Hunter Math & Stat Colloquium

October 1

Vincent Martinez, Hunter College (Department of Mathematics and Statistics)

Title: Navier-Stokes Equations: A brief tour of results past and recent

   Abstract: After giving a brief derivation, we will discuss results, old and new, surrounding its solution theory. We discuss other problems motivated from the study of turbulence that remain open.

October 15 (Recording)

Wenjian Liu, Queensborough Community College (Department of Mathematics and Computer Science)

Title:  When Does Information Survive Noise? Reconstruction on Random Trees

   Abstract: Imagine a message being passed through a branching network, where each transmission introduces noise. If we observe only the messages far away from the source, can we still recover the original information? This question leads to the reconstruction problem on trees, with connections to probability, information theory, and statistical inference.

In this talk, I will explain how the competition between noise and branching determines whether information survives. We will discuss the classical Kesten-Stigum bound and why nonlinear effects can sometimes allow reconstruction below this threshold. I will then present recent results on asymmetric binary channels on Poisson Galton-Watson trees, showing how channel asymmetry influences whether the classical threshold is sharp. The talk will focus on intuition, key results, and broader connections to learning from noisy data.

October 29 (Recording)

Leonardo Toso, Columbia University (Department of Electrical Engineering)

Title: Physics-informed learning under mixing: How physical knowledge speeds up learning

   Abstract: Physics-informed learning offers a way to incorporate prior physical knowledge into learning. In applications such as climate modeling, fluid dynamics, and engineering, physical laws, conservation principles, and structural constraints often provide valuable prior information beyond the available data. A major challenge in physics-informed machine learning, however, is to understand when, and by how much, the prior physical knowledge accelerates learning, especially when data samples are temporally dependent.

In this talk, we will focus on empirical risk minimization with physics-informed regularization and derive complexity-dependent bounds on the excess risk in probability and in expectation. We prove that, when the physical prior information is well aligned with the ground truth hypothesis, the learning rate improves from the (slow) Sobolev minimax rate to the (fast) optimal i.i.d. one without any sample-size deflation due to data dependence.

The talk is based on the work presented at ICLR 2026: https://arxiv.org/pdf/2509.24801

November 12

Siddhartha Nandy, University of Maryland-Baltimore County (Department of Mathematics and Statistics)

Title: Consistent Estimation of Low-Rank Spatial Covariance Matrix: A Penalized Random Effects Approach

   Abstract: Discerning dependence to prevent potential misinterpretations in statistical contexts involving spatial processes is pivotal for making accurate inferences and predictions. Despite the existing plethora of approaches for spatial covariance matrix estimation, there is a scarcity of viable methods for handling large spatial non-stationary covariance matrices with robust theoretical underpinnings. To bridge this gap, we consider a non-stationary covariance structure by a linear combination of random effects with basis functions that accommodate spatial structures and develop a theoretically valid estimation approach. Our specific interest lies in estimating the number of random effects and their corresponding covariance structure, which is subsequently employed in spatial prediction. We have innovatively leveraged a group LASSO penalized likelihood method to select and estimate rows of the Cholesky factor for the covariance matrix of random effects, with each row penalized as a group. The procedure remains computationally simple. We have probed into the selection consistency and oracle property of the estimated rows of the lower triangular Cholesky factor. Simulation studies support our theoretical findings. Evaluating the prediction performance of our method using real data is also provided in the supplementary materials.

December 3 

Phanuel Mariano, Union College (Department of Mathematics)

Title: The Hot Spots Problem 

   Abstract: Consider a perfectly insulated 1-dimensional rod, or a 2-dimensional plate, or better yet, a 3-dimensional room. Perfectly insulated means that heat cannot escape this room. The Hot Spots Problem asks about what happens to the location of the ``hot spots'' and ``cold spots'' of this insulated body over a long period of time. To understand this problem we will introduce the equation that describes the evolution of heat over time. Moreover, we will discuss what is known (and not known) about this problem. We end the talk by discussing the connection between the Hot Spots Problem and Probability theory. In particular, this connection will be through a theory of random particles called Brownian motion.

December 10 (Student Research Presentations)

   Olivia Bayer, Title

   Sai Chauhan, Title

December 17 (Student Research Presentations)

Brian Holliday, Title