|Monday 2 October 2023|
|Events for day: Wednesday 01 March 2023|
| 14:00 - 15:00 Combinatorics and Computing Weekly Seminar|
The Analytic Representation of Quantum Mechanics
I will talk about the analytic representation of quantum mechanics, known as the stellar representation, which captures the quantum states of Bosonic systems and their role in quantum computations. Using this representation, I will explain a quantum-inspired proof of the MacMahon Master theorem in enumerative combinatorics.
This week's talk will be on our Gharar room:
15:30 - 17:00 Geometry and Topology Seminar
Knots in 3-manifolds, Knotted Surfaces in 4-manifolds and Heegaard-Floer Theory
The study of knots in the 3-space (and more generally, in arbitrary 3-manifolds) has been the source of interesting challenges for mathematicians for the past two centuries. We review some of the results, problems and open conjectures which have amazingly simple statements. We also discuss how some advanced tools from gauge theory and Heegaard-Floer theory may be used to (fully or partially) answer some of the questions which are otherwise difficult to handle. We also address the case of knotted surfaces in 4-manifolds and report some progress in using Heegaard-Floer invariants to distinguish them from one-another and extract some of their to ...
17:30 - 19:00 Algebraic Geometry Biweekly Webinar
On the Computation of Staggered Linear Bases
Grobner bases are a powerful tool in polynomial ideal theory with many applications in various areas of science and engineering. A Grobner basis is a particular generating set for a given ideal which represents many useful properties of the ideal. The general theory of Grobner bases along with the first algorithm for constructing them were introduced by Buchberger in 1965 in his Ph.D. thesis. An staggered linear basis is indeed a linear basis containing a Grobner basis for a given ideal. This notion was first introduced by Gebauer and Moller in 1988, however the algorithm that they described for computing these bases was not complete. In thi ...