# MSCS Seminar Calendar

Tuesday April 17, 2018

**Mathematics Education Colloquium**

Concept Image and Concept Definition in Mathematics

Zak Fox (UIC)

1:00 PM in SEO 612

We will have a discussion of Tall and Vinner's paper "Concept Image and Concept Definition in Mathematics".
As usual everyone is welcome to join. If you wish to obtain a copy of the paper, please contact Aida (aalibe2@uic.edu)

**Joint Model Theory and MCS Seminar**

A Tutorial on Statistical Queries

Lev Reyzin (UIC)

1:00 PM in SEO 427

In this tutorial, I shall introduce the concept of statistical queries and give an extensive overview of statistical query dimension (SQ-DIM). SQ-DIM is a notion dimension for a family of functions that has interesting connections to their learnability (from a machine learning standpoint), as well as connections to many other areas.
This talk is intended for a broad audience with an interest in computer science and machine learning. The first part of the tutorial will be focused on basic definitions and general results. The second part will concern modern applications. There will be a short break in between the two parts.

This is a two hour seminar, 1-3pm.

Wednesday April 18, 2018

**Statistics Seminar**

Optimal Portfolio under Fractional Stochastic Environment

Jean-Pierre Fouque (UCSB)

3:00 PM in SEO 636

Rough stochastic volatility models have attracted a lot of attention recently, in particular for the linear option pricing problem. In this talk, starting with power utilities, we propose to use a martingale distortion representation of the optimal value function for the nonlinear asset allocation problem in a (non-Markovian) fractional stochastic environment (for all Hurst index $H \in (0, 1)$). We rigorously establish a first order approximation of the optimal value, when the return and volatility of the underlying asset are functions of a stationary slowly varying fractional Ornstein-Uhlenbeck process. We prove that this approximation can be also generated by the zeroth order trading strategy providing an explicit strategy which is asymptotically optimal in all admissible controls. Furthermore, we extend the discussion to general utility functions, and obtain the asymptotic optimality of this strategy in a specific family of admissible strategies. If time permits, we will also discuss the problem under fast mean-reverting fractional stochastic environment.
Joint work with Ruimeng Hu (UCSB).

**Graduate Algebraic Geometry Seminar**

Stability conditions on surfaces: a slippery slope

Jay Kopper (UIC)

3:00 PM in SEO 712

I introduce various notions of stability for sheaves. I will pay special attention to the case of sheaves on surfaces and discuss some modern results regarding moduli spaces of sheaves and cohomology.

**Algebraic Geometry Seminar**

A decomposition theorem for projective manifolds with nef anticanonical bundles

Junyan CAO (Jussieu University, Paris)

4:00 PM in SEO 427

Let X be a simply connected projective manifold with nef anticanonical bundle.
We prove that X is a product of a rationally
connected manifold and a manifold with trivial canonical bundle.
As an application we describe the MRC fibration of any
projective manifold with nef anticanonical bundle.
It is a joint work with Andreas Höring

**Statistics Seminar**

Counting Process Based Dimension Reduction Methods for Censored Outcomes

Ruoqing Zhu (UIUC)

4:00 PM in SEO 636

We propose a class of dimension reduction methods for right censored survival data using a counting process representation of the failure process. Semiparametric estimating equations are constructed to estimate the dimension reduction subspace for the failure time model. The proposed method addresses two fundamental limitations of existing approaches. First, using the counting process formulation, it does not require any estimation of the censoring distribution to compensate the bias in estimating the dimension reduction subspace. Second, the nonparametric part in the estimating equations is adaptive to the structural dimension, hence the approach circumvents the curse of dimensionality. Asymptotic normality is established for the obtained estimators. We further propose a computationally efficient approach that requires only a singular value decomposition to estimate the dimension reduction subspace. Numerical studies suggest that the proposed methods exhibit significantly improved performance for estimating the true dimension reduction subspace. We further conducted a real data analysis on a skin cutaneous melanoma dataset from The Cancer Genome Atlas. The findings have important biological implications. The proposed methods are implemented in the R package ``orthoDr'', which efficiently solves the semiparametric estimating equations within the Stiefel manifold of the parameter space.

Thursday April 19, 2018

**Thesis Defense**

Topological $K$-theory and invertibility

Tasos Moulinos (UIC)

4:30 PM in SEO 712

Topological K-theory of dg-categories is an invariant of $\mathbb{C}$-linear dg-categories
taking values in the $\infty$-category of $KU$-modules. I will describe a relative version
of this construction. Using this, I give a characterization, in terms of twisted $K$-theory, of the topological $K$-theory of the dg-category $Perf(X, A)$ of modules over an Azumaya algebra $A$ over $X$.
I then deduce a certain decomposition, for $X$ a finite CW-complex equipped with a bundle of projective
spaces $π : P → X$, of $KU(P)$ in terms of the twisted topological K-theory of $X$ ; this is
a topological analogue of a result of Quillen’s on the algebraic K-theory of Severi-Brauer
schemes.

