# Colloquium

The Colloquium is held on Mondays at 4pm in 208 University Hall.

### Fall Quarter, 2022

- October 13,
**Svetlana Jitomirskaya** (UC Irvine)

Fractal properties of the Hofstadter butterfly, eigenvalues, and topological phase transitions
**Abstract**: We will give a brief introduction to the spectral theory of ergodic operators, assuming only introductory graduate courses as background. Then we will discuss several remarkable spectral phenomena present in the class of quasiperiodic operators and illustrate using the almost Mathieu (aka Harper’s) operator – a model behind the Hofstadter’s butterfly and Thouless theory of the Quantum Hall Effect. We will discuss the fascinating history of this model, that is now heavily studied in physics and linked to several Nobel and IMU prizes, and then will describe several recent results that resolve some long-standing conjectures.

- October 31,
**Ben Webster** (U Waterloo and Perimeter Institute)

Canceled due to COVID
- November 14,
**Siu-Cheong Lau** (Boston U)

Mirror correspondences between quiver representations and sheaves
**Abstract**: Quiver representations emerge from Lie theory and mathematical physics. In this talk, I will first explain the basic setting of quiver representations, with motivations coming from modeling branes and brains. Second, I will recall some well-known correspondences between quiver algebras and geometry of sheaves. Finally, I will talk about our project on constructing these algebro-geometric correspondences from mirror symmetry.

- November 21,
**Sebastian Schreiber** (UC Davis)

Canceled
- November 28, Mock AMS talks

Alonso Delfin ,Greg Knapp, Marissa Masden

**Previous years:** 2021 2020 2019 2018 2017 2016 2015 2013 2012 2011 2010