Upcoming Events

Industrial Problems Seminar 

Morteza Mardani (NVIDIA Corporation)

Abstract

In the rapidly evolving landscape of AI, a transformative shift from content retrieval to content generation is underway. Central to this transformation are diffusion models, wielding remarkable power in visual data generation. My talk touches upon the nexus of generative AI and NVIDIA's influential role therein. I will then navigate through diffusion models, elucidating how they establish the bedrock for leveraging foundational models. An important question arises: how to integrate the rich prior of foundation models in a plug-and-play fashion for solving downstream tasks such as inverse problems and parametric models? Through the lens of variational sampling, I present an optimization framework for sampling diffusion models that only needs diffusion score evaluation. Not only does it provide controllable generation, but the framework also establishes a connection with the well-known regularization by denoising (RED) framework, unveiling its extensive implications for text-to-image/3D generation.

Data Science Seminar

Wuchen Li (University of South Carolina)

Abstract

We study the Lyapunov convergence analysis for degenerate and non-reversible stochastic differential equations (SDEs). We apply the Lyapunov method to the Fokker-Planck equation, in which the Lyapunov functional is chosen as a weighted relative Fisher information functional. We derive a structure condition and formulate the Lypapunov constant explicitly. Given the positive Lypapunov constant, we prove the exponential convergence result for the probability density function towards its invariant distribution in the L1 norm. Several examples are presented: underdamped Langevin dynamics with variable diffusion matrices, quantum SDEs in Lie groups (Heisenberg group, displacement group, and Martinet sub-Riemannian structure), three oscillator chain models with nearest-neighbor couplings, and underdamped mean field Langevin dynamics (weakly self-consistent Vlasov-Fokker-Planck equations).

Industrial Problems Seminar 

Thomas Grandine (University of Washington)

Abstract

In this talk, I will discuss the details of two algorithms for parametrizing planar curves in an industrial design context. The first algorithm, developed in an academic setting by world class researchers, solves the problem posed by the researchers in a very satisfying and elegant way. Yet that algorithm, elegant though it may be, turns out to be ineffective in a real world engineering environment. The second algorithm is an extension of the first that eliminates the issues that caused it to be inadequate for industrial use.
 

Data Science Seminar

Melanie Weber (Harvard University)

Abstract

The problem of identifying geometric structure in heterogeneous, high-dimensional data is a cornerstone of Representation Learning. In this talk, we study this problem from the perspective of Discrete Geometry. We start by reviewing discrete notions of curvature with a focus on discrete Ricci curvature. Then we discuss how curvature is linked to mesoscale structure in graphs, which gives rise to applications in graph machine learning, such as (unsupervised) node clustering. For downstream machine learning and data science applications, it is often beneficial to represent graph-structured data in a continuous space, which may be Euclidean or Non-Euclidean. We show that discrete curvature allows for characterizing the geometry of a suitable embedding space both locally and in the sense of global curvature bounds, which have implications for spectral graph machine learning.

Industrial Problems Seminar

Julie Mitchell (Oak Ridge National Laboratory)

Abstract

Being effective in industrial and team science settings requires the ability to work across disciplines. In this talk, I will reflect on how to be successful working across disciplines and what types of opportunities exist for mathematicians working at national laboratories. I will also reflect on past projects I’ve pursued, which include high-performance computing and machine learning approaches to the understanding of macromolecular structure and binding.

Data Science Seminar

Yimin Zhong (Auburn University)

Industrial Problems Seminar 

Sandhya Prabhakaran (Moffitt Cancer Centre)

Abstract

The talk will be geared towards a general audience. The goal of this talk is to explain importance of data, and the many ways data can be analyzed to benefit patient care. In this talk, I will focus on Non-small cell lung cancer (NSCLC), the patient data we obtained, the computational approaches used, and the potential biomarkers we identified in this process.

Data Science Seminar

Lecture: Jiajia Yu (Duke University)

Data Science Seminar

Alex Gittens (Rensselaer Polytechnic Institute)

Industrial Problems Seminar 

Christopher Bemis (X Cubed Capital Management)