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Please join the Department of Mathematical Sciences as we welcome Dr. Brian Hopkins, Professor at Saint Peter's University.

Title: Six years of the crank-mex theorem
Abstract: In 2020, two pairs of researchers, George Andrews & David Newman along with the speaker & James Sellers, published a surprising connection between two statistics on integer partitions.  The crank, named by Freeman Dyson in 1944 in hopes for a way to better understand results of Ramanujan, was not found until 1988 by Andrews and Frank Garvan.  As one would guess from the 44 year delay, the definition is tricky, yet the crank has become one of the most important statistics in the field.  The mex, a portmanteau of minimal excludant and borrowed from combinatorial game theory, is much simpler to define and compute.  The theorem of the title shows that these two statistics are essentially equivalent.  In the short time since the connection was established, around 50 papers have built on the ideas.  We will sample some of that work with a bias towards combinatorial results.  The talk will be accessible to a wide audience, including several examples and beginning with the definition of integer partitions. 

Bio: Brian Hopkins received his Ph.D. from the University of Washington in 1997 and has been on the faculty at Saint Peter's University in Jersey City, New Jersey, since 2001.  He has also taught at New York University, Harvey Mudd College, Seattle University, Quest University in British Columbia, and Mahidol University International College in Thailand.  He was recognized with a Haimo teaching award from the Mathematical Association of America, served as editor of the College Mathematics Journal, and recently published a colorful book Hands-On Combinatorics with the American Mathematical Society.

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Location: Fisher Hall Room 133

Date: Friday, April 10, 2026

Time: 1:00 - 2:00 p.m.

Refreshments will be provided.