##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Zavosh Amir Khosravi

#### Caltech

## Special cycles on non-compact Picard modular varieties

##### Abstract:

We'll discuss an extension of the work of Kudla-Millson on the modularity of special cycles on a non-compact Shimura variety associated to U(n,1) over a split CM field. The volume of their intersections with a diagonally embedded Shimura subvariety is related to Fourier coefficients of a Hilbert modular form coming from the restriction of an Eisenstein series on U(n,n). The main new idea is an application of the regularized Siegel-Weil formula of Gan-Qiu-Takeda.

Host: Claus Sorensen

### February 21, 2019

### 1:00 PM

### AP&M 7321

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