Seminars and Colloquia by Series

Obstructions to nice branch sets for branched coverings

Series
Geometry Topology Student Seminar
Time
Wednesday, October 9, 2019 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Sudipta KolayGeorgia Tech

It is a classical theorem of Alexander that every closed oriented manifold is a piecewise linear branched covering of the sphere. In this talk, we will discuss some obstructions to realizing a manifold as a branched covering of the sphere if we require additional properties (like being a submanifold) on the branch set.

 

H-cobordisms and corks

Series
Geometry Topology Student Seminar
Time
Wednesday, October 2, 2019 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Agniva RoyGeorgia Tech

Stephen Smale’s h-cobordism Theorem was a landmark result in the classification of smooth manifolds. It paved the way towards solutions for the topological Poincaré and Schoenflies conjectures in dimensions greater than 5. Later, building on this, Freedman’s work applied these techniques to 4 manifolds. I shall discuss the ideas relating to h-cobordisms and the proof, which is a wonderful application of handlebody theory and the Whitney trick. Time permitting, we shall explore the world of smooth 4 manifolds further, and talk about cork twists.

Graph Theory and Heegaard Floer Homology

Series
Geometry Topology Student Seminar
Time
Wednesday, September 25, 2019 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Hyun Ki MinGeorgia Tech

I will talk about a connection between graph theory and sutured Floer homology. In fact, there is a one to one correspondence between hypergraphs of a planar bipartite graph and the dimension of sutured Floer homology of a complement of a neighborhood of special alternating link In a three sphere. This is based on the work of Juhas, Kalman and Rasmussen.

Surface bundles in topology, algebraic geometry, and group theory

Series
Geometry Topology Student Seminar
Time
Wednesday, September 18, 2019 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Justin LanierGeorgia Tech

I will give an introduction to surface bundles and will discuss several places where they arise naturally. A surface bundle is a fiber bundle where the fiber is a surface. A first example is the mapping torus construction for 3-manifolds, which is a surface bundle over the circle. Topics will include a construction of 4-manifolds as well as section problems related to surface bundles. The talk will be based on a forthcoming Notices survey article by Salter and Tshishiku.

Unfoldings of 3D Polyhedra

Series
Geometry Topology Student Seminar
Time
Wednesday, September 11, 2019 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Nicholas Barvinok

Cutting a polyhedron along some spanning tree of its edges will yield an isometric immersion of the polyhedron into the plane. If this immersion is also injective, we call it an unfolding. In this talk I will give some general results about unfoldings of polyhedra. There is also a notion of pseudo-edge unfolding, which involves cutting on a pseudo edge graph, as opposed to an edge graph. A pseudo edge graph is a 3-connected graph on the surface of the polyhedron, whose vertices coincide with the vertices of the polyhedron, and whose edges are geodesics. I will explain part of the paper "Pseudo-Edge Unfoldings of Convex Polyhedra," a joint work of mine with Professor Ghomi, which proves the existence of a convex polyhedron with a pseudo edge graph along which it is not unfoldable. Finally, I will discuss some connections between pseudo edge graphs and edge graphs. 

0-Concordance of 2-Knots

Series
Geometry Topology Student Seminar
Time
Wednesday, September 4, 2019 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Anubhav Mukherjee

 A 2-knot is a smooth embedding of S^2 in S^4, and a 0-concordance of 2-knots is a concordance with the property that every regular level set of the concordance is just a collection of S^2's. In his thesis, Paul Melvin proved that if two 2-knots are 0-concordant, then a Gluck twist along one will result in the same smooth 4-manifold as a Gluck twist on the other. He asked the following question: Are all 2-knots 0-slice (i.e. 0-concordant to the unknot)? I will explain all relevant definitions, and mostly follow the paper by Nathan Sunukjian on this topic.

Swindles in Mathematics

Series
Geometry Topology Student Seminar
Time
Wednesday, April 17, 2019 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Sudipta KolayGeorgia Tech

We will see some instances of swindles in mathematics, primarily focusing on some in geometric topology due to Barry Mazur.

Definition of Casson Invariant

Series
Geometry Topology Student Seminar
Time
Wednesday, April 10, 2019 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Hongyi ZhouGeorgia Institute of Technology

Casson invariant is defined for the class of oriented integral homology 3-spheres. It satisfies certain properties, and reduce to Rohlin invariant after mod 2. We will define Casson invariant as half of the algebraic intersection number of irreducible representation spaces (space consists of representations of fundamental group to SU(2)), and then prove this definition satisfies the expected properties.

Dynamics and Topology of Contact 3-Manifolds with negative $\alpha$-sectional curvature: Lecture 4

Series
Geometry Topology Student Seminar
Time
Wednesday, February 6, 2019 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Surena HozooriGeorgia Institute of Technology
In this series of (3-5) lectures, I will talk about different aspects of a class of contact 3-manifolds for which geometry, dynamics and topology interact subtly and beautifully. The talks are intended to include short surveys on "compatibility", "Anosovity" and "Conley-Zehnder indices". The goal is to use the theory of Contact Dynamics to show that conformally Anosov contact 3-manifolds (in particular, contact 3-manifolds with negative α-sectional curvature) are universally tight, irreducible and do not admit a Liouville cobordism to the tight 3-sphere.

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