Seminars and Colloquia by Series

Computing the fractional Dehn twist coefficient of braids using non-crossing partition diagrams

Series
Geometry Topology Seminar
Time
Monday, October 12, 2026 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker

The dual Garside left canonical form is used to solve the conjugacy problem in braid theory, introduced by Xu (3-braids), Kang-Ko-Lee (4-braids) and Birman-Ko-Lee (n-braids). The fractional Dehn twist coefficient (FDTC) is a measurement of the boundary twist of a surface homeomorphism, introduced by Honda-Kazez-Matic. In contact geometry, it is a powerful tool to detect tightness/overtwistedness of a given contact structure. In this talk, I will give applications of the left canonical form to the computation of the FDTC of 4-braids.

Ribbon minimal knots and links

Series
Geometry Topology Seminar
Time
Monday, September 28, 2026 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Gary Dunkerley – UGA

It has been observed that the relationship of ribbon concordance induces monotonic behavior across several link invariants. 

Resolving a famous open question of Gordon, Agol unified these observations by showing that ribbon concordance induces a partial order on knots in the 3-sphere.

Agol's argument can be extended to show that ribbon concordance likewise induces a partial order on arbitrary links in the 3-sphere.

Perhaps motivated by the slice-ribbon conjecture, it is natural and interesting to ask which knots and links are minimal with respect to this partial order. 

Leveraging recent developments in link Floer homology, I will share new examples of ribbon minimal knots and links. 

Some of this work is joint with Jaewon Lee and Alessio Di Prisa.

Supersqueezed surfaces

Series
Geometry Topology Seminar
Time
Monday, September 21, 2026 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Hongda Qiu – Georgia Tech

We discuss a new problem by Dmitri Burago and Anton Petrunin. Consider a $C^2$-smooth surface embedded in $\RR^3$ with principal curvatures $\leq 1$. Does such a surface necessarily enclose a volume at least that of the unit ball? We address results from two opposite perspectives: On the one hand, we can construct a counterexample by deforming Lagunov's fishbowl (a fattened Bing's house); on the other hand, there are positive results with additional conditions. Many problems remain open.

Ziggurats and taut foliations

Series
Geometry Topology Seminar
Time
Monday, September 14, 2026 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jonathan Zung – Georgia Tech –

Given a link in a closed 3-manifold, which Dehn surgery multislopes give rise to 3-manifolds with taut foliations? In this talk, I will discuss the ziggurat phenomenon: restricting to those foliations transverse to a fixed flow on the link complement, the set of multislopes typically has a fractal staircase shape with rational corners. In joint work with Thomas Massoni, we explain the ziggurat phenomenon in some contexts using tools from contact geometry. For those who have already seen a talk about this work, I'll try to emphasize some different aspects.

The tau-invariant of braided and squeezed satellites

Series
Geometry Topology Seminar
Time
Monday, August 31, 2026 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Alex Eldridge – Georgia Tech

The Ozsvath-Szabo tau-invariant is a concordance invariant coming from knot Floer homology. The tools of bordered Heegaard Floer homology provide a way to study the knot Floer homology of satellite knots, and for many patterns have given formulas for the behavior of tau under satelliting. We give formulas for tau and epsilon of satellite knots whose patterns are braided, meaning they wind around the solid torus without reversing, and we do this without the use of bordered Heegaard Floer homology. Our methods lead us to define the class of squeezed patterns, analogous to squeezed knots as defined by Feller-Lewark-Lobb. We show that all braided patterns are squeezed, and we give a tau formula for squeezed patterns as well. Also, towards a conjecture of Hedden, we show that no squeezed pattern, and thus no braided pattern, with winding number at least 2 induces a homomorphism on the concordance group.

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