### TBA by Franco Vargas Pallete

- Series
- Geometry Topology Seminar
- Time
- Monday, April 26, 2021 - 14:00 for 1 hour (actually 50 minutes)
- Location
- ONLINE
- Speaker
- Franco Vargas Pallete – Yale University – franco.vargaspallete@yale.edu

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- Series
- Geometry Topology Seminar
- Time
- Monday, April 26, 2021 - 14:00 for 1 hour (actually 50 minutes)
- Location
- ONLINE
- Speaker
- Franco Vargas Pallete – Yale University – franco.vargaspallete@yale.edu

- Series
- Geometry Topology Seminar
- Time
- Monday, April 19, 2021 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Speaker
- Christine Ruey Shan Lee – University of South Alabama – crslee@southalabama.edu

- Series
- Geometry Topology Seminar
- Time
- Monday, April 19, 2021 - 14:00 for 1 hour (actually 50 minutes)
- Location
- ONLINE
- Speaker
- Marco Golla – Université de Nantes – marco.golla@univ-nantes.fr

- Series
- Geometry Topology Seminar
- Time
- Monday, April 5, 2021 - 14:00 for 1 hour (actually 50 minutes)
- Location
- ONLINE
- Speaker
- Diana Hubbard – Brooklyn College, CUNY – diana.hubbard@brooklyn.cuny.edu

- Series
- Geometry Topology Seminar
- Time
- Monday, March 29, 2021 - 14:00 for 1 hour (actually 50 minutes)
- Location
- ONLINE
- Speaker
- Yan Mary He – University of Toronto – yanmary.he@mail.utoronto.ca

- Series
- Geometry Topology Seminar
- Time
- Monday, March 22, 2021 - 14:00 for 1 hour (actually 50 minutes)
- Location
- ONLINE
- Speaker
- Tyrone Ghaswala – CIRGET, Université du Québec à Montréal – tyrone.ghaswala@cirget.ca

- Series
- Geometry Topology Seminar
- Time
- Monday, March 15, 2021 - 14:00 for 1 hour (actually 50 minutes)
- Location
- ONLINE
- Speaker
- Lvzhou Chen – UT Austin – lvzhou.chen@math.utexas.edu

- Series
- Geometry Topology Seminar
- Time
- Monday, February 22, 2021 - 14:00 for 1 hour (actually 50 minutes)
- Location
- ONLINE
- Speaker
- InSung Park – Indiana University Bloomington – park433@iu.edu

**Please Note:** Office hours will be held 3-4pm EST.

Complex dynamics is the study of dynamical systems defined by iterating rational maps on the Riemann sphere. For a rational map *f*, the Julia set *Jf* is a beautiful fractal defined as the repeller of the dynamics of *f*. Fractal invariants of Julia sets, such as Hausdorff dimensions, have information about the complexity of the dynamics of rational maps. Ahlfors-regular conformal dimension, abbreviated by ARconfdim, is the infimum of the Hausdorff dimension in a quasi-symmetric class of Ahlfors-regular metric spaces. The ARconfdim is an important quantity especially in geometric group theory because a natural metric, called a visual metric, on the boundary of any Gromov hyperbolic group is determined up to quasi-symmetry. In the spirit of Sullivan's dictionary, we can use ARconfdim to understand the dynamics of rational maps as well. In this talk, we show that the Julia set of a post-critically finite hyperbolic rational map f has ARconfdim 1 if and only if there is an *f*-invariant graph G containing the post-critical set such that the dynamics restricted to G has topological entropy zero.

- Series
- Geometry Topology Seminar
- Time
- Monday, February 8, 2021 - 14:00 for 1 hour (actually 50 minutes)
- Location
- ONLINE
- Speaker
- Peter Feller – ETH Zurich – peter.feller@math.ethz.ch

The writhe of a braid (=#pos crossing - #neg crossings) and the fractional Dehn twist coefficient of a braid (a rational number that measures "how much the braid twists") are the two most prominent examples of what is known as a quasimorphism (a map that fails to be a group homomorphism by at most a bounded amount) from Artin's braid group on n-strands to the reals.

We consider characterizing properties for such quasimorphisms and talk about relations to the study of knot concordance. For the latter, we consider inequalities for quasimorphism modelled after the so-called slice-Bennequin inequality:

writhe(B) ≤ 2g_4(K) - 1 + n for all n-stranded braids B with closure a knot K.

Based on work in progress.

- Series
- Geometry Topology Seminar
- Time
- Monday, February 1, 2021 - 14:00 for 1 hour (actually 50 minutes)
- Location
- ONLINE
- Speaker
- Ahmad Issa – University of British Columbia – aissa@math.ubc.ca

Given a knot K in the 3-sphere, the 4-genus of K is the minimal genus of an orientable surface embedded in the 4-ball with boundary K. If the knot K has a symmetry (e.g. K is periodic or strongly invertible), one can define the equivariant 4-genus by only minimising the genus over those surfaces in the 4-ball which respect the symmetry of the knot. I'll discuss some work with Keegan Boyle trying to understanding the equivariant 4-genus.

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