##### Department of Mathematics,

University of California San Diego

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### Food For Thought Seminar

## Shubham Sinha

#### UCSD

## Journey to the core of partitions!

##### Abstract:

Integer partitions have been an interesting combinatorial object for centuries but we still have a lot left to understand. In this talk we will see an uncommon way to view partitions using 'Abaci' and use this to illustrate partition division (defining t-cores and t-quotients of a given integer partition). I am planning to go in more detail with a special kind of partition called t-core partitions and discuss different ways to enumerate them. I will end my talk by stating an interesting results by Prof. Ken Ono, which shows how the related objects enumerates some important algebraic invariants like class groups of certain imaginary quadratic number fields.

### November 20, 2018

### 12:00 PM

### AP&M 7321

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