# MSCS Seminar Calendar

Tuesday January 16, 2018

**Special Colloquium**

Principal Component Analysis for Functional Data on Riemannian Manifolds and Spheres

Xiongtao Dai (The University of California at Davis)

3:00 PM in SEO 636

Functional data analysis on nonlinear manifolds has drawn recent interest. Sphere-valued functional data, which are encountered for example as movement trajectories on the surface of the earth, are an important special case. In this talk, we consider a principal component analysis for smooth Riemannian manifold-valued functional data, which respects the intrinsic geometry of the manifold. Riemannian functional principal component analysis (RFPCA) is carried out by first mapping the manifold-valued data through Riemannian logarithm maps to linear tangent spaces around the time-varying Frechet mean function, and then performing a classical multivariate functional principal component analysis. Representations of the sample functions and the eigenfunctions on the original manifold are then obtained with exponential maps. We derive a central limit theorem for the mean function, as well as root-n uniform convergence rates for other model components. Our applications include a novel framework for the analysis of longitudinal compositional data, achieved by mapping longitudinal compositional data to trajectories on the sphere, illustrated with longitudinal fruit fly behavior patterns. Riemannian functional principal component analysis is shown to be superior in terms of trajectory recovery and predictive power in comparison to an unrestricted method.

**Quantum Topology / Hopf Algebra Seminar**

Coloring Knots, Graphs and Knotted Graphs

Louis H Kauffman (UIC)

3:00 PM in SEO 612

In this talk we will compare the coloring of knots (so called Fox coloring and generalized to the subject of the
fundamental group and quandles (oriented and unoriented) of the knot) and colorings of graphs. We are
particularly interested in edge colorings of graphs where distinct sets of colors are incident to each node.
The two subjects intersect for three colorings of knots and graphs and extend to colorings of knotted graphs
with trivalent nodes. We will discuss how the four color problem and the knot theory interact in this
formulation.

Wednesday January 17, 2018

**Special Colloquium**

Theory Informs Practice: Smoothing Parameters Selection for Smoothing Spline ANOVA Models in Large Samples

Xiaoxiao Sun (University of Georgia)

3:00 PM in SEO 636

Large samples have been generated routinely from various sources. Classic statistical models, such as
smoothing spline ANOVA models, are not well equipped to analyze such large samples due to expensive
computational costs. In particular, the daunting computational costs of selecting smoothing parameters
render the smoothing spline ANOVA models impractical. In this talk, I will present an asympirical
(asymptotic + empirical) smoothing parameters selection approach for smoothing spline ANOVA models
in large samples. The proposed method can significantly reduce computational costs of selecting
smoothing parameters in high-dimensional and large-scale data. We show smoothing parameters
chosen by the proposed method tend to the optimal smoothing parameters minimizing a risk function.
In addition, the estimator based on the proposed smoothing parameters achieves the optimal
convergence rate. Extensive simulation studies will be presented to demonstrate numerical advantages
of our method over competing methods. I will further illustrate the empirical performance of the
proposed approach using real data.

Thursday January 18, 2018

**Quantum Topology / Hopf Algebra Seminar**

Coloring Knots, Graphs and Knotted Graphs

Louis H Kauffman (UIC)

3:00 PM in SEO 612

(Continued from Tuesday, January 6,2018)
In this talk we will compare the coloring of knots (so called Fox coloring and generalized to the subject
of the fundamental group and quandles (oriented and unoriented) of the knot) and colorings of graphs.
We are particularly interested in edge colorings of graphs where distinct sets
of colors are incident to each node. The two subjects intersect for three colorings of knots and graphs
and extend to colorings of knotted graphs with trivalent nodes.
We will discuss how the four color problem and the knot theory interact in this formulation.

