps towards an eventual complete classification of TPMSs of genus 3.
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