Seminars and Colloquia by Series

On Extremal Polynomials: 5. Upper Estimates and Irregularity of Widom Factors

Series
Mathematical Physics and Analysis Working Seminar
Time
Friday, February 10, 2023 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Burak HatinogluGeorgia Institute of Technology

We will continue to focus on Cantor-type sets we introduced last week. Using them we will consider maximal growth rate and irregular behavior of Widom factors (nth Chebyshev number divided by nth power of logarithmic capacity). We will also discuss a recent result of Jacob Christiansen, Barry Simon and Maxim Zinchenko, which shows that Widom factors of Parreau-Widom sets are uniformly bounded.

On Extremal Polynomials: 4. Estimates of Chebyshev Numbers and Weakly Equilibrium Cantor-type Sets

Series
Mathematical Physics and Analysis Working Seminar
Time
Friday, February 3, 2023 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Burak HatinogluGeorgia Institute of Technology

We will continue to discuss lower and upper estimates of Widom factors. We will also introduce Cantor-type sets, constructed as the intersection of the level domains for simple sequences of polynomials. Using these Cantor-type sets we will prove some results on growth of Widom factors.

On Extremal Polynomials: 3. Asymptotic and Estimates of Chebyshev Numbers

Series
Mathematical Physics and Analysis Working Seminar
Time
Friday, January 27, 2023 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Burak HatinogluGeorgia Institute of Technology

After finishing the proof of equivalence of the Chebyshev constant of a set and its logarithmic capacity, we will start to discuss classical and recent results on estimates and asymptotics of Chebyshev numbers.

On Extremal Polynomials: 2.Chebyshev Polynomials and Potential Theory

Series
Mathematical Physics and Analysis Working Seminar
Time
Friday, January 20, 2023 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Burak HatinogluGeorgia Institute of Technology

In the first talk of this series we introduced the definition of Chebyshev polynomials on compact subsets of the complex plane and discussed some properties. This week, after a short review of  the first talk, we will start to discuss asymptotic properties of Chebyshev polynomials and how they are related with logarithmic potential theory. Our main focus will be the necessary concepts from potential theory needed in the study of asymptotic properties of Chebyshev polynomials.