• Speaker: Kesong Yan, MSU and Guangxi University of Finance and Economics
• Title: Local entropy for topological dynamical systems
• Date: 05/01/2019
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall

In this talk, we will review the local entropy theory for topological dynamical systems.

• Speaker: Ian Jauslin, Princeton University
• Title: Time-evolution of electron emission from a metal surface
• Date: 05/02/2019
• Time: 11:00 AM - 12:00 PM
• Place: C517 Wells Hall

The electrons in a metal can be extracted from the metal by a variety of processes: for instance by applying a strong electric field (field emission), or shining an intense laser pulse (photoemission). In the case of field emission, the celebrated and widely used Fowler-Nordheim equation predicts a value for the current of electrons outside the metal. In this talk, I will show that the Fowler-Nordheim equation emerges as the long-time asymptotic solution of a Schrodinger equation with a realistic initial condition, thereby justifying the use of the Fowler Nordheim equation in real setups. As for photoemission, the expression for the current has been predicted by Faisal et al, and I will discuss ongoing work to show that this prediction emerges as the long-time asymptotic solution of a Schrodinger equation. In both cases, I will discuss the time scale of the convergence.

• Speaker: Jane Zimmerman, MSU
• Title: MTH 103A/B: Experiences from the classroom and future directions
• Date: 05/02/2019
• Time: 2:30 PM - 3:30 PM
• Place: C109 Wells Hall

No abstract available.

• Speaker: Eiko Kin, Osaka University, Japan
• Title: A construction of pseudo-Anosov braids with small normalized entropies
• Date: 05/07/2019
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall

We consider pseudo-Anosov braids b. The logarithm of the stretch factor of the pseudo-Anosov braid b is called the entropy. By normalized entropy of b with n strands, we mean the n times (the entropy of b). Let b_n be a sequence of pseudo-Anosov braids. We say that the sequence b_n has a small normalized entropy if the number of strands of b_n behaves like n and the normalized entropy of b_n is bounded from above by a constant which does not depend on n. We give a construction of sequences of pseudo-Anosov braids having small normalized entropies. As an application, we explain the smallest entropy among skew-palindromic braids with n strands is comparable to 1/n. This is joint work with Susumu Hirose.