**Graduate Student Colloquium**

Dimension theory and iterated function systems

Daniel Ingebretson (UIC)

5:00 PM in SEO 636

This will be an elementary and accessible introduction to the dimension theory of a simple class of fractals, the attractors of iterated function systems.

Pizza will be served at 5.

Friday April 20, 2018

**Departmental Colloquium**

PDE Methods for the Numerical Simulation of Compressible Fluids

Steve Shkoller (University of California at Davis)

3:00 PM in SEO 636

The motion of compressible fluids is difficult to simulate numerically, particular in multiple space dimensions, due to the presence of wave patterns with sharp discontinuities, such as shock waves. In this lecture, I will describe how some ideas from PDE (partial differential equations) can be used to develop accurate numerical methods which allow for highly singular phenomenon, such as shock waves colliding with walls and bouncing back, in a very stable manner. The talk will be fairly self-contained so no prior knowledge of fluids or numerics is necessary, and I will mostly use short videos of our numerical results to demonstrate the schemes.

Monday April 23, 2018

**Algebraic K-Theory Seminar**

Lie algebras and v_n-periodic spaces

Gijs Heuts (Universiteit Utrecht)

1:00 PM in SEO 1227

I will discuss a homotopy theory obtained from that of pointed spaces by inverting the maps inducing isomorphisms in v_n-periodic homotopy groups. The case n = 0 corresponds to rational homotopy theory. In analogy with Quillen’s results in the rational case, I will outline how this v_n-periodic homotopy theory is equivalent to the homotopy theory of Lie algebras in the category of T(n)-local spectra. One can also compare it to the homotopy theory of cocommutative coalgebras in the category of T(n)-local spectra. For n > 0 these theories are no longer equivalent; the failure can be expressed in terms of the convergence of the Goodwillie tower of the identity in periodic homotopy.

**Geometry, Topology and Dynamics Seminar**

Hausdorff dimension of Kuperberg minimal sets

Daniel Ingebretson (UIC)

3:00 PM in SEO 636

In 1994, Kuperberg constructed a smooth flow on a three-manifold with no periodic orbits. It was later shown that a generic Kuperberg flow preserves a codimension one laminar minimal set. We develop new techniques to study the symbolic dynamics and dimension theory of the minimal set, by relating it to the limit set of a graph directed pseudo-Markov system over a countable alphabet.

**Stat Lab Seminars**

Robust Optimal Scoring Discriminant Analysis & Discrete Wavelet Packet Transform Based Discriminant Analysis for Whole Genome Sequences

Prof. Hsin-Hsiung Huang (University of Central Florida)

4:00 PM in SEO 612

We develop a novel classification model which is robust against outliers by introducing a loss function to optimal scoring discriminant analysis.
The discriminant vectors and scoring vectors are solved by an iteratively reweighted least squares algorithm.
It inherits good properties from these two ideas for reducing the influence of these outliers on estimating the discriminant directions.
In the asymptotic stability analysis, we show that the influence function is bounded and discriminant vectors
and scoring vectors are both consistent as the percentage of outliers goes to zero.
The experimental results are presented to confirm that the robust optimal scoring discriminant analysis is effective and efficient.
In recent years, alignment-free methods have been widely applied for genome sequences comparisons,
since these methods compute efficiently and provide desirable phylogenetic analysis results.
These methods have been successfully combined with hierarchical clustering methods for finding phylogenetic trees.
However, it may not be suitable to apply these alignment-free methods directly to the existing statistical classification methods, since
there still lacks an appropriate statistical classification theory for integrating with the alignment-free representation methods.
In this article, we propose a discriminant analysis method which uses discrete wavelet packet transform to
represent the whole genome sequences and discriminant analysis to classify the genome sequences.
We show that the proposed alignment-free representation statistics of features approximately follow normal distributions.
The data analysis results indicate that the proposed method provides accurate classification in real time.

Drink and snack will be served for this talk.

**Analysis and Applied Mathematics Seminar**

The random gas of hard spheres

Rafail Abramov (UIC)

4:00 PM in SEO 636

I will explain what is happening with the model of gas consisting of hard spheres,
what are the problems with the conventional understanding, how it can be
rectified, and what comes out of it.

