Seminars and Colloquia by Series

Convex hypersurface theory in all dimensions

Series
Geometry Topology Working Seminar
Time
Friday, November 5, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Austin ChristianGeorgia Tech

In dimension three, Giroux developed the theory of convex surfaces in contact manifolds, and this theory has been used to prove many important results in contact geometry, as well as to establish deep connections with topology.  More recently, Honda and Huang have reformulated the work of Giroux in order to extend the theory to higher dimensions.  The purpose of this sequence of talks is to understand this reformulation and to see some of its applications.

Applications of Donaldson's Diagonalization Theorem

Series
Geometry Topology Working Seminar
Time
Friday, October 15, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jonathan SimoneGeorgia Tech

Please Note: Donaldson’s Diagonalization Theorem has been used extensively over the past 15 years as an obstructive tool. For example, it has been used to obstruct: rational homology 3-spheres from bounding rational homology 4-balls; knots from being (smoothly) slice; and knots from bounding (smooth) Mobius bands in the 4-ball. In this multi-part series, we will see how this obstruction works, while getting into the weeds with concrete calculations that are usually swept under the rug during research talks.

Applications of Donaldson's Diagonlization Theorem

Series
Geometry Topology Working Seminar
Time
Friday, October 8, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jonathan SimoneGeorgia Tech

Donaldson’s Diagonalization Theorem has been used extensively over the past 15 years as an obstructive tool. For example, it has been used to obstruct: rational homology 3-spheres from bounding rational homology 4-balls; knots from being (smoothly) slice; and knots from bounding (smooth) Mobius bands in the 4-ball. In this multi-part series, we will see how this obstruction works, while getting into the weeds with concrete calculations that are usually swept under the rug during research talks.

Applications of Donaldson's Diagonalization Theorem

Series
Geometry Topology Working Seminar
Time
Friday, October 1, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jonathan SimoneGeorgia Tech

Donaldson’s Diagonalization Theorem has been used extensively over the past 15 years as an obstructive tool. For example, it has been used to obstruct: rational homology 3-spheres from bounding rational homology 4-balls; knots from being (smoothly) slice; and knots from bounding (smooth) Mobius bands in the 4-ball. In this multi-part series, we will see how this obstruction works, while getting into the weeds with concrete calculations that are usually swept under the rug during research talks.

Whitney Towers, Higher Order Intersections, and Tree-Valued Invariants, Part 2

Series
Geometry Topology Working Seminar
Time
Friday, September 24, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Miriam KuzbaryGeorgia Tech

In this pair of talks I will survey some of the machinery developed by Conant, Schneiderman, and Teichner to study Whitney towers, and their applications to the study of knot and link concordance. Whitney towers can be thought of as measuring the failure of the Whitney trick in dimension 4 and can be used, in a sense, to approximate slice disks. The talks will be based on various papers of Schneiderman, Conant-Schneiderman-Teichner, Cochran-Orr-Teichner and lecture notes by those authors. 

Whitney Towers, Higher Order Intersections, and Tree-Valued Invariants

Series
Geometry Topology Working Seminar
Time
Friday, September 17, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Miriam KuzbaryGeorgia Tech

In this pair of talks I will survey some of the machinery developed by Conant, Schneiderman, and Teichner to study Whitney towers, and their applications to the study of knot and link concordance. Whitney towers can be thought of as measuring the failure of the Whitney trick in dimension 4 and can be used, in a sense, to approximate slice disks. The talks will be based on various papers of Schneiderman, Conant-Schneiderman-Teichner, Cochran-Orr-Teichner and lecture notes by those authors.

Nonlinear Mechanics of Accretion

Series
Geometry Topology Working Seminar
Time
Friday, April 19, 2019 - 14:00 for 2 hours
Location
Skiles 006
Speaker
Arash Yavari and Fabio Sozio, School of Civil and Environmental EngineeringGeorgia Tech
We formulate a geometric nonlinear theory of the mechanics of accretion. In this theory the material manifold of an accreting body is represented by a time-dependent Riemannian manifold with a time-independent metric that at each point depends on the state of deformation at that point at its time of attachment to the body, and on the way the new material isadded to the body. We study the incompatibilities induced by accretion through the analysis of the material metric and its curvature in relation to the foliated structure of the accreted body. Balance laws are discussed and the initial-boundary value problem of accretion is formulated. The particular cases where the growth surface is either fixed or traction-free are studied and some analytical results are provided. We numerically solve several accretion problems and calculate the residual stresses in nonlinear elastic bodies induced from accretion.

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