Seminars and Colloquia by Series

Morphisms of Curve Graphs and Surfaces

Series
Geometry Topology Student Seminar
Time
Wednesday, April 20, 2022 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Katherine BoothGeorgia Tech

Ivanov’s metaconjecture says that every object naturally associated to a surface S with a sufficiently rich structure has the mapping class group as its group of automorphisms. In this talk, I will present several cases of curve graphs that satisfy this metaconjecture and some extensions to even richer structures.

An exotic contractible 4 manifold

Series
Geometry Topology Student Seminar
Time
Wednesday, February 23, 2022 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Sierra KnavelGeorgia Tech

We will discuss Akbulut's construction of two smooth, contractible four-manifolds whose boundaries are diffeomorphic and extend to a homeomorphism but not to a diffeomorphism of the manifolds. 

Topological Methods in Convexity

Series
Geometry Topology Student Seminar
Time
Wednesday, February 16, 2022 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Kevin ShuGeorgia Tech

Topological methods have had a rich history of use in convex optimization, including for instance the famous Pataki-Barvinok bound on the ranks of solutions to semidefinite programs, which involves the Borsuk-Ulam theorem. We will give two proofs of a similar sort involving the use of some basic homotopy theory. One is a new proof of Brickman's theorem, stating that the image of a sphere into R^2 under a quadratic map is convex, and the other is an original theorem stating that the image of certain matrix groups under linear maps into R^2 is convex. We will also conjecture some higher dimensional analogues.

The slice-ribbon conjecture and 3-stranded pretzel knots

Series
Geometry Topology Student Seminar
Time
Wednesday, February 9, 2022 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Hugo ZhouGeorgia Tech

This is an expository talk about the slice-ribbon conjecture. A knot is slice if it bounds a disk in the four ball. We call a slice knot ribbon if it bounds a slice disk with no local maxima. The slice-ribbon conjecture asserts all slice knots arise in this way. We also give a very brief introduction to Greene, Jabuka and Lecuona's works on the slice-ribbon conjecture for 3-stranded pretzel knots.

Teichmüller space via skein algebras

Series
Geometry Topology Student Seminar
Time
Wednesday, February 2, 2022 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006 (also in BlueJeans)
Speaker
Tao YuGeorgia Tech

Quantum Teichmüller space was first introduced by Chekhov and Fock as a version of 2+1d quantum gravity. The definition was translated over time into an algebra of curves on surfaces, which coincides with an extension of the Kauffman bracket skein algebra. In this talk, we will discuss the relation between the Teichmüller space and the Kauffman bracket, and time permitting, the quantized version of this correspondence.

Meeting URL: https://bluejeans.com/106460449/5822

 

An introduction to Cork twists, Gluck twists, and Logarithmic transformations of 4-manifolds.

Series
Geometry Topology Student Seminar
Time
Wednesday, December 1, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006 (also in BlueJeans)
Speaker
Sierra KnavelGeorgia Tech

Please Note: BlueJeans link: https://bluejeans.com/609527728/0740

The main goal of manifold theory is to classify all n-dimensional topological manifolds. For a smooth 4-manifold X, we aim to understand all of the exotic smooth structures there are to the smooth structure on X. Exotic smooth structures are homeomorphic but not diffeomorphic. Cork twists, Gluck twists, and Log transforms are all ways to construct possible exotic pairs by re-gluing embedded surfaces in the 4-manifold. In this talk, we define these three constructions.  

An Alexander method for infinite-type surfaces

Series
Geometry Topology Student Seminar
Time
Wednesday, November 17, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
Online (via BlueJeans)
Speaker
Roberta ShapiroGeorgia Tech

Please Note: BlueJeans link: https://bluejeans.com/575457754/6776

Given a surface S, the Alexander method is a combinatorial tool used to determine whether two self-homeomorphisms of S are isotopic. This statement was formalized in the case of finite-type surfaces, which are surfaces with finitely generated fundamental groups. A version of the Alexander method was extended to infinite-type surfaces by Hernández-Morales-Valdez and Hernández-Hidber. We extend the remainder of the Alexander method to include infinite-type surfaces. 

 

In this talk, we will talk about several applications of the Alexander method. Then, we will discuss a technique useful in proofs dealing with infinite-type surfaces and provide a "proof by example" of an infinite-type analogue of the Alexander method.

This will be practice for a future talk and comments and suggestions are appreciated.

G-equivariant PL-Morse theory

Series
Geometry Topology Student Seminar
Time
Wednesday, November 3, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006 (also in BlueJeans)
Speaker
Daniel MinahanGeorgia Tech

Please Note: BlueJeans link: https://bluejeans.com/473141052/9784

Morse theory is a standard concept used in the study of manifolds.  PL-Morse theory is a variant of Morse theory developed by Bestvina and Brady that is used to study simplicial complexes.  We develop an extension of PL-Morse theory to simplicial complexes equipped with an action of a group G.  We will discuss some of the basic ideas in this theory and hopefully sketch proofs of some forthcoming results pertaining to the homology of the Torelli group.

Automorphisms of B_n via Total Symmetry

Series
Geometry Topology Student Seminar
Time
Wednesday, October 27, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006 (also in BlueJeans)
Speaker
Noah CaplingerGeorgia Tech

Please Note: BlueJeans link: https://bluejeans.com/208969592/1051

In this talk, I will present a proof of Dyer-Grossman's description of Aut(B_n) inspired by Kordek-Margalit's work classifying homomorphisms B_n' to B_n. Time permitting, I will also discuss how these techniques can be used to classify homomorphisms B_n to B_m.

Smooth concordance, homology cobordism, and the figure-8 knot

Series
Geometry Topology Student Seminar
Time
Wednesday, October 20, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006 (also in BlueJeans)
Speaker
Sally CollinsGeorgia Tech

Please Note: BlueJeans link: https://bluejeans.com/936509442/0487

Given two knots K_1 and K_2, their 0-surgery manifolds S_0^3(K_1) and S_0^3(K_2) are homology cobordant rel meridian if they are homology cobordant preserving the homology class of the positively oriented meridian. It is known that if K_1 ∼ K_2, then S_0^3(K_1) and S_0^3(K_2) are homology cobordant rel meridian. The converse of this statement was first disproved by Cochran-Franklin-Hedden-Horn.  In this talk we will provide a new counterexample, the pair of knots 4_1 and M(4_1) where M is the Mazur satellite operator. S_0^3(4_1) and S_0^3(M(4_1)) are homology cobordant rel meridian, but 4_1 and M(4_1) are non-concordant and have concordance orders 2 and infinity, respectively. 

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