Time: Wednesday 4:00 pm (unless otherwise noted)
schedule for the semester (Spring 2025)
March 5: Ron Lifshitz (School of Physics & Astronomy, Tel Aviv University)
March 19: Juhun Baik (KAIST)
April 16: Ethan Ackelsberg (École Polytechnique Fédérale de Lausanne)
May 7: Jiyoung Han (Pusan National University)
May 21: Minsung Kim (KTH Royal Institute of Technology)
3.5: Ron Lifshitz
Title: What is a Crystal? A new paradigm for an old question
Abstract: The discovery of quasicrystals signalled the beginning of a remarkable scientific revolution, in which some of the most basic notions of condensed matter physics and material science have undergone a thorough re-examination. Over four decades later, the field continues to intrigue us with scientific puzzles, surprising discoveries, and new possibilities for applications. I will focus on some current issues from my own research – such as soft matter quasicrystals and photonic applications based on metamaterials – but only after giving a concise overview for non-specialists of what quasicrystals are, and why their discovery was so important.
March 19: Juhun Baik
Title: Quadratic polynomials and big mapping classes
Abstract: The Cantor set arises naturally in various dynamical systems. In particular, the iteration of a complex polynomial yields an invariant set (called Julia set), which is often homeomorphic to a Cantor set. In this talk, I will focus on the iteration of quadratic polynomials and how the Julia set changes when the parameter varies. The behavior of the Julia set produce a mapping class of a plane-Cantor set as a result. I will also discuss how to construct the mapping class of the plane - Cantor set which reflects the polynomial dynamics. This is a joint work with Prof. Hyungryul Baik.
April 16: Ethan Ackelsberg
Title: Equidistribution of orbits in 2-step nilpotent translational systems and applications
Abstract: Solutions to several major problems in additive combinatorics rely on a dichotomy between “structure” and “randomness,” characterized in many cases by Gowers uniformity norms. In the ergodic theory context, there is a corresponding family of seminorms (the Host—Kra seminorms) producing Host—Kra factors as the “structure” behind combinatorial phenomena. A recent result of Jamneshan, Shalom, and Tao (2024) describes order 2 Host—Kra factors for actions of abelian groups as inverse limits of 2-step nilpotent translational systems defined on homogeneous spaces of 2-nilpotent locally compact Polish groups.
In this talk, we will discuss a new Ratner-type equidistribution theorem for orbits in 2-step nilpotent translational systems, generalizing previous equidistribution results for (2-step) nilsystems. We will also discuss a combinatorial application of the equidistribution theorem to a problem about infinite triple sumsets in sets of positive density in abelian groups.
Based on joint work with Asgar Jamneshan.