Seminars and Colloquia by Series

Electromagnetism and Falling Cats II

Series
Geometry Topology Working Seminar
Time
Friday, October 20, 2023 - 14:00 for 1.5 hours (actually 80 minutes)
Location
Skiles 006
Speaker
Daniel IrvineGeorgia Institute of Technology

In this talk I will continue to develop a parallel between the classical field theory of electromagnetism and geometric mechanics of animal locomotion. The focus of the previous talk was on electromagnetism, and the focus of this talk will be on the geometric mechanics of animal locomotion. We will investigate the aphorism that a cat dropped (from a safe height) upside-down always lands on her feet. I will explain how non-trivial topology of the configuration space of the cat can act as a "source" of locomotion.

No prior knowledge of classical field theory will be assumed. I will rely on some results from part 1, but I will review the relevant definitions.

Electromagnetism and Falling Cats

Series
Geometry Topology Working Seminar
Time
Friday, September 22, 2023 - 14:00 for 1.5 hours (actually 80 minutes)
Location
Skiles 006
Speaker
Daniel IrvineGeorgia Institute of Technology

In this talk I will develop a parallel between the classical field theory of electromagnetism and geometric mechanics of animal locomotion. I will illustrate this parallel using some informative examples from the two disciplines. In the realm of electromagnetism, we will investigate the magnetic monopole, as classically as possible. In the realm of animal locomotion, we will investigate the aphorism that a cat dropped (from a safe height) upside-down always lands on her feet. It turns out that both of these phenomena are caused by the presence of non-trivial topology.

No prior knowledge of classical field theory will be assumed, and this talk may continue into a second session at a later date.

Constructing Exotic 4-manifolds

Series
Geometry Topology Working Seminar
Time
Friday, April 21, 2023 - 14:00 for 1.5 hours (actually 80 minutes)
Location
Skiles 006
Speaker
Jon SimoneGeorgia Tech

This week, we'll continue discussing the rational blowdown and use it to construct small exotic 4-manifolds. We will see how we can view the rational blowdown as a "monodromy substitution." Finally, if time allows, we will discuss knot surgery on 4-manifolds. 

Lefschetz Fibrations and Exotic 4-Manifolds IV

Series
Geometry Topology Working Seminar
Time
Friday, April 14, 2023 - 14:00 for 1.5 hours (actually 80 minutes)
Location
Skiles 006
Speaker
Nur SaglamGeorgia Tech

Lefschetz fibrations are very useful in the sense that they have one-one correspondence with the relations in the Mapping Class Groups and they can be used to construct exotic (homeomorphic but not diffeomorphic) 4-manifolds. In this series of talks, we will first introduce Lefschetz fibrations and Mapping Class Groups and give examples. Then, we will dive more into 4-manifold world. More specifically, we will talk about the history of  exotic 4-manifolds and we will define the nice tools used to construct exotic 4-manifolds, like symplectic normal connect sum, Rational Blow-Down, Luttinger Surgery, Branch Covers, and Knot Surgery. Finally, we will provide various constructions of exotic 4-manifolds.

Lefschetz Fibrations and Exotic 4-Manifolds I

Series
Geometry Topology Working Seminar
Time
Friday, March 10, 2023 - 14:00 for 1.5 hours (actually 80 minutes)
Location
Skiles 006
Speaker
Nur Saglam

Lefschetz fibrations are very useful in the sense that they have one-one correspondence with the relations in the Mapping Class Groups and they can be used to construct exotic (homeomorphic but not diffeomorphic) 4-manifolds. In this series of talks, we will first introduce Lefschetz fibrations and Mapping Class Groups and give examples. Then, we will dive more into 4-manifold world. More specifically, we will talk about the history of  exotic 4-manifolds and we will define the nice tools used to construct exotic 4-manifolds, like symplectic normal connect sum, Rational Blow-Down, Luttinger Surgery, Branch Covers, and Knot Surgery. Finally, we will provide various constructions of exotic 4-manifolds.

Using Morse homology to understand persistence modules II

Series
Geometry Topology Working Seminar
Time
Friday, December 2, 2022 - 14:00 for 1.5 hours (actually 80 minutes)
Location
Skiles 006
Speaker
Daniel IrvineGeorgia Tech

Morse theory and Morse homology together give a method for understanding how the topology of a smooth manifold changes with respect to a filtration of the manifold given by sub-level sets. The Morse homology of a smooth manifold can be expressed using an algebraic object called a persistence module. A persistence module is a module graded by real numbers, and in this setup the grading on the module corresponds to the aforementioned filtration on the smooth manifold.

This is the second of a series of talks that aims to explain the relationship between Morse homology and persistence modules. In this second talk, I will define persistence modules, explain how to compute Morse homology using persistence modules, and explain how the Künneth theorem and the cup product work with persistence modules. The material from the first part of this series will be assumed.

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