# MSCS Seminar Calendar

Monday April 22, 2019

**Geometry, Topology and Dynamics Seminar**

The Extended Haagerup fusion categories

Emily Peters (Loyola University)

3:00 PM in 636 SEO

Sometimes, two fields of math realize they are talking about the same objects, but in sufficiently different ways that it is hard to know whether they are seeing the same aspects in different disguises, or authentically distinct aspects. This is the story of what happened when subfactors and fusion categories were observed to be two sides of the same coin. In this case the work of translation turned out to be highly profitable: subfactor examples disproved some conjectures about fusion categories, and recently, fusion category techniques have provided a framework to answer some questions about subfactors, including the question of Morita equivalence. This talk will attempt to explain the connection between these fields and one of these results (arXiv:1810.06076), without assuming any background on subfactors or fusion categories. This is joint work with Grossman, Morrison, Penneys and Snyder.

**Mathematical Computer Science Seminar**

Sparse random graphs with overlapping community structure

Samantha Petti (Georgia Tech)

3:00 PM in 427 SEO

In this talk we introduce two different random graph models that produce sparse graphs with overlapping community structure and discuss community detection in each context. The Random Overlapping Community (ROC) model produces a sparse graph by constructing many Erdos Renyi random graphs (communities) on small randomly selected subsets of vertices. By varying the size and density of these communities, ROC graphs can be tuned to exhibit a wide range normalized of closed walk count vectors, including those of hypercubes. This is joint work with Santosh Vempala. In the second half of the talk, we introduce the Community Configuration Model (CCM), a variant of the configuration model in which half-edges are assigned colors and pair according to a matching rule on the colors. The model is a generalization of models in the statistical physics literature and is a natural finite analog for classes of graphexes. We describe a hypothesis testing algorithm that determines whether a graph came from a community configuration model or a traditional configuration model. This is joint work with Christian Borgs, Jennifer Chayes, Souvik Dhara, and Subhabrata Sen.

Tuesday April 23, 2019

**Midwest Model Theory Day**

Rigidity and bi-interpretability with Z for higher rank lattices.

Nir Avni (Northwestern)

1:00 PM in 636 SEO

A lattice in a Lie group is a discrete subgroup with finite co-volume. In many contexts, there is a dichotomy between lattices in Lie groups of rank one and lattices in Lie groups of higher rank, where the two classes behave in qualitatively different ways. I will talk about this dichotomy in the context of Model Theory.
This talk is part of Midwest Model Theory Day. http://homepages.math.uic.edu/~freitag/MWMT13

**Midwest Model Theory Day**

Fraisse constructions in the free group

Rizos Sklinos (Stevens Institute)

2:30 PM in 636 SEO

In an influential paper Fraisse obtained the ordered rationals as a limit of finite linear orders through amalgamations. Furthermore his construction implied the (ultra)-homogeneity, the countability and universality of the limit structure. Since then various adaptations of Fraisse's method had given very interesting examples in many mathematical disciplines. The random graph in graph theory and Philip Hall's universally locally finite group in group theory to name a few.
In joint work with Kharlampovich and Myasnikov we look into the possibility of applying Fraisse constructions in classes of groups that played a central role in answering Tarski's question on nonabelian free groups. In particular, we modify Fraisse's method to prove that nonabelian limit groups form a ∀
∀-Fraisse class and finitely generated elementary free groups form an elementary-Fraisse class.
This talk is part of Midwest Model Theory Day, http://homepages.math.uic.edu/~freitag/MWMT13

**Quantum Topology / Hopf Algebra Seminar**

Three Variants of Welded Knot Theory

Jonathan Schneider (UIC)

3:00 PM in 612 SEO

Welded Knot Theory was originally conceived by Rourke & Fenn in terms of (framed) braids,
and was subsequently expanded by Kauffman, Rourke and Fenn into a quotient of Virtual Knot Theory.
Satoh and Rourke have shown that the theory is modeled by toral surfaces or fiberwise-embedded toral
surfaces. The latter model, however, requires a slight refinement of the the- ory, which we call
“Roto-Welded Knot Theory”. This refinement omits the virtual I-move, and thus represents a partial return
to the original braid concept. In this talk I will compare Welded, Roto-Welded,
and Framed Welded Knot Theories. In particular, only Roto-Welded admits a proven complete
topological model.

