Upcoming Department Seminars

Oct. 19, 2026

Algebraic Geometry Seminar

TBA
Matt Larson of Princeton : 3 p.m. in 636 SEO

Analysis and Applied Mathematics Seminar

Itô–Stratonovich-type formula for rough sheets.
Youssef Hakiki of Purdue University : 4 p.m. in 636 SEO

Abstract

We present a new approach to developing an Itô–Stratonovich-type formula for rough sheets. Historically, planar integration for irregular paths has been notoriously difficult. The emergence of 'mixed differential' terms in 2D leads to overlapping iterated integrals, the construction of which previously required exhaustive combinatorial structures. One example of such a structure is the substantial 36-element planar signature introduced by K. Chouk and M. Gubinelli (Rough Sheets, arxiv.org/abs/1406.7748, 2014). In this work, we propose a simplified setting for rough sheet calculus that relies on elementary Taylor expansions in a more fundamental way. We claim that this simple trick significantly streamlines the complexity of planar algebraic integration. We illustrate the methodology in three regimes. Firstly, we present a special Rough-Young framework (joint work with S. Tindel, arxiv.org/abs/2606.20908) for paths with ‘’asymmetric'' Hölder regularity: H₁ > 1/3 in direction 1 and H₂ > 1/2 in direction 2. Relying on structured controlled path expansions, we rigorously minimize the set of iterated integrals required in the signature to 4 elements. We extend the classical planar change-of-variable formula to this regime and express it as an explicit limit of Riemann sums. The signature elements required for this are then constructed for the fractional Brownian sheet with 1/3<H₁<1/2 and H₂ > 1/2. Secondly, we consider the fully rough regime, where 1/3< H₁ ,H₂ < 1/2 (joint work with S. Tindel). Here, a symmetric second-order Taylor expansion produces a planar integral with a signature of 10 elements instead of 36 compared to Chouk-Gubinelli’s paper. Third, we demonstrate that the class of controlled sheets is not stable under integration. However, in the Rough-Young regime, the rough sheet integral can be interpreted as a one-parameter infinite-dimensional rough path integral (ongoing work with M. R. Lahwate). This allows us to interpret some Goursat PDEs as infinite-dimensional RDEs.

Oct. 20, 2026

Logic Seminar

TBA
Joey Lakerdas-Gayle of Waterloo : 3 p.m. in 636 SEO

Oct. 21, 2026

MATH Club

Analytic Solutions for D-optimal Designs under Generalized Linear Models
Jie Yang of UIC : noon in SEO 1227

Abstract

In order to find D-optimal designs in statistics, we often need to maximize a homogeneous polynomial as a function of proportions. We introduce two analytic approaches to solve D-optimal approximate designs under generalized linear models. The first approach provides analytic D-optimal allocations for generalized linear models with two factors. The second approach leads to explicit solutions for a class of generalized linear models with more than two factors. There are many other similar optimization problems of homogeneous polynomials that are open and have potential applications in statistics. Pizza will be served.

Geometry, Topology and Dynamics Seminar

Superrigidity of rich representations
Alex Maldague of UIC : 4 p.m. in 636 SEO

Abstract

I will introduce a superrigidity criterion for representations of real or complex hyperbolic lattices into adjoint, almost-simple real algebraic groups. The criterion is formulated within the theory of algebraic representations of ergodic actions developed by Bader and Furman. I will also discuss an application to geodesically rich representations. These generalize the representations used by Bader--Fisher--Miller--Stover to prove that finite-volume real or complex hyperbolic manifolds containing infinitely many maximal, properly immersed totally geodesic submanifolds of real dimension at least two are arithmetic.

Statistics and Data Science Seminar

Geodesic Causal Inference
Hans-Georg Müller of UC Davis : 4 p.m. in 636 SEO

Abstract

Adjusting for confounding and imbalance when establishing statistical relationships is an important task. Causal inference methods have emerged as a popular tool to achieve this for regression relationships with scalar responses and also distributional responses. We introduce a general framework for causal inference when responses reside in geodesic metric spaces, drawing on a novel geodesic calculus, which facilitates the quantification of treatment effects through the concept of geodesic average treatment effect (GATE). Employing Fréchet regression, we obtain doubly robust estimation of GATE with rates of convergence. Theoretical results are complemented with various data illustrations. Based on joint work with Daisuke Kuriso, Yidong Zhou and Taisuke Otsu.

Statistics and Data Science Seminar

BEGIN with BEAUTY: Distribution-free Inference and Modeling Using Data Bits
Kai Zhang of UNC : 5 p.m. in 636 SEO

Abstract

Interpretability and computational efficiency are central challenges in AI. This talk explores how data bits can address these challenges while providing a common foundation for statistical inference and modeling. We begin with the binary expansion approximation of uniformity (BEAUTY) equation, which approximates the characteristic function of any copula distribution, in any dimension, using expectations of interactions among data bits. Building on this representation, we develop distribution-free tests of independence through symmetry statistics of data bits. These tests are powerful, interpretable, and computational efficient. We then use the atomic linearity of data bits to express the conditional mean of a binary response as a linear combination of interactions among predictor bits. This representation provides new insights into generalized linear models and neural networks. Finally, we present the binary expansion group intersection network (BEGIN), which characterizes conditional independence among binary vectors in terms of covariance matrices and graphical models. Together, these developments provide a foundation for AI methods that combine flexible modeling, transparent statistical explanations, and efficient computation.