Department of

# Mathematics

Seminar Calendar
for events the day of Friday, February 25, 2022.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
     January 2022          February 2022            March 2022
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Friday, February 25, 2022

1:00 pm in Zoom,Friday, February 25, 2022

#### Dimension distortion and applications

###### Efstathios Konstantinos Chrontsios Garitsis (UIUC Math)

Abstract: Since Hausdorff dimension was first introduced in 1918, many different notions of dimension have been defined and used throughout many areas of Mathematics. An interesting topic has always been the distortion of said dimensions of a given set under a specific class of mappings. More specifically, Gehring and V\"ais\"al\"a proved in 1973 a theorem concerning the distortion of Hausdorff dimension under quasiconformal maps, while Kaufman in 2000 proved the analogous result for Box-counting dimension. In this talk, an introduction to the different types of dimensions will be presented, along with the results of of Gehring, V\"ais\"al\"a and Kaufman. We will then proceed to discuss analogous theorems we proved for the Assouad dimension and spectrum, which describe how K-quasiconformal maps change these notions of a given subset of $\mathbb{R}^n$. We will conclude the talk by demonstrating how said theorems can be applied to fully classify polynomial spirals up to quasiconformal equivalence. Contact: ryanm12@illinois.edu for Zoom coordinates.

1:00 pm in Zoom,Friday, February 25, 2022

#### Dimension distortion and applications

###### Efstathios Konstantinos Chrontsios Garitsis (UIUC Math)

Abstract: Since Hausdorff dimension was first introduced in 1918, many different notions of dimension have been defined and used throughout many areas of Mathematics. An interesting topic has always been the distortion of said dimensions of a given set under a specific class of mappings. More specifically, Gehring and V\"ais\"al\"a proved in 1973 a theorem concerning the distortion of Hausdorff dimension under quasiconformal maps, while Kaufman in 2000 proved the analogous result for Box-counting dimension. In this talk, an introduction to the different types of dimensions will be presented, along with the results of of Gehring, V\"ais\"al\"a and Kaufman. We will then proceed to discuss analogous theorems we proved for the Assouad dimension and spectrum, which describe how K-quasiconformal maps change these notions of a given subset of $\mathbb{R}^n$. We will conclude the talk by demonstrating how said theorems can be applied to fully classify polynomial spirals up to quasiconformal equivalence. Contact: ryanm12@illinois.edu for Zoom coordinates.

3:00 pm in 341 Altgeld Hall,Friday, February 25, 2022