# MSCS Seminar Calendar

Monday September 30, 2024

**Combinatorics and Discrete Probability Seminar**

Minimum Norm Interpolation Meets The Local Theory of Banach Spaces

Gil Kur (ETH Zurich (& IDEAL visitor))

3:00 PM in 1227 SEO

Minimum-norm interpolators have recently gained attention primarily as an analyzable model to shed light on the double descent phenomenon observed for neural networks. The majority of the work has focused on analyzing interpolators in Hilbert spaces, where typically an effectively low-rank structure of the feature covariance prevents a large bias. More recently, tight vanishing bounds have also been shown for isotropic high-dimensional data for $\ell_p$-spaces with $p\in[1,2)$, leveraging the sparse structure of the ground truth.
This work takes a first step towards establishing a general framework that connects generalization properties of the interpolators to well-known concepts from high-dimensional geometry, specifically, from the local theory of Banach spaces.

**Algebraic Geometry Seminar**

Patching techniques for computing Chow rings of stacks

Martin Bishop (Northwestern)

3:00 PM in 636 SEO

We will discuss the importance of Chow rings in algebraic geometry, as well as one of the central issues in their computation: can one find the Chow ring of a space given the Chow ring of an open and its complement? This is the so called patching problem, and we will discuss multiple ways of solving it. Our main examples will be the moduli stack of curves, as well as root gerbes and root stacks.

**Analysis and Applied Mathematics Seminar**

Smoothness property of hypoelliptic kinetic equations near boundaries

Yuzhe Zhu (University of Chicago)

4:00 PM in 636 SEO

The boundary regularization effect for hypoelliptic
kinetic equations is limited. The solution with the simplest
zero inflow boundary conditions exhibits at most Hölder continuity
near the singular set of the boundary. We will discuss recent
results on hypoelliptic regularity and explain the smoothness
properties of solutions in the presence of boundary conditions
in certain cases.

Tuesday October 1, 2024

**Logic Seminar**

Some Computabiity-theoretic Aspects of Partition Regularity over Algebraic Structures

Gabriela Laboska (University of Chicago)

4:00 PM in 636 SEO

An inhomogeneous system of linear equations over a ring $R$ is partition
regular if for any finite coloring of $R$, the system has a monochromatic
solution. In 1933, Rado showed that an inhomogeneous system is partition
regular over $\mathbb{Z}$ if and only if it has a constant solution.
Following a similar approach, Byszewski and Krawczyk showed that the
result holds over any integral domain. In 2020, Leader and Russell
generalized this over any commutative ring $R$, with a more direct
proof than what was previously used. We analyze some of these combinatorial
results from a computability-theoretic point of view, starting with
a theorem by Straus used directly or as a motivation to many of the
previous results on the subject.

Wednesday October 2, 2024

**Louise Hay Logic Seminar**

A Rigidity Theorem for Homeomorphisms

Carl Tang (UIC)

2:00 PM in 427 SEO

How much information first-order logic can detect is a natural question in logic. In this talk, I will present Thomas Koberda's proof of first-order rigidity of homeomorphism groups of compact manifolds.

**Geometry/Topology Seminar**

Simultaneous uniformization for SL(3,C)

Nathaniel Sagman (University of Luxembourg)

3:00 PM in 427 SEO

Given a closed surface S of genus at least 2, Bers' simultaneous uniformization provides a way to holomorphically associate pairs of oppositely oriented complex structures on S to quasi-Fuchsian hyperbolic 3-manifolds. In this talk, we'll discuss joint work with Christian El Emam in which we give a procedure for holomorphically associating (many, but not all) pairs of Hitchin representations into SL(3,R) to representations to SL(3,C). Along the way, we'll introduce conformal harmonic maps into holomorphic Riemannian symmetric spaces and other related objects.

**Statistics and Data Science Seminar**

Definitive Screening Designs: What, Why, & How

Bradley Jones (Adsurgo LLC)

4:00 PM in 636 SEO

Definitive Screening Designs (DSDs) were introduced in 2011. Since then they have become popular for industrial applications. This talk describes what a DSD is. It then explains why engineers prefer them to standard two-level fractional factorial designs. Finally, it shows how to construct them and block them.

