Presentations (Universal Time Coordinated)

Upcoming Presentations

11/18/2025

Restoration of Noisy Grain Orientation Maps

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

Date and Time: Tuesday, November 18, 2025, 1:00 AM - 1:50 AM (UTC)

Abstract: The microstructure of Polycrystalline materials, such as metals and alloys, is composed of grains, regions of similar crystalline orientations. The grain orientations are extracted using a technique called Electron Backscatter Diffraction(EBSD). Unfortunately, such measurements result in noisy data and missing regions. In this talk, we present the utility of weighted vectorized TV flow for denoising grain orientations obtained using Electron Backscatter Diffraction. We will also introduce a novel hybrid algorithm for addressing missing orientation values in Traditional inpainting techniques, including exemplar-based methods and machine-learning approaches designed for natural images, which often fall short when applied to EBSD data due to the unique characteristics of grain geometries and orientation datasets. To tackle this, we adapted a classical exemplar-based inpainting algorithm and a partial convolutional neural network method to suit the demands of EBSD data better. However, each approach has its limitations. Our proposed solution—a hybrid algorithm—combines the strengths of these methods. It starts with a deep learning model to provide an initial estimate of missing regions, followed by refinement using an adapted exemplar-based method to preserve grain boundaries and structural integrity. Using synthetic EBSD images generated with the open-source software, DREAM3D, we demonstrate that our hybrid approach achieves greater accuracy and visual coherence than standalone techniques. This method enhances EBSD map reconstruction and shows promise for broader applications in orientation-based datasets.

12/2/2025

Combine Variational Models and Deep Learning to Dress Overfitting and Interpretability in Image Segmentation

Speaker: Weihong Guo (Department of Mathematics, Applied Mathematics, and Statistics, Case Western Reserve University)

Date and Time: Tuesday, December 2, 2025, 1:00 AM - 1:50 AM (UTC)

Abstract: Variational models and deep learning are distinct approaches in image analysis, each with unique strengths. Variational models minimize energy functionals that encode properties like smoothness or boundary sharpness, offering interpretable control over image features through one or more regularization terms. They work well with limited data since they rely on mathematical priors rather than learned features. In contrast, deep learning models automatically learn image features from data, directly mapping inputs to outputs. This makes them efficient and powerful for large-scale datasets and complex patterns, often outperforming traditional methods. However, deep learning requires extensive labeled data, high computational resources, and often lacks interpretability. Without sufficient data or regularization, these models risk overfitting and poor generalization. In this talk, we will present our recent work on combining variational models and deep learning to address mathematical interpretability and small training data in image segmentation.

12/9/2025

TBA

Speaker: Wei Zhu (Department of Mathematics, The University of Alabama)

Date and Time: Monday, December 9, 2025, 1:00 AM - 1:50 AM (UTC)

Abstract: TBA

Previous Presentations

11/11/2025

Geometry of Lattice Patterns in R^n

Speaker: Roy He (Department of Mathematics, City University of Hong Kong)

Date and Time: Tuesday, November 11, 2025, 1:00 AM - 1:50 AM (UTC)

Abstract: Lattices are ubiquitous patterns in many scientific fields. Their representations are highly non-unique, which makes it difficult to quantify their differences. In this talk, we describe a quotient space of lattices based on modular group actions. It yields an elegant description of equivalent patterns. We equip this abstract space with the Poincare metric, which turns out to be compatible with our visual perception. We show that this powerful model can be generalized to higher dimensions and discuss some applications in material sciences.

10/28/2025

Mathematical and Computational Understanding of Neural Networks: From Representation to Learning and From Shallow to Deep, and Beyond

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

Date and Time: Monday, October 28, 2025, 0:00 AM - 0:50 AM (UTC)

Abstract: In this talk I will present some understanding of a few basic mathematical and computational questions for neural networks, as a particular form of nonlinear representation, and show how the network structure, activation function, and parameter initialization can affect its approximation properties and the learning process. In particular, we propose structured and balanced multi-component and multi-layer neural networks (MMNN) using sine as the activation function with an initialization scaling strategy.  At the end, I will discuss a few issues and challenges when using neural networks to solve partial differential equations.

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.

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.

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.