**Departmental Colloquium**

Randomized computational problems and the cavity method

Will Perkins (University of Birmingham)

3:00 PM in SEO 636

Random instances of computational problems play an important role in computer science as a source of hard instances, a testbed for algorithms, and as practical constructions of error correcting codes. The biggest breakthrough in our understanding of these problems in the last decade has come from statistical physicists who were originally interested in the properties of glasses. Their intricate but non-rigorous "cavity method” gives a series of detailed predictions of the behavior of randomized computational problems.
I will describe a mathematical vindication of the cavity method in a broad class of models. Using a mix of tools, new and old, we make rigorous the calculations the physicists have been doing all along. Some consequences of our results include determining the information theoretic threshold in the disassortative stochastic block model and the condensation threshold in the random graph coloring problem. Based in part on joint work with A. Coja-Oghlan, F. Krzakala, and L. Zdeborova.

There will be tea at 4pm, after the talk

Friday January 19, 2018

**Special Colloquium**

The Complexity of Learning Neural Networks

John Wilmes (Georgia Institute of Technology)

3:00 PM in SEO 636

The empirical successes of ``deep learning'' currently lack rigorous theoretical explanation. As a first step, we ask whether data generated by
neural networks with a single hidden layer, smooth activation functions and benign input distributions can be learned efficiently. We give a surprisingly
general polynomial-time analysis of gradient descent when the hidden layer uses unbiased sigmoid gates, exploiting new connections we make with tools from
spherical harmonics. However, when the generating network uses arbitrary biases, the problem appears intractable. We construct a family of simple neural
networks that is hard to learn in the sense that any statistical query algorithm (including all known variants of stochastic gradient descent with any
loss function, for any model architecture) needs an exponential number of queries on data labeled by such a network even using tolerance inversely
proportional to the input dimensionality. Joint work with Le Song, Santosh Vempala, and Bo Xie.

Monday January 22, 2018

**Geometry, Topology and Dynamics Seminar**

Geometry & topology of complex hyperbolic 2-manifolds

Matthew Stover (Temple University)

3:00 PM in SEO 636

I will discuss the geometry and topology of complex hyperbolic 2-manifolds, highlighting open questions and recent progress directly inspired by the last 40 years of work on hyperbolic 2- and 3-manifolds. Emphasis will be on explicit topological constructions (particularly of minimal volume manifolds), fibrations, and betti numbers. Much of this will cover joint work with Luca Di Cerbo.

Tuesday January 23, 2018

**Model Theory Seminar**

Organizational meeting

James Freitag (UIC)

1:00 PM in SEO 427

This semester, the model theory seminar will be topical, generally around o-minimal geometry, a natural generalization of semi-algebraic geometry over the real numbers. Please consider attending if you are interested -
no particular background is required.

**Special Colloquium**

Constrained Factor Models for High-Dimensional Matrix-Variate Time Series

Elynn Y. Chen (Rutgers University)

3:00 PM in SEO 636

In many scientific fields, including economics, biology, and meteorology, high dimensional matrix-variate data are routinely collected over time. To incorporate the structural interrelations between columns and rows and to achieve significant dimension reduction when dealing with high-dimensional matrix-variate time series, Wang et al 2017 proposed a matrix factor model that is shown to be effective in analyzing such data. In this paper, we establish a general framework for incorporating domain or prior knowledge induced linear constraints in the matrix-variate factor model. The constraints can be used to achieve parsimony in parameterization, to facilitate interpretation of the latent matrix factor, and to target specific factors of interest based on domain knowledge. Fully utilizing the constraints results in more efficient and accurate modeling, inference, dimension reduction as well as a clear and better interpretation of the results. In this paper, constrained, multi-term, and partially constrained factor models for matrix-variate time series are developed, with efficient estimation procedures and their asymptotic properties. We show that the convergence rates of the constrained factor loading matrices are much faster than those of the conventional matrix factor analysis under many situations. Simulation studies are carried out to demonstrate the finite-sample performance of the proposed method and its associated asymptotic properties. We illustrate the proposed model in three applications, where the constrained matrix-factor models outperform their unconstrained counterparts in the power of variance explanation under the out-of-sample 10-fold cross-validation setting.

Tea time at 4pm at SEO 300.

