Show threadCharlotte Kirchhoff-LukatDec 20, 2022
#ExplainingMyResearch
In order to say something, you first need to have the words for it, and so it is with #physics and #mathematics.
(I know that many pure #mathematicians view their work very differently, but this is how I approach it.)
Show threadCharlotte Kirchhoff-LukatDec 20, 2022
#ExplainingMyResearch
Very early in my studies, one of the things that gripped me most was how on its face very #abstract #mathematics serves as a language to describe physical phenomena. I got into #math and in particular #geometry and #topology more and more because it is the #language that physics is written in.
The research that I do day-to-day now is far removed from physics, but this is still how I view my work: I develop this language, the language of the universe, if you want.
Show threadCharlotte Kirchhoff-LukatDec 20, 2022
#ExplainingMyResearch
(Here, I am not going to go into how this can, on occasion, make physicists arrogant, insufferable and very wrong. As a physicist, you always have to be careful to not view the entire world as nails just because you have this really neat hammer.)
https://xkcd.com/793/
Physicists

xkcd
Charlotte Kirchhoff-LukatDec 20, 2022
#ExplainingMyResearch
Something different today: Since I've already turned this hashtag into a birds-eye view of my research, today I want to talk about how I understand my work in a broader context.
I started studying #physics at uni, and I am still fascinated by it: Of course the boundaries between different scientific disciplines are and have always been permeable - whether something is physics, #biology or #chemistry is often a question of interpretation and tools, rather than content.
Charlotte Kirchhoff-LukatDec 16, 2022
Since I turned #ExplainingMyResearch into a fairly general rumination on my larger #research area, I'm starting another more specialist hashtag for what I'm actually doing on a more day-to-day basis: #TodaysMath
(I will not post for it every day, nor will I abandon the more general one.)
#math #geometry
Show threadCharlotte Kirchhoff-LukatDec 9, 2022
#ExplainingMyResearch 23
To start, I am working on 2-dimensional "universes" like the disc with boundary, which are not strictly speaking GC, but similar enough to be useful.
My #preprint
https://arxiv.org/abs/2207.06894
describes how to define #Floer #cohomology for so-called log-#symplectic surfaces. I am currently finishing off the full description of the category of branes in this setting, so keep your eyes open! ๐Ÿ™‚
Log Floer cohomology for oriented log symplectic surfaces

This article provides the first extension of Lagrangian Intersection Floer cohomology to Poisson structures which are almost everywhere symplectic, but degenerate on a lowerdimensional submanifold. The main result of the article is the definition of Lagrangian intersection Floer cohomology, referred to as log Floer cohomology, for orientable surfaces equipped with log symplectic structures. We show that this cohomology is invariant under suitable isotopies and that it is isomorphic to the log de Rham cohomology when computed for a single Lagrangian.

arXiv.org
Show threadCharlotte Kirchhoff-LukatDec 9, 2022
#ExplainingMyResearch 22
Now I mentioned before that I am chiefly interested in #GeneralizedComplex geometry underlying all this: All universes that exhibit #MirrorSymmetry are GC, and #branes are GC objects.
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.
Show threadCharlotte Kirchhoff-LukatDec 9, 2022
#ExplainingMyResearch 21
The example I showed earlier with the lines inside a circle is one extremely simple version of a #category of #branes: The disc with the circular boundary is the "universe" and the lines are the branes. The interaction between the branes is given by the cohomology associated to the intersection points. Because of its low dimension, this example is much less complex for higher dimensional universes like our own (which in string theory is 10-dim!).
Show threadCharlotte Kirchhoff-LukatDec 9, 2022
#ExplainingMyResearch 20
This is Kontsevich's famous Homological Mirror Symmetry #Conjecture. It has been demonstrated in examples, but it is certainly not fully understood fully yet (and it is also not exactly what physicists understand mirror symmetry to be).
Show threadCharlotte Kirchhoff-LukatDec 9, 2022
#ExplainingMyResearch 19
It turns out that #MirrorSymmetry can be described in terms of #branes, which I have described before: For each of the two different mirror geometries, we can define a #category of branes (again, this is very simplified and not exactly right), which is a mathematical structure encoding not only the branes themselves, but also in some sense their interactions. Two universes are mirror if the categories of branes are equivalent in a certain way.