**Midwest Model Theory Day**

Scott sentence of finitely-generated groups

Turbo Ho (Purdue)

4:00 PM in 636 SEO

Scott showed that for every countable structure A, there is a L_{\omega_1,\omega} sentence, called the Scott sentence, whose countable models are the isomorphic copies of A. The quantifier complexity of a Scott sentence can be thought of as a measure of the complexity of the structure. Knight et al. have studied the Scott sentences of many structures. In particular, Knight and Saraph showed that a finitely-generated structure always has a \Sigma_3 Scott sentence. In this talk, we will focus on finitely-generated groups. On the one hand, most "natural" finitely-generated groups have a d-\Sigma_2 Scott sentence. On the other hand, we give a characterization of finitely-generated structures where the \Sigma_3 Scott sentence is optimal. We then give a construction of a finitely-generated group where the \Sigma_3 Scott sentence is optimal.
This is joint work with Matthew Harrison-Trainor.
This talk is part of Midwest Model Theory Day, http://homepages.math.uic.edu/~freitag/MWMT13

Wednesday April 24, 2019

**Algebraic Geometry Seminar**

Volumes and intersection theory on moduli spaces of abelian differentials

Dawei Chen (Boston College/IAS)

4:00 PM in 427 SEO

Computing volumes of moduli spaces has significance in many fields. For instance, the celebrated Witten's conjecture regarding intersection numbers on the Deligne-Mumford moduli space of stable curves has a fascinating connection to the Weil-Petersson volume, which motivated Mirzakhani to give a proof via Teichmueller theory, hyperbolic geometry, and symplectic geometry. The initial two other proofs of Witten's conjecture by Kontsevich and by Okounkov-Pandharipande also used various ideas in ribbon graphs, Gromov-Witten theory, and Hurwitz theory. In this talk I will introduce an analogous formula of intersection numbers on moduli spaces of abelian differentials that computes the Masur-Veech volumes. This is joint work with Moeller, Sauvaget, and Zagier (arXiv:1901.01785).

**Statistics Seminar**

Sufﬁcient dimension folding via distance covariance

Wenhui Sheng (Marquette University)

4:00 PM in 636 SEO

We propose a new sufﬁcient dimension folding method using distance covariance for regression in which the predictors are matrix- or array-valued. The method works efﬁciently without strict assumptions on the predictor. It is modelfree and neither smoothing techniques or selection of tuning parameters is needed. Moreover, it works for both univariate and multivariate response cases. We use two approaches to estimate the structural dimensions: bootstrap method and a new method of local search. Simulations and real data analysis support the efﬁciency and effectiveness of the method.

Friday April 26, 2019

**Departmental Colloquium**

Data perturbation for data science

Richard Samworth (University of Cambridge)

3:00 PM in 636 SEO

When faced with a dataset and a statistical problem of interest, should we propose a statistical model and use that to inform an appropriate algorithm, or dream up a potential algorithm and then seek to justify it? The former is the more traditional statistical approach, but the latter appears to be becoming more popular. I will present an example of a 20th century analysis that falls into the first category, and explain why it may not be as suitable for modern statistical challenges. I'll then discuss a class of algorithms that belong in the second category, namely those that involve data perturbation (e.g. subsampling, random projections, artificial noise, knockoffs,...). As an illustration, I will consider Complementary Pairs Stability Selection for variable selection.

Monday April 29, 2019

**Geometry, Topology and Dynamics Seminar**

Sublinear boundaries of CAT(0) spaces and CAT(0) groups

Yulan Qing (University of Toronto)

3:00 PM in 636 SEO

Croke and Kleiner showed that the visual boundary of CAT(0) groups such as right-angled Artin groups (RAAG) is not well-defined, since quasi-isometric CAT(0) spaces can have non-homeomorphic boundaries. For any sublinear function, we consider a subset of the visual boundary called

*sublinear boundary*and show that it is a QI-invariant. That is to say, the sublinear boundary of a CAT(0) group is well-defined. In the case of right-angled Artin group, we show that the Poisson boundary is naturally identified with the (log t) boundary. This talk is based on projects with Kasra Rafi and Giulio Tiozzo.**Mathematical Computer Science Seminar**

Powers of Hamiltonian cycles in randomly augmented graphs

Andrzej Dudek (Western Michigan University)

3:00 PM in 427 SEO

It follows from the theorems of Dirac and of Koml\'os, Sark\"ozy, and Szemer\'edi, who
confirmed the Pos\'a-Seymour conjecture, that for every $k\ge 1$
and sufficiently large $n$ already the minimum degree $\delta(G) \ge \frac{k}{k+1} n$
for an $n$-vertex graph $G$ alone suffices to ensure the existence of the $k$-th power of a Hamiltonian cycle.
In this talk we will determine the number of random edges one has to add to a graph $G$ with minimum degree $\delta(G) \ge \left(\frac{k}{k+1} +\varepsilon\right)n$ (with $\varepsilon>0$) in order to create an $\ell$-th power of a Hamiltonian cycle, where $\ell\ge k+1$.
This is joint work with Sylwia Antoniuk, Christian Reiher, Andrzej Ruci\'nski and Mathias Schacht.

