added to *modular form* a brief paragraph with a minimum of information on modular forms *As automorphic forms*. Needs to be expanded.

have added a tad more content to *Stein manifold* and cross-linked a bit more

added a definition to *beta-gamma system*

wrote out the definition *In complex geometry*

created

*Weil uniformization theorem*with a brief idea of the statement and a pointer to the decent review Sorger 99added the statement in a bit more detail to

*moduli space of bundles*(but it still needs more discussion there);used the pointer to the new entry (in place of some previous text) to streamline the function field analogy – table a little bit.

started a minimum at *hard Lefschetz theorem* and *Lefschetz decomposition*

created an entry for *Koszul-Malgrange theorem*

I have added to *Teichmüller theory* a mini-paragraph Complex structure on Teichmüller space with a minimum of pointers to the issue of constructing a complex structure on Teichmüller space itself.

Maybe somebody has an idea on the following: The Teichmüller orbifold itself should have a neat general abstract construction as the full subobject on the étale maps of the mapping stack formed in smooth $\infty$-groupoids/smooth $\infty$-stacks into the Haefliger stack for complex manifolds : via Carchedi 12, pages 37-38.

Might we have a refinement of this kind of construction that would produce the Teichmüller orbifold directly as on objects in $\infty$-stacks over the complex-analytic site?

]]>noticed that we didn’t have *complex Lie group*, so I put in a bare minimum. Also a stub for *complex Lie algebra*. Just so that it’s there.

started a category:reference entry

in the course of this I added some stuff here and there, for instance at *Abel-Jacobi map*. But very stubby for the moment.

Have added more of the original (“historical”) References with brief comments and further pointers.

]]>started *stable vector bundle*, but still vague

I am starting *Wick algebra*. So far I have an Idea-section, references, and a discussion of the finite dimensional case, showing how the traditional “normal ordered Wick product” is the Moyal star product of an almost-Kähler vector space.

I spelled out the elementary definitions, relations and examples at *Kähler vector space* and *Hermitian space*.

This started out as a section that I added to *Kähler manifold*.

At *line integral* I have added missing pointers to *Cauchy integral theorem* and *Cauchy integral formula*.

I wonder if we should better split off an entry *contour integral* from *line integral* (presently the former redirects to the latter). That’s what Wikipedia does, too. At least if we ever bring a decent chunk of material on complex contour integrals in.

created a stub for *pseudoholomorphic vector bundle*, for the moment just to record references

Together with Dennis Borisov I’ll be running an informal seminar (working group) on *F-theory* at the MPI in Bonn. I’ll be showing the schedule and developing notes here:

am starting *complex analytic infinity-groupoid* (in line with “smooth infinity-groupoid” etc.) and *higher complex analytic geometry*. Currently there is mainly a pointer to Larusson. To be expanded.

started a stub for *moduli space of Calabi-Yau spaces*. Nothing really there yet, except some references and some cross-links.

brief entry *holomorphic line 2-bundle*, just to have the link and to record the reference there

started something at *Friedlander-Milnor isomorphism conjecture*. But handle with care, I am only just watching the video linked to there.

added the following story to the Properties-section of *Dedekind eta function* and also to the Examples-section of *functional determinant* and *zeta function of an elliptic differential operator*:

For $E = \mathbb{C}/(\mathbb{Z}\oplus \tau \mathbb{Z})$ a complex torus (complex elliptic curve) equipped with its standard flat Riemannian metric, then the zeta function of the corresponding Laplace operator $\Delta$ is

$\zeta_{\Delta} = (2\pi)^{-2 s} E(s) \coloneqq (2\pi)^{-2 s} \underset{(k,l)\in \mathbb{Z}\times\mathbb{Z}-(0,0)}{\sum} \frac{1}{{\vert k +\tau l\vert}^{2s}} \,.$The corresponding functional determinant is

$\exp( E^\prime(0) ) = (Im \tau)^2 {\vert \eta(\tau)\vert}^4 \,,$where $\eta$ is the Dedekind eta function.

]]>gave *zeta function regularization* its own entry and expanded a bit, added more pertinent references

collected some introductions and surveys

]]>created a bare minimum at *branched cover of Riemann sphere*, just to record the fact that every compact connected Riemann surface admits this structure.