Host: Dibyen Majumdar

**Combinatorics and Discrete Probability Seminar**

Realizability of Hypergraphs and High-Dimensional Contingency Tables from Random Partitions

Nicholas Christo (UIC)

4:00 PM in 712 SEO

A theorem due to Erd\H{o}s and Gallai fully answers the question of when one can realize a provided integer sequence as the degree sequence of a graph with an easy-to-check, necessary and sufficient condition. If one considers a random integer partition as the provided integer sequence, a theorem of Pittel's shows that with high probability a random partition is not the degree sequence of a graph. We consider the analogous question for 3-uniform hypergraphs and show that with high probability a random partition can indeed be realized as the degree sequence of a 3-uniform hypergraph. We will further consider the realizability question of whether one can realize three random integer partitions as the marginals of an associated three-dimensional contingency table. We will briefly discuss how this latter result resolves two conjectures of Pak and Panova regarding Kronecker coefficients

Thursday October 3, 2024

**Quantum Topology Seminar**

Coloring Trivalent Graphs: A Defect TFT Approach.

Amit Kumar (LSU)

12:00 PM in Zoom

We show that the combinatorial matter of graph coloring is, in fact, quantum in the sense of satisfying the sum over all the possible intermediate state properties of a path integral. In our case, the topological field theory (TFT) with defects gives meaning to it. This TFT has the property that when evaluated on a planar trivalent graph, it provides the number of Tait-Coloring of it. This can be considered a generalization of groups. With the Klein-four group as a 1-defect condition, we reinterpret graph coloring as sections of a certain bundle, distinguishing a coloring (global-sections) from a coloring process (local-sections.) These constructions also lead to an interpretation of the word problem, for a finitely presented group, as a cobordism problem and a generalization of (trivial) bundles at the level of higher categories.
See https://arxiv.org/abs/2410.00378.

Monday October 7, 2024

**Algebraic Geometry Seminar**

Semi-Orthogonal Decompositions of Moduli Spaces

Jenia Tevelev (University of Massachusetts, Amherst)

3:00 PM in 636 SEO

Given a Fano manifold M with extremal contractions to Fano manifolds A and B, it is expected that the derived category of M contains two semi-orthogonal decompositions, related by the action of the braid group, which refine the semi-orthogonal decompositions of the derived categories of A and B. I will discuss strategies for proving this expectation when the Fano manifolds have moduli interpretations. As one application, we construct a semi-orthogonal decomposition of the derived category of the moduli space of stable rank 2 vector bundles on a smooth projective curve, as conjectured by Narasimhan and by Belmans, Galkin, and Mukhopadhyay.

**Combinatorics and Discrete Probability Seminar**

On growth of regular partitions in 3-uniform hypergraphs

Caroline Terry (UIC)

3:00 PM in 1227 SEO

It was first observed by Alon, Fox and Zhao that VC-dimension can be used to characterize a dichotomy in the growth of regular partitions of graphs. Specifically, if a hereditary graph property H has finite VC-dimension, then results of Alon-Fischer-Newman and Lov'{a}asz-Szegedy imply all graphs is H have $\epsilon$-regular partitions of size polynomial in $1/\epsilon$. On the other hand, if H has infinite VC-dimension, then results of Gowers and Fox-Lov\'{a}sz show there are graphs in H whose smallest $\epsilon$-regular partition has size at least an exponential tower of height polynomial in $1/\epsilon$. In this talk, I present several analogous dichotomies in the setting of hereditary properties of 3-uniform hypergraphs. These dichotomies are all characterized by various analogues of VC-dimension for 3-uniform hypergraphs.