Tuesday April 30, 2019

Wednesday May 1, 2019

**Statistics Seminar**

Weak Dependence Conditions for High-Dimensional Inference: Applications to Group Comparisons

Solomon Harrar (University of Kentucky)

4:00 PM in 636 SEO

Recent results for high-dimensional inference make assumptions that require weak dependence (pseudo independence) between the variables. These requirements fail to be satisfied, for example, for all elliptically contoured distributions except for normal distribution. In this talk, we present weaker dependence conditions for high-dimensional asymptotic theory. With these conditions the scope of application of many high-dimensional results broadens substantially. For example, mixing-type dependence and general conditions on variance of quadratic forms are covered. The application of the new conditions will be demonstrated with high-dimensional tests for comparing group differences in terms of means and in terms of Mann-Whitney effects. The later is particularly useful for non-metric data such as ordered categorical data, and also for skewed and heavy tailed continuous data. Simulation results show favorable performance of these tests. Data from Electroencephalograph (EEG) experiment is analyzed to illustrate these applications.
The results presented in this talk are joint works with Xiaoli Kong, Department of Mathematics and Statistics, Loyola University-Chicago

**Algebraic Geometry Seminar**

Local volumes, equisingularity and generalized smoothability

Antoni Rangachev (University of Chicago)

4:00 PM in 427 SEO

In this talk I will introduce a class of singularities that generalizes the class of smoothable singularities: these are all singularities that admit deformations to singularities with deficient conormal spaces. I will discuss how this new class arises from problems in differential equisingularity and how it relates to the local volume of a line bundle.

Thursday May 2, 2019

**AWM@UIC : Invited Speaker Series**

Conversation and Refreshments

Amie Wilkinson (UChicago)

3:00 PM in 636 SEO

The talks in our invited speaker series feature a conversation and refreshments period to strengthen the community of women practicing mathematics in the Chicago area and to promote the work of women in mathematics. This is an opportunity for everyone in our department to become familiar with a few of the many accomplished women who currently practice mathematics in or near the city.

We will be serving light refreshments.

Friday May 3, 2019

**Special Colloquium**

Exotic Structures, Homology Cobordisms and Chern-Simons Functional

Aliakbar Daemi (Columbia University)

3:00 PM in 636 SEO

An exotic structure on a smooth manifold X is another smooth manifold which is homeomorphic but not diffeomorphic to X. There are many closed 4-manifolds which admit exotic smooth structures. However, it is still an open question whether there are exotic structures on simple closed 4-manifolds such as the 4-dimensional sphere (smooth Poincare conjecture) and S^1xS^3. Motivated by the latter case, Akbulut asked whether there are an integral homology sphere Y with non-trivial Rokhlin invariant and a simply connected homology cobordism from Y to itself. In this talk, I will introduce various invariants of homology cobordism classes of 3-manifolds and discuss some of their topological applications. In particular, we answer Akbulut’s question for various integral homology spheres and propose a plan to completely address his conjecture.

Followed by mini-tea in 636 SEO from 4:00pm to 4:15pm.

Monday May 6, 2019

**Analysis and Applied Mathematics Seminar**

The Navier-Stokes-End-Functionalized polymer system

Theodor Drivas (Princeton University)

4:00 PM in 636 SEO

The problem of minimizing energy dissipation and wall drag in turbulent pipe and channel
flows is a classical one which is of great importance in practical engineering applications.
Remarkably, the addition of trace amounts of polymer into a turbulent flow has a pronounced
effect on reducing friction drag. To study this mathematically, we introduce a new boundary
condition for Navier-Stokes equations which models the situation where polymers are irreversibly
grafted to the wall. For engineering applications, the effects of polymer on drag reduction are
thought to be most pronounced near the boundary and therefore such wall-grafted polymer chains
are often employed as drag-reducing agents. Our boundary condition - derived from a fluid-polymer
stress balance - closes in the macroscopic fluid variables and becomes an evolution equation for the
vorticity along the solid walls. We prove global well-posedness for the resulting system in two spatial
dimensions and show that it captures the drag reduction effect in the sense that the vanishing viscosity
limit holds with a rate. Consequently, we obtain bounds on energy dissipation rate and drag which
qualitatively agree with observations of drag reduction in laminar flow.
Talk is based on joint work with Joonhyun La.

Monday May 13, 2019

Tuesday May 28, 2019

Wednesday August 28, 2019

Monday September 9, 2019

Wednesday September 25, 2019

Wednesday October 9, 2019

Wednesday October 23, 2019

Friday November 1, 2019

Monday November 4, 2019