Tuesday April 24, 2018

**Model Theory Seminar**

Invariant Types in NIP Theories, Part I

Roland Walker (UIC)

1:00 PM in SEO 427

So far in the seminar we have been discussing o-minimal theories. For the final two weeks, we will broaden our scope to include all NIP theories and study the behavior of invariant types.
My source will be Pierre Simon's paper of the same name (see link below). We will be covering Section 2.
https://www.worldscientific.com/doi/pdf/10.1142/S0219061315500063
A preview of my slides is available at http://homepages.math.uic.edu/~roland/

**Logic Seminar**

Colorings of finite subgraphs of the universal triangle-free graph

Natasha Dobrinen (University of Denver)

3:30 PM in SEO 427

It is a central question in the theory of homogeneous relational structures as to which structures have finite big Ramsey degrees. This question, of interest for several decades, has gained recent momentum as it was brought into focus by Kechris, Pestov, and Todorcevic in 2005. An infinite structure S is homogeneous if any isomorphism between two finitely generated substructures of S can be extended to an automorphism of S. A homogeneous structure S is said to have finite big Ramsey degrees if for each finite substructure A of S, there is a number n, depending on A, such that any coloring of the copies of A in S into finitely many colors can be reduced down to no more than n colors on some substructure S’ isomorphic to S. This is interesting not only as a Ramsey property for infinite structures, but also because of its implications for topological dynamics.
Prior to work of the speaker, finite big Ramsey degrees had been proved for a handful of homogeneous structures: the rationals (Devlin 1979) the Rado graph (Sauer 2006), ultrametric spaces (Nguyen Van Thé 2008), and enriched versions of the rationals and related circular directed graphs (Laflamme, Nguyen Van Thé, and Sauer 2010). According to Nguyen Van Thé , "so far, the lack of tools to represent ultrahomogeneous structures is the major obstacle towards a better understanding of their infinite partition properties." We address this obstacle by providing new tools to represent the homogeneous triangle-free graph and developing the necessary Ramsey theory to deduce finite big Ramsey degrees. The methods developed seem robust enough that correct modifications should likely apply to a large class of homogeneous structures omitting some finite substructure.

Wednesday April 25, 2018

**Statistics Seminar**

Concordance-Assisted Learning for Individualized Treatment Regimes

Rui Song (North Carolina State University)

4:00 PM in SEO 636

In the first part of the talk, we propose a new concordance-assisted
learning for estimating optimal individualized treatment regimes. We
first introduce a type of concordance function for prescribing
treatment and propose a robust rank regression method for estimating
the concordance function. We then find treatment regimes, up to a
threshold, to maximize the concordance function, named prescriptive
index. Finally, within the class of treatment regimes that maximize
the concordance function, we find the optimal threshold to maximize
the value function. Although this method makes better use of the
available information through pairwise comparison, the objective
function is discontinuous and computationally hard to optimize. In the
second part of the talk, we consider a convex surrogate loss function
to solve this problem. In addition, our algorithm ensures sparsity of
decision rule and makes it easy to interpret. Simulation results of
various settings and application to STAR*D both illustrate that the
proposed method can still estimate optimal treatment regime
successfully when the numb of covariates is large.

**Algebraic Geometry Seminar**

Valuations, Thresholds, and K-stability

Harold Blum (University of Michigan)

4:00 PM in SEO 427

In this talk, we will discuss two invariants that measure the singularities of anticanonical divisors on Fano varieties. The first is the global log canonical threshold, which is also known as Tian’s alpha invariant. The second is the stability threshold, an invariant recently introduced by Fujita and Odaka. Our approach to understanding these invariants involves valuations. Using results of Fujita and Li, we show that the K-semistability of a Fano variety is detected by the stability threshold. This talk is based on joint work with Mattias Jonsson.

**Algebraic Geometry Seminar**

Hodge theory and o-minimal geometry

Benjamin Bakker (University of Georgia)

5:00 PM in SEO 427

Hodge structures on cohomology groups are fundamental invariants of algebraic varieties; they are parametrized by quotients $D/\Gamma$ of periods domains by arithmetic groups. Except for a few very special cases, such quotients are never algebraic varieties, and this leads to many difficulties in the general theory. We explain how to partially remedy this situation by equipping $D/\Gamma$ with an o-minimal structure, and show that period maps are "definable" with respect to this structure. As a consequence, we obtain an easy proof of a result of Cattani--Deligne--Kaplan on the algebraicity of Hodge loci, a strong piece of evidence for the Hodge conjecture. The proof of the main theorem relies heavily on work of Schmid, Kashiwara, and Cattani--Kaplan--Schmid on the asymptotics of degenerations of Hodge structures. This is joint work with B. Klingler and J. Tsimerman.

