Date and Time: 16 June 2020, 6:30 pm IST - 7:30 pm IST (joining time :
6:15 pm IST - 6:30 pm IST)
Google meet link:
https://meet.google.com/gkc-hydx-fkn
Speaker: Madhusudan Manjunath, IIT Bombay.
Title: Frobenius numbers.
Abstract: For a natural number $k$, the $k$-th (generalised) Frobenius
number of relatively prime natural numbers $(a_1, \dots, a_n)$ is the
largest natural number that cannot be written as a non-negative integral
combination of $(a_1, \dots, a_n)$ in $k$ distinct ways. We study the
$k$-th Frobenius number from a commutative algebraic perspective. We
interpret the $k$-th Frobenius number in terms of the Castelnuovo-Mumford
regularity of certain modules associated to $(a_1, \dots, a_n)$. We study
these modules in detail and using this study, show that the sequence of
generalised Frobenius numbers form a finite difference progression, i.e. a
sequence whose set of successive differences form a finite set. This talk
is based on a joint work with Ben Smith.