Memorial Mathematics Working Seminar
Fall Schedule: HH 3017 12 – 1 pm
| November 5th | Tom Baird - The Cohomology of
Sheaves (part 4) I will explain how a short exact sequence of sheaves gives rise to a long exact sequence in cohomology, and use this to prove that cohomology can calculated with acyclic resolutions. This lecture will include a multimedia segment. |
| October 29th | Tom Baird - The Cohomology of
Sheaves (part 3) We will finish proving that injective resolutions of sheaves exist and are unique up to homotopy, so that sheaf cohomology is well-defined. Next we show that a short exact sequence of sheaves determines a long exact sequence in cohomology, which is essential for calculations. |
| October 22nd | Tom Baird - The Cohomology of
Sheaves (part 2) Having defined the category of sheaves in lecture 1, in this lecture I will introduce stalks, the global sections functor, and sheaf cohomology. |
| October 15th | Tom Baird - The Cohomology of
Sheaves Sheaves and their cohomology play a fundamental role in algebra, geometry, and topology. In this series of lectures, I will introduce these concepts, develop their theory, and explore applications. In this first lecture, I will explain what a sheaf is and why is interesting, and then define the cohomology of a sheaf. |
| October 8th | Daniel Offin (Queen’s University)
- Dynamics and symmetry: minimizing brake orbits After Newton proposed his universal laws of motion, there was a lively debate in the 18th c concerning the principle of least action championed by Maupertuis and later Euler and Lagrange. This approach was based on Maupertuis’s principle of minimum action: \(\mathrm{inf}_\gamma\int_\gamma pdq\). Maupertuis’s principle of least action states that in all natural phenomena a quantity called ‘action’ tends to be minimised. We shall give a short history of this principle and its modern formulations culminating in the study of the spectrum of minimizers, bringing together symplectic geometry, dynamical systems and symmetry groups. |