Thursday April 26, 2018

**Graduate Geometry, Topology and Dynamics Seminar**

Geometrically motivated partial orders on simplicial complexes

Jānis Lazovskis (UIC)

4:00 PM in SEO 636

A simplicial complex is a pair $(V,S)$, where $V$ is a (finite) set and $S$ is a subset of the power set $\mathcal P(V)$ closed under taking appropriate subsets ("faces"). The natural partial order from this definition is inclusion, which also makes some geometric sense. I will introduce two other partial orders, based on the Vietoris-Rips and Čech constructions of a simplicial complex from a vertex set and a radius. These orders correspond with the interpretation of a "path" in the universal space over the product of the Ran space (space of all finite subsets of some other space) and the non-negative real numbers.

Friday April 27, 2018

**Number Theory Seminar**

The Sato-Tate conjecture and Nagao's conjecture

Seoyoung Kim (Brown University)

12:00 PM in SEO 612

Nagao's conjecture relates the rank of an elliptic surface to a limit formula arising from a weighted average of fibral Frobenius traces, and it is further generalized for smooth irreducible projective surfaces by M. Hindry and A. Pacheco. We show that the Sato-Tate conjecture based on the random matrix model implies Nagao's conjecture for certain twist families of elliptic curves and hyperelliptic curves.

**Departmental Colloquium**

Multiple Dirichlet series and moments of L-functions

Adrian Diaconu (University of Minnesota)

3:00 PM in SEO 636

L-functions --- vast generalizations of the Riemann zeta-function --- are fundamental objects of study in number theory. In the 1980's the idea emerged that it could be useful to tie
together a family of related L-functions in one variable to create a double, or multiple, Dirichlet series, which could be used to study the average behavior of the original family of L-functions.
The local structure of these multiple Dirichlet series shows a rich connection to the theory of automorphic forms, and representation theory. On the automorphic side, Whittaker functions
on p-adic groups and their covers are the fundamental objects. Whittaker functions and their relatives are expressible in terms of combinatorial structures on the associated L-group, its flag variety, or Schubert varieties. In the combinatorial theory, crystal graphs, Demazure characters, the Schubert calculus and Kazhdan-Lusztig theory all enter.
In this talk, I will focus on the most important case, namely the multiple Dirichlet series associated to moments of L-functions. I will discuss the connection (established recently in joint work with Vicentiu Pasol) between the local parts of these series and the compactifications of certain
moduli spaces of curves, and how this information can be combined with the (conjectural in general) analytic continuation of the multiple Dirichlet series to obtain precise asymptotics for moments, for example, of the classical family of quadratic Dirichlet L-functions.
This talk is designed for a general mathematical audience.

Monday April 30, 2018

**Analysis and Applied Mathematics Seminar**

Boundary Control of the Ericksen-Leslie System in Dimension Two

Changyou Wang (Purdue University)

4:00 PM in SEO 636

In this talk, I will first discuss the initial-boundary value problem of the Ericksen-Leslie system for time-dependent boundary data of the nematic liquid crystal director field.
I will present some result on the global existence in dimension two. Then I will describe an application to the optimal boundary control for such a system in dimension two.

Tuesday May 1, 2018

**Model Theory Seminar**

Invariant Types in NIP Theories, Part II

Roland Walker (UIC)

1:00 PM in SEO 427

So far in the seminar we have been discussing o-minimal theories. For the final two weeks, we will broaden our scope to include all NIP theories and study the behavior of invariant types.
My source will be Pierre Simon's paper of the same name (see link below). We will be covering Section 2.
https://www.worldscientific.com/doi/pdf/10.1142/S0219061315500063
A preview of my slides is available at http://homepages.math.uic.edu/~roland/

**Quantum Topology / Hopf Algebra Seminar**

1D Lattice KMS States, Powers Factors, and Jones Subfactors

Jim Otto (UIC)

3:00 PM in SEO 612

We attempt to flesh out Construction B on page 25 of Jones, Subfactors and Knots, AMS, 1991. We start by constructing Powers factors using KMS states for spin 1/2 particles on a 1D lattice in a constant magnetic field.

Wednesday May 2, 2018

**Statistics Seminar**

My (Mis)Adventures in Modeling and Simulation

Peter Bonate (Astellas Pharma)

4:00 PM in SEO 636

Dr. Peter Bonate has over 20 years experience in modeling and simulation in the pharmaceutical industry. Dr. Bonate
will discuss his career and the role modeling and simulation has played in the development of many different pharmaceutical
products.