Abstract

The Weyl algebra has two generators \(D\) and \(U\) and the defining relation \(DU - UD = 1\). One possible interpretation is that \(D\) is the differentiation operator, and \(U\) is multiplication by \(x\), both acting on polynomials or power series in \(x\). It is possible that distinct monomials in the Weyl algebra are equal, for example \(UDDU = DUUD\). This caused Richard Stanley to put forward several questions and conjectures about equivalence classes of monomials. In this talk, the solutions to these questions will be discussed: specifically, a combinatorial characterization of equivalence classes of monomials and several enumerative results on these equivalence classes.

Joint work with Darij Grinberg, Tom Roby, and Mei Yin.

Speaker: Prof. Stephan Wagner | Institute of Discrete Mathematics  | Graz University of Technology (TU Graz)

Seminar Coordinator: Dr. Ralph Agyei Twum | Department of Mathematics | University of Ghana 

Meeting ID: 396 914 344 747 824 | Passcode: kY9Ht7Uu | Teams: Link 

All are cordially invited.

Bio

Stephan Wagner grew up in Graz (Austria), where he also received his education. He obtained a PhD from Graz University of Technology under the supervision of Robert Tichy in 2006. He then moved to South Africa, where he was working at Stellenbosch University from 2007 to 2019, and later to Uppsala University in Sweden, where he started in 2020. In 2024, he returned to Austria to become a professor in the Institute of Discrete Mathematics at Graz University of Technology. Stephan is interested in a wide range of topics in discrete mathematics and particularly enjoys enumerative, analytic and probabilistic combinatorics as well as graph-theoretical questions. He has been involved in a number of mathematical initiatives, such as the African Institute for Mathematical Sciences (AIMS), and mathematical Olympiads on national and international level.