Intro to Research at UCR seminar 2026
Intro to Research at UCR seminar 2026
Thursday 3:30-4:30 in 284 Skye Hall
Thursday 3:30-4:30 in 284 Skye Hall
Schedule:
April 2: Zhenghe Zhang
Title: Introduction to Ergodic Schrödinger operators.
Abstract: Ergodic Schrödinger operators arise naturally in the study of Schrödinger equations, which model the motion of a quantum particle in a disordered medium. On the other hand, the spectral analysis of such operators can often be reformulated as problems in dynamical systems. In this talk, I will briefly introduce how these three areas--mathematical physics, spectral analysis, and dynamical systems--interact in my research.
April 9: Sarah Yeakel
Title: Homotopy theory: a framework for topology
Abstract: In this talk, we will introduce fundamental concepts in homotopy theory, the study of spaces under continuous deformations, and the long-term project of computing algebraic invariants of spaces, including homology and homotopy groups. We will focus on the history of a class of examples called lens spaces, nontrivial 3-manifolds which are completely classified up to homeomorphism.
April 16: Siting Liu
Title: From ICON to GenICON: In-Context Operator Learning with Uncertainty Quantification
Abstract: I will introduce In-Context Operator Networks (ICON), a framework in which a single neural network learns solution operators for differential equations directly from a few prompted input-output examples at inference time, without any weight updates. ICON acts as a few-shot learner across forward and inverse problems for ODEs, PDEs, and mean-field control. I will then present a probabilistic interpretation: under a random differential equation data model, ICON implicitly computes the posterior predictive mean given the context, linking operator learning to Bayesian inference. This motivates GenICON, a generative variant that samples from the posterior predictive for principled uncertainty quantification, yielding a unified Bayesian view of in-context operator learning.
April 23: David Weisbart
April 30: Wee Liang Gan
May 7: Qixuan Wang
May 14: Tom Gannon
May 21: Fred Wilhelm
May 28: Yat Tin Chow
June 4: Agniezska Zelerowicz