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## Department of Mathematics

### Function Theory Study Seminar

Wednesdays 3:30pm-4:20pm in Cardwell 120
Organizers: Tanya Firsova (tanyaf@math.ksu.edu), Hrant Hakobyan (hakobyan@math.ksu.edu), Pietro Poggi-Corradini (pietro@math.ksu.edu), and Lizaveta Ihnatsyeva (ihnatsyeva@math.ksu.edu)

The seminar where people report on classic papers, obscure old papers, brand new preprints not yet checked, or go into more details about proofs in their own work.

### Wednesday, Sep. 20

• Tanya Firsova, Kansas State University

Title: Growth and distortion estimates for univalent functions.

Abstract: Univalent functions are holomorphic one-to-one maps. They are main characters in Riemann mapping theorem and are important for SLEs. We will discuss the growth and distortion estimates on univalent functions. In particular, we will prove Bieberbach's Theorem: if $f(z)=z+a_2z+\dots$ is a univalent function, then $|a_2|<2$. The methods used in the talk are elementary and the talk will be accessible to graduate students with basic knowledge of holomorphic functions.

### Wednesday, Sep. 27

• Jared Hoppis, Kansas State University

Title: Introduction to Modulus of Curve Families and Measures.

Abstract: We will discuss the definition of Modulus, properties and why we care about it, and some basic examples for connecting curve families. The talk will be accessible to the new graduate students.

### Wednesday, Oct. 4

• Pietro Poggi-Corradini, Kansas State University

Title: Report on "Extremal length of vector measures" by Aikawa and Ohtsuka, I

Abstract: Extremal length is a concept closely related to the notions of modulus and capacity. We will begin by recalling the notion of modulus of measures developed by Fuglede. And then give an overview of the main results of the paper.

### Wednesday, Oct. 11

• Pietro Poggi-Corradini, Kansas State University

Title: Report on "Extremal length of vector measures" by Aikawa and Ohtsuka, II

Abstract: Extremal length is a concept closely related to the notions of modulus and capacity. We will begin by recalling the notion of modulus of measures developed by Fuglede. And then give an overview of the main results of the paper.