Event Type:

Department Colloquium

Date/Time:

Monday, May 23, 2022 - 16:30 to 17:20

Location:

Pharmacy Building 305 and Zoom

Local Speaker:

Abstract:

The study of integer partitions is a fascinating and far-reaching area of study. Integer partitions with parts that differ by at least $d$, called $d$-distinct partitions, arise in a famous identity of Euler and the first Rogers-Ramanujan identity. The Alder-Andrews Theorem, namely that there are at least as many $d$-distinct partitions of $n$ as partitions of $n$ into parts that are $\pm 1$ modulo $d+3$, was proved in 2011 after more than 50 years of work. In 2020, Kang and Park constructed an extension of Alder's conjecture which relates to the second Rogers-Ramanujan identity. In this talk we discuss some of the history of this problem, as well as recent work to prove Kang and Park's conjecture and further generalizations. We will conclude with a discussion of some remaining open questions.

This work is joint with Adriana Duncan, Simran Khunger, and Ryan Tamura. It was initiated during the 2020 Oregon State University summer REU program, funded by NSF grant DMS-1757995 and Oregon State University.

This talk is part of the Pi Mu Epsilon Induction Ceremony which begins at 4pm. The talk should be accessible to a general mathematical audience.

Host: