Fall 2026

Jiwon Park (UMass Lowell): Shared genetic architecture across complex traits: Applications and Extensions
New Faculty Colloquium

Abstract: Genetic variants may be associated with more than one complex trait, and identifying these shared associations can be challenging when trait-specific association statistics are correlated. PLeiotropic Analysis under Composite Otherwise (PLACO+) is a composite-null testing framework that uses Genome-Wide Association Study (GWAS) summary statistics to detect genetic variants associated with two traits while accounting for this dependence. This talk will focus on applications of PLACO+ to lipid traits and inflammatory bowel disease, including settings with correlated phenotypes and overlapping study samples. I will also compare the findings with commonly used approaches and discuss how the identified shared signals differ across methods. Ongoing extensions beyond two traits will be mentioned briefly at the end.


Matthew Badger (University of Connecticut): 3d Brownian motion and sets of dimension 2.999999

Abstract: As you breathe, air eventually reaches the alveoli in your lungs. You might wonder if a particle of air is equally likely to reach all parts of your lungs. The answer is emphatically no! Mathematically one explanation is a theorem of Bourgain, which states that for any closed set in space, there is always a subset of Hausdorff dimension less than 3, which contains all the points of the set where a randomly moving particle can land. In this talk, I will present explicit numerical bounds on the dimension of the subset in Bourgain's theorem, obtained in joint work with Michael Albert and Alyssa Genschaw. I will focus on the story of how we arrived at these results, the role of software and Artificial Intelligence (AI) in mathematical exploration, and potential for future improvements.


Sunita Chepuri (University of Puget Sound): Orbitmesy and promotion on self-dual posets

Abstract: Dynamical algebraic combinatorics studies the dynamics of actions on combinatorial objects with algebraic significance. One key phenomenon is homomesy, where a statistic has a constant average on each orbit of the action. In this talk I will introduce the notion of orbitmesy, a generalization of homomesy. An orbit is said to be orbitmesic with respect to a statistic if the orbit’s average statistic value is equal to the global average. I will give some examples, provide a general framework of how we can find orbitmesies using a known homomesy, and present a few results along these lines that give orbitmesic promotion orbits of self-dual posets. If time allows, I will share a classification of all of the orbitmesic promotion orbits for the zig-zag poset with four elements.


Ke Huang (UMass Lowell): Statistical learning theory for Convolutional Neural Networks (CNNs)
New Faculty Colloquium

Abstract: Convolutional neural networks (CNNs) have achieved remarkable empirical success, yet a theoretical explanation of why they can be so powerful and how their architecture affects statistical performance remains poorly understood. In this talk, I will present statistical theory for CNNs trained by empirical risk minimization under Lipschitz losses. The framework covers a flexible class of CNN architectures and applies to both regression and classification tasks.

I will discuss non-asymptotic error bounds that characterize how approximation and estimation errors depend on key architectural features of CNNs. I will also show that when the target function lies on a low-dimensional manifold, CNNs can mitigate the curse of dimensionality. Finally, I will illustrate a theory-supported CNN on electrocardiogram (ECG) data, demonstrating strong predictive performance and architectural flexibility compared with existing theoretically supported models.


Omar Hurtado (Georgia Tech):

Abstract: to be announced.


Caitlin Lienkaemper (Massachusetts Institute of Technology (MIT)):

Abstract: to be announced.

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This colloquium is coordinated by: Emily Gunawan, Amanda Redlich, Joris Roos, Bobbie Wu, Shiwen Zhang