Geometry, Representations and Some Physics.
The GRaSP seminar series at Purdue
Variable day/time/location
Exact details given at Math Seminars
Page.
|
|
Schedule
| Date | Speaker | Title/Abstract |
| 01/25 | Artur Jackson | Geometry of Orbifolds Orbifolds are topological spaces which are largely similar to manifolds outside of some singular points, whose neighborhoods can be modeled by quotients of Euclidean space by finite isometry groups. Such spaces abound in mathematics and physics, e.g., moduli spaces of curves and in string theory. This talk will sketch the construction of these mildly singular spaces (which includes carrying around a heap of extra data). |
| 01/31 | Nick Miller | A Brief Glimpse of Grothendieck Topologies A Grothendieck topology is a topology that one can put on a category C which generalizes and gives explicit axioms for the notion of an open cover. In this talk I will attempt to motivate the definition and use of Grothendieck topologies past the standard "Grothendieck thought about it so you should too", and show some of the consequences of using such a categorical construction. In particular we will define the Étale Topology and briefly discuss how this provides us with a robust cohomology theory. |
| 02/07 | Artur Jackson | Geometry of Orbifolds II: Metrics, Connections and
Universality In this talk we'll take a pedestrian approach to (defining and) constructing differentiable maps between orbifolds. This will lead us to the notion of ``orbibundles'' and automatically provide us with standard geometric gadgets such as metrics and connections. We will also make an attempt at using these orbibundles to produce objects solving universal problems, e.g., in moduli theory. |
| 02/15 | Tamás Darvas | Chern classes from the point of view of differential
geometry There are many approaches one can take in defining Chern classes of vector bundles. In this talk we introduce these invariants from the point of view of differential geometry and we will discuss a limited amount of applications due to time constraints. Students with an understanding of differential geometry at the level of MA562 should be able to follow the talk for the most part. |
| TBA | Andrés Figueroa | Geometric Invariant Theory and GIT Quotients [abstract] |
| TBA | Artur Jackson | Introduction to Stacks in Geometry We'll quickly recall some background topics in geometry, e.g., principle G-bundles, and sheaves. We will then immediately motivate geometric stacks in a very lucid manner. If time permits the talk may touch on the topic of representing orbifolds as Deligne-Mumford stacks. |
Notes:
The GRaSP seminar aims to be a useful seminar series whose target audience is graduate students and intends to focus on topics (broadly) related to geometry, representation theory, and mathematical physics. This semester will largely be devoted to covering background material in both geometry and physics which is required to get the seminar off the ground before trecking into deeper topics.Loose topics list:
- Complex geometry
- 3- and 4-manifolds
- Knot theory
- Dynamical systems
- Group theory
- Representation theory
- Geometric Langlands
- Conformal field theory (CFT)
- Geometric invariant theory (GIT)
- Resolution of singularities
- String theory
- Quantum field theory
- Geometric quantization
- Quantum groups
- Higher categories
- D-branes
- K-theory
- Yang-Mills
- Gauge theory
- Geometric Analysis
- General Relativity