# MSCS Seminar Calendar

Monday February 19, 2024

**Algebraic Geometry Seminar**

The K-moduli space of a family of conic bundles

Lena Ji (University of Michigan)

3:00 PM in 636 SEO

In this talk, we study the 6-dimensional moduli space of a family of Fano threefolds, and we construct a compactification using K-stability. These threefolds admit a conic bundle structure---we relate the K-moduli space of the threefolds to the GIT moduli space of the discriminant curves, and we study the behavior of the conic bundle structure on the boundary. The technique we use is wall-crossings in K-moduli for certain log Fano pairs (X, cD) as the coefficient c varies. Our work is the first to systematically study these K-moduli spaces when D is not proportional to the anticanonical divisor of X, and we find surprising wall-crossing behavior in this setting. This work is joint with Kristin DeVleming, Patrick Kennedy-Hunt, and Ming Hao Quek.

Wednesday February 21, 2024

**Combinatorics and Probability Seminar**

Intersection patterns of pseudo-segments

Andrew Suk (UCSD)

3:00 PM in 512 SEO

In this talk, I will discuss some new results on intersection graphs of pseudo-segments in the plane and their applications in graph drawing. These results are joint work with Jacob Fox and Janos Pach.

**Statistics and Data Science Seminar**

High-dimensional Transformation of Single Transcript Measurements for Identifying Structural Variants in Cancer

Hyo Young Choi (University of Tennessee)

4:00 PM in Zoom

Over the last decade, many innovative technologies have generated vast amounts of large-scale biological data. The accumulation of so-called “big data”, especially from next generation sequencing technologies, has created many exciting areas in statistics as well as biology. In particular, statistical tools and machine learning techniques have proven to be critical in cancer genomics, transforming large and complex data into clinically relevant knowledge. While many computational tools have been developed for analyzing such big data, unprecedented challenges remain in turning it into meaningful and actionable insights. This talk primarily concerns the issue of high-dimensional outliers which are often challenging to identify in high-throughput sequencing data due to the special structure of high dimensional space. We introduce a new notion of high dimensional outliers that embraces various types and provides deep insights into understanding the behavior of these outliers based on several asymptotic regimes. As an important application, we introduce a statistical method for unsupervised screening of a range of structural alterations in RNA-seq data. We identify a number of biologically important outliers along with the successful characterization of the subspace associated with outliers, which holds promise for identifying otherwise obscured signals.

Thursday February 22, 2024

Friday February 23, 2024

**Departmental Colloquium**

Topology meets Physics: Scissors Congruences and TQFTs.

Carmen Rovi (Loyola University Chicago)

3:00 PM in 636 SEO

In this talk, we will be concerned with a relation between TQFTs and the controlled cut-and-paste invariants of manifolds introduced by Karras, Kreck, Neumann, and Ossa. The controlled cut-and-paste invariants (SKK invariants) are functions on the set of smooth manifolds whose values on cut-and-paste equivalent manifolds differ by an error term depending only on the gluing diffeomorphisms. I will present a natural group homomorphism between the group of invertible TQFTs and the group of SKK invariants and describe how these groups fit into a split exact sequence. We conclude in particular that all positive real-valued SKK invariants can be realized as restrictions of invertible TQFTs.

There will be a dinner at 7:15 that evening please email schapos@uic.edu if you'd like to join

Monday February 26, 2024

**Geometry/Topology Seminar**

Finite-sided Dirichlet domains for Anosov representations

Colin Davalo (Heidelberg University)

3:00 PM in 427 SEO

Dirichlet domains provide polyhedral fundamental domains for discrete
subgroups of the isometries of hyperbolic space on the hyperbolic space.
Selberg introduced a similar construction of a polyhedral fundamental
domain for the action of discrete subgroups of the higher rank Lie group
SL(n,R) on the projective model of the associated symmetric space. His
motivation was to study uniform lattices, for which these domains are
finite-sided. We will address the following question asked
by Kapovich: for which Anosov subgroups are these domains finite-sided ?
Anosov subgroups are hyperbolic discrete subgroups satisfying strong
dynamical properties that have infinite covolume in higher rank. We will
first consider an example of an Anosov subgroup for which this
fundamental domain can have infinitely many sides. We then provide a
sufficient condition on a subgroup to ensure that the domain is finitely
sided in a strong sense. This is joint work with Max Riestenberg.

Note unusual time/room

**Algebraic Geometry Seminar**

Higher order versions of Du Bois and rational singularities

Mircea Mustaţă (University of Michigan)

3:00 PM in 636 SEO

I will give an introduction to higher-order versions of the classical notions of Du Bois and rational singularities and I will discuss an invariant that governs these notions for local complete intersections. This is based on joint work with Qianyu Chen, Bradley Dirks, Sebastian Olano,and Mihnea Popa.

