1. Invited Lecturer

Kaloshin教授是動力系統領域的領導人物, 他在Hamiltonian系統穩定性、可積性、天體力學、動態撞球、動態黎曼ζ函數等方向均有開創性的工作. 他近年關於Birkhoff猜想的工作備受矚目(Ann.Math.2016,2017,2018, GAFA 2018), 期望本系列演講能夠顯著提升國內相關領域的國際視野與水平。

https://www.ae-info.org/ae/Member/Kaloshin_Vadim

https://en.wikipedia.org/wiki/Vadim_Kaloshin

https://vadimkaloshin.com/biography

2. Lecture Abstract

The main topic of the minicourse is dynamics of Bikhoff billiards or billiards in convex bounded regions. Motivated by the famous question "Can you hear the shape of a drum?" We shall discuss several notions of deformational spectral rigidity for convex billiards. It turns out that techniques to study these notions are also applicable to perturbative Birkhoff Conjecture about integrable billiards.

3. Lecture Outline & Descriptions

3/3(Friday) 4:30-5:30pm

Lecture 1: Can you hear the shape of a drum? Laplace and length spectra of convex domains, elementary properties.

3/6(Monday) 4:30-5:30pm

Lecture 2: Lazutkin coordinates of convex domains. Action-angle and elliptic coordinates for billiards in an ellipse.

3/7(Tuesday) 4:30-5:30pm

Lecture 3: Deformational Spectral Rigidity of axis-symmetric nearly circular domains.

3/8(Wednesday) 4:30-5:30pm

Lecture 4: Local Birkhoff Conjecture for convex planar billiards.

4. Registration

https://forms.gle/KTtmnoPv5EALBgjT6

5. Join us Online

3/3_Can you hear the shape of a drum? Laplace and length spectra of convex domains, elementary properties.

3/6_Lazutkin coordinates of convex domains. Action-angle and elliptic coordinates for billiards in an ellipse.

3/7_Deformational Spectral Rigidity of axis-symmetric nearly circular domains.

3/8_Local Birkhoff Conjecture for convex planar billiards.

6. Relevant References

https://annals.math.princeton.edu/wp-content/uploads/Kaloshin-Sorrentino.pdf
https://annals.math.princeton.edu/wp-content/uploads/annals-v184-n2-p05-s.pdf
https://annals.math.princeton.edu/wp-content/uploads/annals-v186-n1-p07-s.pdf