**Logic Seminar**

Machine learning and independence

James Freitag (UIC)

3:30 PM in SEO 427

The relationship between machine learning and the independence property (in the sense of model theory) is well-known. This seminar is not about that kind of independence. We will give an example of a natural problem in machine learning whose answer does not follow from ZFC.

Wednesday January 24, 2018

**Special Colloquium**

Modern Classification with Big Data

Boxiang Wang (University of Minnesota)

3:00 PM in SEO 636

Rapid advances in information technologies have ushered in the era of "big data" and revolutionized the scientific research. Big data creates golden opportunities but has also arisen unprecedented challenges due to the massive size and complex structure of the data. Among many tasks in statistics and machine learning, classification has diverse applications, ranging from improving daily life to reaching the new frontiers of science and engineering. This talk will discuss the envisions of broader approaches to modern classification methodologies, as well as computational considerations to cope with the big data challenges. I will present a modern classification method named data-driven generalized distance-weighted discrimination. A fast algorithm with an emphasis on computational efficiency for big data will be introduced. Our method is formulated in a reproducing kernel Hilbert space, and learning theory of the Bayes risk consistency will be developed. In addition, I will use extensive benchmark data applications to demonstrate that the prediction accuracy of our method is highly competitive with state-of-the-art classification methods including support vector machine, random forest, gradient boosting, and deep neural network.

**Algebraic Geometry Seminar**

Singular spaces with trivial canonical class

Stephane DRUEL (Grenoble University)

4:00 PM in SEO 427

The Beauville-Bogomolov decomposition theorem
asserts that any compact Kähler manifold with
numerically trivial canonical bundle admits an
étale cover that decomposes into a product of
a torus, an irreducible, simply-connected Calabi-Yau,
and holomorphic symplectic manifolds.
With the development of the minimal model program,
it became clear that singularities arise as an
inevitable part of higher dimensional life.
I will present recent works in
which a singular version of the decomposition theorem is established.

Thursday January 25, 2018

**Special Colloquium**

Unified tests for functional concurrent linear models and the phase transition from sparse to dense functional data

Ping-Shou Zhong (Michigan State University)

3:00 PM in SEO 636

We consider the problem of testing functional constraints in a class of functional concurrent linear models where both the predictors and the response are functional data measured at discrete time points. We propose test procedures based on the empirical likelihood with bias-corrected estimating equations to conduct both pointwise and simultaneous inferences. The asymptotic distributions of the test statistics are derived under the null and local alternative hypotheses, where sparse and dense functional data are considered in a unified framework. We find a phase transition in the asymptotic null distributions and the orders of detectable alternatives from sparse to dense functional data. Specifically, the proposed tests can detect alternatives of root-$n$ order when the number of repeated measurements per curve is of an order larger than $n^{\eta_0}$ with $n$ being the number of curves. The transition points $\eta_0$ for pointwise and simultaneous tests are different and both are smaller than the transition point in the estimation problem. Simulation studies and real data analyses are conducted to demonstrate the proposed methods.

Monday January 29, 2018

Wednesday February 7, 2018

**Statistics Seminar**

Bayesian Experimental Design and Hierarchical Model for Quantitative and Qualitative Responses

Lulu Kang (Illinois Institute of Technology)

4:00 PM in SEO 636

In many science and engineering systems both quantitative and qualitative output observations are collected. For short, we call such a system QQ system. In this talk, I will talk about a systematical approach for the experimental design and data analysis for the QQ system.
Classic experimental design methods are not suitable here because they often focus on one type of responses. We develop both Bayesian D and A-optimal design methods for experiments with one continuous and one binary responses. Both noninformative and conjugate informative prior distributions on the unknown parameters are considered. The proposed design criterions has meaningful interpretations in terms of the optimality for the models for both types of responses. Efficient design construction algorithms are developed to construct the local D-and A-optimal designs for given parameter values.
To capture a correlation between the two types of responses, we propose a Bayesian hierarchical modeling framework to jointly model a continuous and a binary response. Compared with the existing methods, the Bayesian method overcomes two restrictions. First, it solves the problem in which the model size (specifically, the number of parameters to be estimated) exceeds the number of observations for the continuous response. Second, the Bayesian model can provide statistical inference on the estimated parameters and predictions. Gibbs sampling scheme is used to generate accurate estimation and prediction for the Bayesian hierarchical model. Both simulation and real case study are shown to illustrate the proposed method.

