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**Title**

**Speaker**

**Time**

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Quadratic differentials and extremal problems revealed: the shocking details

Razvan Teodorescu

4:00pm-5:00pm

CMC 130

**Abstract**

Following the comprehensive presentations given by professors Khavinson, Rakhmanov, and Solynin, on the topics mentioned in this title, we'll consider the problem of dynamics of critical trajectories and arrive at what Michael Berry once called “a Victorian discontinuity”.

**Title**

**Speaker**

**Time**

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On extremal problems solved by Quadratic Differentials (QD), Part IV

E. A. Rakhmanov

4:00pm-5:00pm

CMC 130

**Title**

**Speaker**

**Time**

**Place**

On extremal problems solved by Quadratic Differentials (QD), Part III

E. A. Rakhmanov

4:00pm-5:00pm

CMC 130

No seminar this week.

**Title**

**Speaker**

**Time**

**Place**

On extremal problems solved by Quadratic Differentials (QD), Part II

E. A. Rakhmanov

4:00pm-5:00pm

CMC 130

**Title**

**Speaker**

**Time**

**Place**

On extremal problems solved by Quadratic Differentials (QD), Part I

E. A. Rakhmanov

4:00pm-5:00pm

CMC 130

**Abstract**

There is a large class of extremal problems in geometric function theory whose solutions may be presented as a union of critical trajectories of a QD. Such are, say, Minimal Capacity type of problems and (more general) Moduli-type problems. The plan is to make an elementary introduction to the field.

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**Speaker**

**Time**

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Extremal domains for the analytic content, Part II

Dmitry Khavinson

4:00pm-5:00pm

CMC 130

**Title**

**Speaker**

**Time**

**Place**

Extremal domains for the analytic content

Dmitry Khavinson

4:00pm-5:00pm

CMC 130

**Abstract**

The analytic content \(\lambda(K)\) of a set \(K\) is the distance in the uniform norm from \(\bar{z}\) to functions analytic in a neighborhood of \(K\). It was shown more than 30 years ago (H. Alexander & D. Khavinson) that $$ \frac{2\mathrm{Area}(K)} {\mathrm{Perimeter}(K)} \le\lambda(K) \le\sqrt{\frac{\mathrm{Area}(K)}\pi}. $$ The upper bound is attained only for disks (H. Alexander & D. Khavinson). The lower bound was conjectured to hold only for disks and annuli (Khavinson's thesis, 1982). In this talk I shall outline the recent proof of this conjecture obtained in a joint work with A. Abanov (Texas A&M), C. Bénéteau and R. Teodorescu (USF).