##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Joshua Lam - Ph.D. student

#### Harvard University

## Calabi-Yau varieties and Shimura varieties

##### Abstract:

I will discuss the Attractor Conjecture for Calabi-Yau varieties, which was formulated by Moore in the nineties, highlighting the difference between Calabi-Yau varieties with and without Shimura moduli. In the Shimura case, I show that the conjecture holds and gives rise to an explicit parametrization of CM points on certain Shimura varieties; in the case without Shimura moduli, I'll present counterexamples to the conjecture using unlikely intersection theory. \\ \\ Part of this is joint work with Arnav Tripathy.

Host: Kiran Kedlaya

### January 7, 2021

### 1:00 PM

### see https://www.math.ucsd.edu/\~{}nts/

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