Thursday February 8, 2018

**Quantum Topology / Hopf Algebra Seminar**

On Two Invariants of Three Manifolds from Hopf Algebras

Xingshan Cui (Stanford University)

3:00 PM in SEO 612

We prove a conjecture concerning two quantum invariants of three manifolds that are constructed from
finite dimensional Hopf algebras, namely, the Kuperberg invariant and the Hennings-Kauffman-Radford invariant.
The two invariants can be viewed as a non-semisimple generalization of the
Turaev-Viro-Barrett-Westbury (TVBW) invariant and the Witten-Reshetikhin-Turaev (WRT) invariant, respectively.
By a classical result relating TVBW and WRT, it follows that the Kuperberg invariant for a
semisimple Hopf algebra is equal to the Hennings-Kauffman-Radford invariant for the Drinfeld double
of the Hopf algebra. However, whether the relation holds for non-semisimple Hopf algebras has remained
open, partly because the introduction of framings in this case makes the Kuperberg invariant
significantly more complicated to handle. We give an affirmative answer to this question.
An important ingredient in the proof involves using a special Heegaard diagram in which one
family of circles gives the surgery link of the three manifold represented by the Heegaard diagram.
https://arxiv.org/pdf/1710.09524.pdf

Friday February 16, 2018

**Departmental Colloquium**

On the geometry of matrix multiplication

Joseph M. Landsberg (Texas A&M University)

3:00 PM in SEO 636

Our story begins with a spectacular failure:
The standard algorithm to multiply two nxn matrices uses $n^3$ multiplications. In 1969, while attempting to show that the standard algorithm was optimal, V. Strassen discovered an explicit algorithm to multiply 2x2 matrices using 7 multiplications rather than $8=2^3$. It is a central question to determine just how efficiently one can multiply nxn matrices, both practically and asymptotically.
In this talk, I will present a history of the problem, both of upper and lower complexity bounds I will discuss how geometry, more precisely algebraic geometry and representation theory,
are used. In particular, I will explain how, had someone asked him 100 years ago, the algebraic geometer Terracini could have
predicted Strassen's algorithm. The talk will conclude with the recent use of representation theory to construct algorithms, more precisely, rank decompositions.
For those who can't wait for the talk, a detailed history and the state of the art appears in Landsberg, J. (2017). Geometry and Complexity Theory (Cambridge Studies in Advanced Mathematics 169).

Tea at 4:15 PM

Monday February 19, 2018

Wednesday February 21, 2018

Friday February 23, 2018

Monday February 26, 2018

Wednesday March 7, 2018

Friday March 9, 2018

Monday March 12, 2018

Wednesday March 14, 2018

Friday March 16, 2018

Monday March 19, 2018

**Geometry, Topology and Dynamics Seminar**

Group actions on quiver varieties and applications

Victoria Hoskins (Freie Universität Berlin)

3:00 PM in SEO 636

In joint work with Florent Schaffhauser, we study two types of actions on King's moduli spaces of quiver representations over a field k, and we decompose their fixed loci using group cohomology in order to give modular interpretations of the components. The first type of action arises by considering finite groups of quiver automorphisms. The second is the absolute Galois group of a perfect field k acting on the points of this quiver moduli space valued in an algebraic closure of k; the fixed locus is the set of k-rational points, which we decompose using the Brauer group of k and give a moduli theoretic description. Over the field of complex numbers, we describe the symplectic and holomorphic geometry of these fixed loci in hyperkähler quiver varieties using the language of branes.

Friday March 23, 2018

Monday April 2, 2018

Wednesday April 4, 2018

Friday April 6, 2018

Monday April 9, 2018

Tuesday April 10, 2018

Wednesday April 11, 2018

Wednesday April 25, 2018

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.