Upcoming MAMS Seminar Series
Spring 2025
2/11/2025, Tue. 2:30-3:30 pm in Rockefeller 303
Speaker: Michael Roysdon (Case Western Reserve University)
Title: Comparison problems for Radon transforms
Abstract: In 1956 Herbert Busemann and Clinton M. Petty created a list of 10 problems in Convex Geometry, among which only the first had been solved fully in 1999. A key feature of the solution to the first problem is that it (and in fact, the majority of the Busemann-Petty problems) can be reformulated into the language of Harmonic Analysis. Inspired by the Busemann-Petty problems and their connection to Harmonic Analysis, we consider the following natural question for various Radon transforms: Let p>1. Given a pair of nonnegative, even and continuous functions f,g such that the Radon transform of f is pointwise smaller than the Radon transform of g, is it necessarily true that the L^p-norm of f is smaller than the L^p-norm of g? As it turns out, this simple question has a deep connection to the Busemann-Petty problem and the slicing problem of Bourgain. As a consequence of our investigation, we show that this implies reverse Oberlin-Stein type estimates for the spherical Radon transform when p >1; this is complementary to a recent work of Johnathan Bennett and Terence Tao in which similar reverse estimates were proven in the case 0 < p <= 1. We will discuss a similar problem for the dual Radon transform.
2/4/2025, Tue. 2:30-3:30 pm in Rockefeller 303
Speaker: Matthew Wascher (Case Western Reserve University)
Title: The effects of individual-level behavioral responses on SIS epidemic persistence
Abstract: The contact process (SIS epidemic model) has long been studied as a model for the spread of infectious disease through a population. One important question concerns the long-term behavior of the epidemic–does it result in a large outbreak, or does the infection die out quickly? There is a large literature on the effects of the underlying population structure on this long-term behavior. However, the role of individual-level behavioral responses on the epidemic is less studied. In this talk, I will introduce the contact process, some key ideas used to analyze it, and a few notable results. I will then discuss my recent work on modified versions of the contact process that include individual-level behavioral responses to the epidemic. I will present some results on how individual-level behavioral responses can influence the long-term behavior of an epidemic and discuss why analyzing these models is mathematically challenging.
Spring 2025
2/5/2025, Wed. 4-5 pm in Sears 439
Speaker: Professor Sakshi Arya (CWRU)
Title: Semi-Parametric Batched Global Multi-Armed Bandits with Covariates
Abstract: The multi-armed bandits (MAB) framework is a widely used approach for sequential decision-making, where a decision-maker selects an arm in each round with the goal of maximizing long-term rewards. Moreover, in many practical applications, such as personalized medicine and recommendation systems, feedback is delayed and provided in batches, contextual information is available at the time of decision-making, and rewards from different arms are related rather than independent.
We propose a novel semi-parametric framework for batched bandits with covariates and a shared parameter across arms, leveraging the single-index regression (SIR) model to capture relationships between arm rewards while balancing interpretability and flexibility. Our algorithm, Batched single-Index Dynamic binning and Successive arm elimination (BIDS), employs a batched successive arm elimination strategy with a dynamic binning mechanism guided by the single-index direction. We consider two settings: one where a pilot direction is available and another where the direction is estimated from data, deriving theoretical regret bounds for both cases. When a pilot direction is available with sufficient accuracy, our approach achieves minimax-optimal rates (with $d = 1$) for nonparametric batched bandits, circumventing the curse of dimensionality. Extensive experiments on simulated and real-world datasets demonstrate the effectiveness of our algorithm compared to the nonparametric batched bandit method.