Charlotte Kirchhoff-Lukat<p><a href="https://mathstodon.xyz/tags/ExplainingMyResearch" class="mention hashtag" rel="tag">#<span>ExplainingMyResearch</span></a> 22<br />Now I mentioned before that I am chiefly interested in <a href="https://mathstodon.xyz/tags/GeneralizedComplex" class="mention hashtag" rel="tag">#<span>GeneralizedComplex</span></a> geometry underlying all this: All universes that exhibit <a href="https://mathstodon.xyz/tags/MirrorSymmetry" class="mention hashtag" rel="tag">#<span>MirrorSymmetry</span></a> are GC, and <a href="https://mathstodon.xyz/tags/branes" class="mention hashtag" rel="tag">#<span>branes</span></a> are GC objects.<br />However, there is currently no general version for a "GC category of branes". Part of my current work is to define this in certain cases.</p>
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Charlotte Kirchhoff-Lukat<p><a href="https://mathstodon.xyz/tags/ExplainingMyResearch" class="mention hashtag" rel="tag">#<span>ExplainingMyResearch</span></a> 4 <br />My current main research project aims to extend mirror symmetry through the framework of <a href="https://mathstodon.xyz/tags/GeneralizedComplex" class="mention hashtag" rel="tag">#<span>GeneralizedComplex</span></a> geometry. From the generalized complex (GC) POV, symplectic and complex geometry are the same thing: They are both GC. <br />This is an example of this larger pattern in <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="tag">#<span>math</span></a> and science, where finding a unified description for different things can lead to greater/deeper understanding.</p>
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