##### Department of Mathematics,

University of California San Diego

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### Joint Differential Geometry Seminar

## Ved Datar

## Hermitian-Yang-Mills connections on collapsing K3 surfaces

##### Abstract:

Let $X$ be an elliptically fibered K3 surface with a fixed $SU(n)$ bundle $\mathcal{E}$. I will talk about degenerations of connections on $\mathcal{E}$ that are Hermitian-Yang-Mills with respect to a collapsing family of Ricci flat metrics. This can be thought of as a vector bundle analog of the degeneration of Ricci flat metrics studied by Gross-Wilson and Gross-Tosatti-Zhang. I will show that under some mild conditions on the bundle, the restriction of the connections to a generic elliptic fiber converges to a flat connection. I will also talk about some ongoing work on strengthening this result. This is based on joint work with Adam Jacob and Yuguang Zhang.

Organizers: UCI-UCR-UCSD

### May 8, 2018

### 4:40 PM

### UCR Surge 284

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