**Analysis and Applied Mathematics Seminar**

On Some Joint Effects of Dispersion and Dissipation of a Class of Nonlinear Evolution Equations

Bingyu Zhang. (U. of Cincinnati)

4:00 PM in 636 SEO

It is known that the solutions of the Cauchy problem for the Korteweg-de Vries (KdV) equation
$ u_t +uu_x +u_{xxx} =0, \quad u(x,0)= \phi (x), \quad x\in T, \ t\in R,$
and the viscous Burgers equation
$ u_t +uu_x - u_{xx} =0, \quad u(x,0)= \phi (x), \quad x\in T, \ t>0 $
posed on a periodic domain $T$, do not possess the sharp Kato smoothing property:
$ \phi \in H^s (T) \implies \partial ^{s+1}_xu \in L^{\infty}_x (T, L^2 (0,T))$.
Here, we discuss the equation,
$ u_t +uu_x +\alpha (x,t) u_{xxx} - \beta (x,t)u_{xx} =0, \qquad u(x,0)= \phi (x), \quad x\in T, \ t\geq 0, $
and demonstrate that if
$\int _{\mathbb{T}}\frac{\beta (x,t)}{|\alpha (x,t)|} dx >0 \quad \forall t\geq 0,$
and if it is locally well-posed in the space $ H^s (T)$ with $s \geq 0$,
then its solution $u$ possesses the sharp Kato smoothing property,
$ \phi \in H^s (T) \implies \partial ^{s+1}_xu \in L^{\infty}_x (T, L^2 (0,T)), \quad \forall \, s\geq 0. $
In addition, the nonlinear part of its solution $u$ possesses the strong Kato smoothing property,
$ \phi \in H^s (T) \implies (u -v)\in C([0,T]; H^{s+1} (T)), \quad \forall \, s>\frac12, $
and the double sharp Kato smoothing property
$ \phi \in H^s (T) \implies \partial ^{s+2}_x(u -v)\in L^{\infty}_x (\T, L^2 (0,T)), \quad \forall \, s>\frac12, $
with $v$ being the solution of the linear problem
$ v_t+ \alpha (x,t)v_{xxx} - \beta (x,t) v_{xx} =0, \quad v(x,0)=\phi (x), \quad x\in T, \ t>0. $

Wednesday February 28, 2024

**Number Theory Seminar**

Counting elliptic curves with level structure

John Voight (Dartmouth College)

1:00 PM in 636 SEO

We begin by briefly surveying the problem of counting elliptic
curves defined over the rationals with prescribed level structure by
height. We then discuss recent joint work with Grant Molnar where we
count elliptic curves with a 7-isogeny.

Friday March 1, 2024

Monday March 4, 2024

**Algebraic Geometry Seminar**

Counting differentials with fixed residues

Dawei Chen (Boston College)

3:00 PM in 636 SEO

We investigate the count of meromorphic differentials on the Riemann sphere possessing a single zero, multiple poles with prescribed orders, and fixed residues at each pole. Gendron and Tahar previously examined this problem with respect to general residues using flat geometry, while Sugiyama approached it from the perspective of fixed-point multipliers of polynomial maps in the case of simple poles. In our study, we employ intersection theory on compactified moduli spaces of differentials, enabling us to handle arbitrary residue conditions and provide a complete solution to this problem. This is joint work with Miguel Prado.

Wednesday March 6, 2024

**Geometry/Topology Seminar**

Invariant subvarieties and highly transitive group actions [Joint Geometry/Topology & Logic seminar]

James Freitag (UIC)

3:00 PM in TBA

Here are two rather different sounding questions: Given variety V and
an algebraic vector field S from V to its tangent bundle, when are
there S-invariant subvarieties of V or V^n for some n? Given an
algebraic group acting regularly on an algebraic variety, what can you
say about the group when the action is 2-transitive?
We'll explain how these two questions are intimately related through
differential Galois theory. The talk won't assume anything except
familiarity with classical algebraic geometry over the complex
numbers.
If time permits, we'll also talk about a version of the problem where
one replaces the vector field with a rational self-map of the variety.

