Presentations (Universal Time Coordinated)

Talk Slides

Upcoming Presentations

9/30/2025

Kernel Interpolation for Geometric Problems

Speaker: Patrick Guidotti (Department of Mathematics, University of California Irvine)

Date and Time: Tuesday, September 30, 2025, 0:00 AM - 0:50 AM (UTC)

Abstract: We will demonstrate how ideas from kernel interpolation can be extended for use as a tool to understand the geometry of point clouds and perform analysis 

for functions defined on it. Reformulating the relevant interpolation problems as optimization problems also suggests natural a natural regularization that proves 

effective when the data is noisy. The regularization parameter admits a probabilistic interpretation that clarifies its meaning. Numerical experiments will be presented.

10/7/2025

Geometry Preserving Methods for Differential Equations of Spherical-Valued Functions

Speaker: Shing-Yu Leung (Department of Mathematics, Hong Kong University of Science and Technology)

Date and Time: Tuesday, October 7, 2025, 0:00 AM - 0:50 AM (UTC)

Abstract: Differential equations with solutions constrained to the unit sphere appear in applications such as rigid-body dynamics, quantum mechanics, wavefront propagation, and color image processing. This talk presents recent advances in geometry-preserving numerical methods for spherical-valued functions, which solve ordinary and partial differential equations directly on the sphere while maintaining geometric constraints. Applications include p-harmonic flows for color image denoising, where spherical formulations naturally represent chromaticity and provide improved performance compared with conventional Euclidean methods.

10/21/2025

TBA

Speaker: Hongkai Zhao (Department of Mathematics, Duke University)

Date and Time: Tuesday, October 21, 2025, 0:00 AM - 0:50 AM (UTC)

Abstract: TBA

11/18/2025

TBA

Speaker: Prashant Athavale (Department of Mathematics, Clarkson University)

Date and Time: Tuesday, November 18, 2025, 0:00 AM - 0:50 AM (UTC)

Abstract: TBA

Previous Presentations

9/16/2025

Vectorization with Depth

Sung Ha Kang (Department of Mathematics, Georgia Institute of Technology)

Date and Time: Tuesday, September 16, 2025, 0:00 AM - 0:50 AM (UTC)

Abstract: Image vectorization is a process to convert a raster image into a scalable vector graphic format. Objective is to effectively remove the pixelization effect while representing boundaries of image by scaleable parameterized curves. We propose new image vectorization with depth which considers depth ordering among shapes and use curvature-based inpainting for convexifying shapes in vectorization This approach makes editing shapes and images more natural and intuitive. We present various numerical results and comparisons against recent layer-based vectorization methods to validate the proposed model.

9/9/2025

Introduction to Reservoir Computing with an Application to Image Processing

Yunho Kim (Department of Mathematical Sciences, Ulsan National Institute of Science and Technology, South Korea)

Time: Tuesday, September 9, 2025, 0:00 AM - 0:50 AM (UTC)

Abstract: In this talk, I will give a brief introduction to reservoir computing and discuss how we used it for salt-and-pepper noise removal. The concept of reservoir coputing (RC) dates back to 2002 with a neural network called Echo State Networks (ESNs) proposed by H. Jaeger and the actual term 'Reservoir Computing' was coined in later. I will discuss two works of mine, one of which is concatenated RC architecture. The other is an image processing application for salt-and-pepper noise removal despite the fact that reservoir computing is designed to deal with time series data due to its similarity with RNNs.

3/14/2025

Inverse Problems and Image Analysis in Remote Sensing and Atmospheric Sciences

Igor Yanovsky (NASA Jet Propulsion Laboratory & Department of Mathematics, UCLA)

Time: Friday, March 14, 2025, 10:00 PM - 10:50 PM (UTC)

Abstract: Inverse problems and image analysis play a critical role in remote sensing and atmospheric sciences, enabling the extraction of meaningful information from satellite observations. This talk will provide an overview of a range of inverse and image analysis problems, including wind retrieval, separation of cloud layers, derivation of velocity fields in submesoscale eddies, image resolution enhancement, image destriping, and point spread function reconstruction. These problems are addressed using data from different satellite instruments, each presenting unique challenges in terms of noise, resolution, and sensor characteristics. We will highlight key mathematical and computational methodologies used to tackle these problems. This talk aims to illustrate the essential role of applied mathematics in advancing our understanding of atmospheric and oceanic processes.