Integrated Calendar

Abstract: Haglund, Rhoades, and Shimozono generalized the co-invariant quotient $R_n$ of Borel, as a representation of the symmetric group, to quotients $R_{n,k}$. Gillespie and Rhoades constructed higher Specht bases for these quotients, using the higher Specht polynomials of Ariki, Terasoma, and Yamada. We show how to decompose these quotients into ones that sit inside natural stable representations, which have explicit limits as representations of infinite symmetric groups on eventually symmetric functions.

Natural disasters like floods and droughts pose significant threats to communities worldwide, making accurate and timely forecasting essential for mitigation and response. This presentation will delve into the development and implementation of AI-based models for natural disaster forecasting, with a specific focus on floods and droughts.We will explore Google's machine learning-driven hydrologic model for riverine flood forecasting, which has been operational for several years and provides predictions up to seven days in advance. Additionally, we will discuss a flash flood model currently in development. The talk will also cover a machine learning model for drought forecasting, which provides predictions at a three-month lead time.A key focus of this discussion will be the robust evaluation of these models. We'll examine various methods for assessing their skill, including comparisons against historical data, satellite observations, and established performance benchmarks across different regions. This presentation will highlight how advanced AI can enhance our ability to predict and prepare for natural disasters, ultimately supporting global resilience efforts.

De-Gennes’s “ant-in-a-labyrinth” problem reminds us that physicists have an affinity for ants. Like particles, ants come in large groups and interact locally among themselves and with the environment. However, there are large discrepancies between an ensemble of particles and a colony of ants. While groups of particles are governed solely by microscopic laws and large-scale symmetries, ants appear able to sidestep these constraints to display a collective will aimed at macroscopic goals. In doing so, they often exhibit behaviors that resemble intelligence and problem-solving. I will present three puzzle-like configurations that quantify performance and expose limits: the ant-in-a-labyrinth puzzle, the piano-movers problem, and three-dimensional leaf-nest construction. For each, we will compare data to physics-inspired null models to locate where ants deviate from particle baselines and to identify the minimal individual-level ingredients that support an animate, cognitive colony. 

Clouds are among the most influential components of Earth’s radiation budget, modulating radiative transfer across the electromagnetic spectrum. As a result, even processes that contribute relatively weak radiative effects, such as those occurring in clouds’ surroundings, can be substantial compared to clear-sky conditions and therefore important to Earth’s energy budget and the climate it sustains. Over the past two decades, studies have highlighted several mechanisms contributing to the radiative signatures around clouds, including three-dimensional radiative transfer, enhanced aerosol humidification, and subvisible cloud features. Recent work by Eytan et al. (2025) has provided the first quantification of the top-of-atmosphere (TOA) radiative impact of these near-cloud regions. Their findings suggest a shortwave effect of ~9 W/m² over the ocean in the local afternoon, implying that clouds indirectly amplify the aerosol direct radiative effect. In the longwave, a mean effect of ~1 W/m² corresponds to the radiative forcing of an additional ~90 ppm of CO₂, highlighting these regions' climate relevance. In this talk, I will introduce a new framework for partitioning the sky into three radiative categories: cloudy, pure clear-sky, and cloud-influenced clear-sky. I will demonstrate how this refined classification reveals near-cloud regions' hidden but crucial contribution to all-sky radiative fluxes. We will explore how these contributions vary with cloud type, spatial cloud patterns, and background aerosol loading. By explicitly accounting for these previously overlooked regions, this new paradigm opens the door to a more comprehensive understanding of the processes involved in the cloud’s role in Earth’s energy budget and in aerosol–cloud interactions, which are two of the largest sources of uncertainty in climate projections according to the latest IPCC report. Ultimately, this work aims to establish a more unified approach to treating the atmosphere, from dry aerosols to clouds, and to deepen our understanding of how clouds and their surrounding environments influence Earth’s climate. In doing so, it offers a promising path toward reducing one of the most persistent uncertainties in climate change projections.

I will introduce the analytic structure theory of Lie groups through their connection with Lie algebras, which capture the infinitesimal behavior of the group. We will explore how the exponential map and the Baker–Campbell–Hausdorff formula bridge the two, leading to key insights such as the local-to-global correspondence and automatic analyticity of Lie groups. I will mostly follow pages 25–51 in Terrence Tao’s book.