Seminars and Colloquia by Series

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.

Using Morse homology to understand persistence modules I

Series
Geometry Topology Working Seminar
Time
Friday, November 18, 2022 - 14:00 for 1.5 hours (actually 80 minutes)
Location
Skiles 006
Speaker
Daniel IrvineGeorgia Tech

Please Note: Part 1 of a multi-part discussion.

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 first of a series of talks that aims to explain the relationship between Morse homology and persistence modules. In the first talk, I will give a rapid review of Morse theory and a review of Morse homology. An understanding of singular homology will be assumed. 

Smooth structures on open 4-manifolds IV

Series
Geometry Topology Working Seminar
Time
Friday, October 21, 2022 - 14:00 for 1.5 hours (actually 80 minutes)
Location
Skiles 006
Speaker
John EtnyreGeorgia Tech

One of the most interesting and surprising features of manifold topology is the existence of topological 4-manifold that admit infinitely many smooth structures. In these talks I will discuss what is known about these “exotic” smooth structures on open manifolds, starting with R^4 and then moving on to other open 4-manifolds. We will also go over various constructions and open questions about these manifolds.  

Smooth structures on open 4-manifolds III

Series
Geometry Topology Working Seminar
Time
Friday, October 7, 2022 - 14:00 for 1.5 hours (actually 80 minutes)
Location
Skiles 006
Speaker
John EtnyreGeorgia Tech

One of the most interesting and surprising features of manifold topology is the existence of topological 4-manifold that admit infinitely many smooth structures. In these talks I will discuss what is known about these “exotic” smooth structures on open manifolds, starting with R^4 and then moving on to other open 4-manifolds. We will also go over various constructions and open questions about these manifolds.  

Embeddings of lens spaces and rational homology balls in complex projective space II

Series
Geometry Topology Working Seminar
Time
Friday, September 30, 2022 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Agniva RoyGeorgia Tech

Given a symplectic 4 manifold and a contact 3 manifold, it is natural to ask whether the latter embeds in the former as a contact type hypersurface. We explore this question for CP^2 and lens spaces. We will discuss a construction of small symplectic caps, using ideas first laid out by Gay in 2002, for rational homology balls bounded by lens spaces. This allows us to explicitly understand embeddings of these rational balls in CP2 that were earlier understood only through almost toric fibrations. This is joint work with John Etnyre, Hyunki Min, and Lisa Piccirillo.

Embeddings of lens spaces and rational homology balls in complex projective space

Series
Geometry Topology Working Seminar
Time
Friday, September 23, 2022 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Agniva RoyGeorgia Tech

Given a symplectic 4 manifold and a contact 3 manifold, it is natural to ask whether the latter embeds in the former as a contact type hypersurface. We explore this question for CP^2 and lens spaces. In this talk, we will consider the background necessary for an approach to this problem. Specifically, we will survey some essential notions and terminology related to low-dimensional contact and symplectic topology. These will involve Dehn surgery, tightness, overtwistedness, concave and convex symplectic fillings, and open book decompositions. We will also look at some results about these and mention some research trends.

Smooth structures on open 4-manifolds II

Series
Geometry Topology Working Seminar
Time
Friday, September 16, 2022 - 14:00 for 1.5 hours (actually 80 minutes)
Location
Skiles 006
Speaker
John EtnyreGeorgia Tech

Please Note: One of the most interesting and surprising features of manifold topology is the existence of topological 4-manifold that admit infinitely many smooth structures. In these talks I will discuss what is known about these “exotic” smooth structures on open manifolds, starting with R^4 and then moving on to other open 4-manifolds. We will also go over various constructions and open questions about these manifolds.

Smooth structures on open 4-manifolds

Series
Geometry Topology Working Seminar
Time
Friday, September 9, 2022 - 14:00 for 1.5 hours (actually 80 minutes)
Location
Skiles 006
Speaker
John EtnyreGeorgia Tech

One of the most interesting and surprising features of manifold topology is the existence of topological 4-manifold that admit infinitely many smooth structures. In these talks I will discuss what is known about these “exotic” smooth structures on open manifolds, starting with R^4 and then moving on to other open 4-manifolds. We will also go over various constructions and open questions about these manifolds.  

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