**Analysis and Applied Mathematics Seminar**

Stability of bound states for regularized nonlinear Schrödinger equations

John Albert (University of Oklahoma)

4:00 PM in 636 SEO

Dumas, Lannes, and Szeftel have introduced a family of equations designed to model waves in nonlinear optics which have less symmetry than solutions of the nonlinear Schrödinger equation, in that they are not axisymmetric about the axis of propagation. Their equations can include regularization terms which are present in some but not all spatial directions. We study the stability of standing-wave solutions of such regularized nonlinear Schrödinger equations, and find that the regularization can increase the range of nonlinearities for which standing waves are stable. This effect is similar to that seen in the Benjamin-Bona-Mahony regularization of the Korteweg-de Vries equation, but notably, the effect is present even when the regularization terms are not present in all directions.

Wednesday October 9, 2024

**Statistics and Data Science Seminar**

Weighted shape-constrained estimation with applications to Markov chain autocovariance function estimation

Hyebin Song (Pennsylvania State University)

4:00 PM in 636 SEO

In this talk, I will introduce a novel weighted l2 projection method for estimating covariance functions, with an emphasis on estimation of autocovariance sequences from reversible Markov chains. Shape-constrained estimation of a function with discrete support has been investigated and successfully applied to various application problems. Notably, Berg and Song (2023) connected this idea with uncertainty quantification in Markov chain Monte Carlo (MCMC) samples and proposed a shape-constrained estimator for autocovariance sequences. While the least-squares objective is commonly used in shape-constrained regression, it can be suboptimal due to correlation and unequal variances in the input function. To address this, we introduce a weighted least-squares method that defines a weighted norm on transformed data. Our approach involves transforming input data into the frequency domain and weighting the input sequence based on their asymptotic variances, exploiting the asymptotic independence of periodogram ordinates. I will discuss the computational aspects, theoretical properties, and the improved performance of this method compared to its non-weighted counterpart.

Friday October 11, 2024

Monday October 14, 2024

**Combinatorics and Discrete Probability Seminar**

Universal Asymptotics through Orthogonal Polynomial Duality

Jeffrey Kuan (Texas A&M)

3:00 PM in 1227 SEO

We present a new method to determine asymptotics in Markov processes, using orthogonal polynomial duality. This method allows for certain expected values to be decomposed over an orthogonal basis of duality functions in a "simpler" dual Markov process. Estimates for these expectations are then calculated in terms of estimates on the duality functions, which result in "universal" asymptotics.
We demonstrate this method for asymmetric dynamic interacting particle systems, where there had not even been conjectures for asymptotics. These asymptotics are Tracy--Widom fluctuations for certain values of the asymmetry. We will also touch upon the algebraic and combinatorial structures underlying the probabilistic models.

Tuesday October 15, 2024

Wednesday October 16, 2024

**Statistics and Data Science Seminar**

Change Point Inference for Non-Euclidean Data Sequences using Distance Profiles

Paromita Dubey (University of Southern California)

4:00 PM in 636 SEO

We introduce a powerful scan statistic and the corresponding test for detecting the presence and pinpointing the location of a change point within the distribution of a data sequence with the data elements residing in a separable metric space (Ω, d). These change points mark abrupt shifts in the distribution of the data sequence as characterized using distance profiles, where the distance profile of an element ω ∈ Ω is the distribution of distances from ω as dictated by the data. This approach is tuning parameter free, fully non-parametric and universally applicable to diverse data types, including distributional and network data, as long as distances between the data objects are available. We obtain an explicit characterization of the asymptotic distribution of the test statistic under the null hypothesis of no change points, rigorous guarantees on the consistency of the test in the presence of change points under fixed and local alternatives and near-optimal convergence of the estimated change point location, all under practicable settings. To compare with state-of-the-art methods we conduct simulations covering multivariate data, bivariate distributional data and sequences of graph Laplacians, and illustrate our method on real data sequences of the U.S. electricity generation compositions and Bluetooth proximity networks.

Friday October 18, 2024

Monday October 21, 2024

**Analysis and Applied Mathematics Seminar**

Dissipation wavenumber and regularity for electron magnetohydrodynamics

Chao Wu (University of Illinois Chicago)

4:00 PM in 636 SEO

We consider the electron magnetohydrodynamics (MHD) with static background ion flow. A special situation was studied numerically by physicists. In this paper we show the existence of determining wavenumber for the electron MHD, and establish a regularity condition only on the low modes of the solution.