**Statistics and Data Science Seminar**

Causal Inference on Distribution Functions

Dehan Kong (University of Toronto)

4:00 PM in 636 SEO

Understanding causal relationships is one of the most important goals of modern science. So far, the causal inference literature has focused almost exclusively on outcomes coming from the Euclidean space. However, it is increasingly common that complex biomedical datasets are best summarized as data points in non-linear spaces. In this paper, we present a novel framework of causal effects for outcomes from the Wasserstein space of cumulative distribution functions, which in contrast to the Euclidean space, is non-linear. We develop doubly robust estimators and associated asymptotic theory for these causal effects. As an illustration, we use our framework to quantify the causal effect of marriage on physical activity patterns using wearable device data collected through the National Health and Nutrition Examination Survey.

Monday March 11, 2024

**Algebraic Geometry Seminar**

Wall crossing for moduli of stable pairs

Ziquan Zhuang (Johns Hopkins University)

11:00 AM in 636 SEO

Hassett showed that there are natural reduction morphisms between moduli spaces of weighted pointed stable curves when the weights drop. I will discuss some joint work with Fanjun Meng that constructs similar morphisms between moduli of stable pairs in higher dimensions.

Note the irregular time.

**Analysis and Applied Mathematics Seminar**

Non-unique weak solutions of forced SQG

Qirui Peng (University of Illinois Chicago)

4:00 PM in 636 SEO

We construct non-unique weak solutions $\theta \in C^0_t C^{0-}_x$ for forced surface quasi-geostrophic (SQG) equations. This is achieved through a convex integration scheme adapted to the sum-difference system of two distinct solutions. Without external forcing, non-unique weak solutions $\theta$ in space $C^0_t C^\alpha_x$ with $\alpha < -1/5$ were constructed by Buckmaster, Shkoller and Vicol (2019) and Isett and Ma (2021).

Wednesday March 13, 2024

Friday March 15, 2024

Wednesday March 27, 2024

Monday April 1, 2024

Wednesday April 3, 2024

**Statistics and Data Science Seminar**

High-dimensional modeling and computation challenges and solutions via Bayesian ultrahigh dimensional variable selection and manifold-constrained optimization

Hsin-Hsiung Huang (University of Central Florida)

4:00 PM in 636 SEO

High-dimensional data have become prevalent in all fields that need statistical modeling and data analysis. I introduce my recent research in Bayesian ultrahigh dimensional variable selection, low-rank matrix regression and classification, and robust sufficient dimension reduction (SDR). We develop a Bayesian framework for mixed-type multivariate regression with continuous shrinkage priors that enables joint analysis of mixed continuous and discrete outcomes, allowing variable selection from a large number of covariates (p). We investigate the conditions for posterior contraction, especially when the number of covariates (p) grows exponentially relative to the sample size (n) and develop a two-step approach for variable selection with theorems of a sure screening property and posterior contraction and applications with simulation studies and applications to real datasets.
To address challenges in analyzing regression coefficient estimation affected by high-dimensional matrix-valued covariates, we propose a framework for matrix-covariate regression and classification models with a low-rank constraint and additional regularization for structured signals, considering continuous and binary responses, introduce an efficient Riemannian-steepest-descent algorithm for regression coefficient estimation, and prove the consistency of the proposed estimator, showing improvement over existing work in cases where the rank is small with applications through simulations and real datasets of shape images, brain signals, and microscopic leucorrhea images. We propose a novel SDR method robust against outliers using α-distance covariance that effectively estimates the central subspace under mild conditions on predictors without estimating a link function, based on the projection on the Stiefel manifold. We establish convergence properties of the proposed estimation under certain regularity conditions and compare the method's performance with existing SDR methods through simulations and real data analysis, highlighting improved computational efficiency and effectiveness.

Monday April 8, 2024

Wednesday April 10, 2024

Monday April 15, 2024

**Algebraic Geometry Seminar**

CMS criterion and the geography of surfaces with big cotangent bundle

Bruno De Oliveira (University of Miami)

3:00 PM in 636 SEO

We investigate the components determining bigness of the cotangent bundle $\Omega^1_X$ of smooth models $X$ in the birational class $\mathcal {Y}$ of an orbifold surface of general type $Y$, with a focus on the contribution given by the singularities of $Y$. A criterion for bigness of $\Omega_X^1$ is given involving only topological and singularity data on $Y$. We single out a special case, the Canonical Model Singularities (CMS) criterion, when $Y$ is the canonical model of $\mathcal Y$. We study the singularity invariants appearing in the criterion and determine them for $A_n$ singularities. Knowledge of these invariants for $A_n$ singularities allows one to evaluate the $(c_2,c^2_1)-$geographical range of the CMS criterion and compare it to other criteria. We obtain new examples of surfaces with big cotangent bundle. (Joint work with Y. Asega and M.Weiss)

Wednesday April 17, 2024

Wednesday April 24, 2024

Friday April 26, 2024

Wednesday May 8, 2024

Friday September 20, 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/