## Number Theory Seminar

### Tuesday, January 22nd, 2019

**Time:** 1:00-2:00 p.m. **Place:** Jeffery Hall 422

**Speaker:** Steven Spallone (Indian Institute of Science Education and Research, Pune)

**Title:** A Chinese Remainder Theorem for Young Diagrams.

**Abstract:** Given a natural number 't' and a Young Diagram 'Y', there is a notion of a "remainder of Y upon division by t", called the t-core of Y. Let s,t be relatively prime, and consider the map taking a given st-core Y to the pair consisting of its s-core and t-core. The fibres of this map are infinite. More precisely, we have proven that the cardinality of the set of length k members of a given fibre is a quasipolynomial in k, of degree st-s-t. This is joint work with K. Seethalakshmi.