Tuesday October 22, 2024

Wednesday October 23, 2024

**Statistics and Data Science Seminar**

Organizational Effectiveness: A New Strategy to Leverage Multisite Randomized Trials for Valid Assessment

Guanglei Hong (University of Chicago)

4:00 PM in 636 SEO

In education, health, and human services, an intervention program is usually implemented by many local organizations. Determining which organizations are more effective is essential for theoretically characterizing effective practices and for intervening to enhance the capacity of ineffective organizations. In multisite randomized trials, site-specific intention-to-treat (ITT) effects are likely invalid indicators for organizational effectiveness and may lead to inequitable decisions. This is because sites differ in their local ecological conditions including client composition, alternative programs, and community context. Applying the potential outcomes framework, this study proposes a mathematical definition for the relative effectiveness of an organization. The estimand contrasts the performance of a focal organization with those that share the features of its local ecological conditions. The identification relies on relatively weak assumptions by leveraging observed control group outcomes that capture the confounding impacts of alternative programs and community context. We propose a two-step mixed-effects modeling (2SME) procedure. Simulations demonstrate significant improvements when compared with site-specific ITT analyses or analyses that only adjust for between-site differences in the observed baseline participant composition. We illustrate its use through an evaluation of the relative effectiveness of individual Job Corps centers by reanalyzing data from the National Job Corps Study, a multisite randomized trial that included 100 Job Corps centers nationwide serving disadvantaged youths. The new strategy promises to alleviate consequential misclassifications of some of the most effective Job Corps centers as least effective and vice versa.

Friday October 25, 2024

Monday October 28, 2024

Tuesday October 29, 2024

Wednesday October 30, 2024

**Statistics and Data Science Seminar**

Methods for Informative Censoring in Time-to-Event Data Analysis

Dr. Mandy Jin (AbbVie Inc.)

4:00 PM in Zoom

In oncology clinical trials, subjects prematurely discontinuing from the assigned treatment prior to experiencing an event of interest are often handled by noninformative censoring under censor-at random assumption. Such methods can be challenged with respect to the robustness of the ignorable or noninformative censoring and sensitivity analyses using informative censoring are often required.
In a recently published article (Jin and Fang, 2024), reference-based methods (including Jump to Reference and Copy Reference) and tipping point analysis for time-to-event data with possibly informative censoring were proposed. These are novel methods to fit the gap in literature for time-to-event analysis with applications in oncology clinical trials. We will describe and facilitate the implementation of these methods in this presentation.
Illustrative examples are provided to demonstrate the reference-based methods and tipping point analysis.

Monday November 4, 2024

Friday November 8, 2024

Monday November 11, 2024

Wednesday November 13, 2024

Friday November 15, 2024

**Departmental Colloquium**

TBA

Noah Giansiracusa (Bentley University)

3:00 PM in 636 SEO

TBA

Please let Laura Schaposnik at schapos@uic.edu know if you'd like to join Noah for dinner, or if you'd like to meet him during the day. He's doing a lot of interesting interdisciplinary maths: https://www.noahgian.com/

Monday November 18, 2024

**Algebraic Geometry Seminar**

Rational normal curves, phylogenetic trees, and tropical geometry

Noah Giansiracusa (Bentley University)

3:00 PM in 636 SEO

I'll discuss joint work with Alessio Caminata, Luca Schaffler, and Han-Bom Moon in which we study equations defining (the closure of) the locus of n points in projective space that lie on a rational normal curve and apply these equations to resolve a question of Lior Pachter and David Speyer from 2004 on the tropical geometry of the space of phylogenetic trees.

Tuesday November 19, 2024

Wednesday November 20, 2024

Monday November 25, 2024

Monday December 2, 2024

Tuesday December 3, 2024

Wednesday December 4, 2024

Friday January 24, 2025

Friday February 7, 2025

Monday February 10, 2025

Friday February 28, 2025

Monday March 10, 2025

Monday March 31, 2025