Seminars and Colloquia Schedule

TBD by Songhao Zhu

Series
Algebra Seminar
Time
Monday, September 30, 2024 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Songhao Zhu – Georgia Tech

Existence of optimal flat ribbons

Series
Geometry Topology Seminar
Time
Monday, September 30, 2024 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Matteo Raffaelli – Georgia Tech

We revisit the classical problem of constructing a developable surface along a given Frenet curve $\gamma$ in space. First, we generalize a well-known formula, introduced in the literature by Sadowsky in 1930, for the Willmore energy of the rectifying developable of $\gamma$ to any (infinitely narrow) flat ribbon along the same curve. Then we apply the direct method of the calculus of variations to show the existence of a flat ribbon along $\gamma$ having minimal bending energy. Joint work with Simon Blatt.

Smooth Discrepancy and Littlewood's Conjecture

Series
Analysis Seminar
Time
Wednesday, October 2, 2024 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Niclas Technau – University of Bonn –

Given x in $[0,1]^d$, this talk is about the fine-scale distribution of the Kronecker sequence $(n x mod 1)_{n\geq 1}$.
After a general introduction, I will report on forthcoming work with Sam Chow.
Using Fourier analysis, we establish a novel deterministic analogue of Beck’s local-to-global principle (Ann. of Math. 1994),
which relates the discrepancy of a Kronecker sequence to multiplicative diophantine approximation.
This opens up a new avenue of attack for Littlewood’s conjecture.

Introduction to Bergman geometry

Series
Geometry Topology Seminar
Time
Wednesday, October 2, 2024 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jihun Yum – Gyeongsang National University in South Korea

The Poincaré metric on the unit disc $\DD \subset \CC$, known for its invariance under all biholomorphisms (bijective holomorphic maps) of $\DD$, is one of the most fundamental Riemannian metrics in differential geometry.

In this presentation, we will first introduce the Bergman metric on a bounded domain in $\CC^n$, which can be viewed as a generalization of the Poincaré metric. We will then explore some key theorems that illustrate how the curvature of the Bergman metric characterizes bounded domains in $\mathbb{C}^n$ and more generally, complex manifolds. Finally, I will discuss my recent work "Bergman local isometries are biholomorphisms" related to these concepts.