# MSCS Seminar Calendar

Monday February 18, 2019

**Special Colloquium**

Towards a unified theory of approximate optimization

Euiwoong Lee (NYU)

3:00 PM in 636 SEO

The theory of approximate optimization faces new challenges and opportunities thanks to its increasing interaction with other fields of optimization. Such growth and diversity call for a unified theory of approximate optimization, where various algorithms and complexity results can be connected to one another and explained by a few general principles. My research aims to contribute to such a theory, by building a unified theory for general classes of optimization problems and exploring connections between such classes. This talk will showcase results in both directions.
1. For the class of graph cut problems, I will present a general framework for proving optimal hardness results for many directed cut problems. I will also show my recent algorithmic results that improve long-standing barriers for the k-cut problem in various settings.
2. Finally, I will introduce some recently discovered connections between continuous and discrete optimization. These connections involve well-studied problems in the respective fields including low-rank approximation, operator norms, and small set expansion.

Colloquium tea to follow at 4PM in SEO 300.

**Analysis and Applied Mathematics Seminar**

Simulating Multilayer Plasmonic Devices with Domain Decomposition Methods: High-Order Perturbation of Surfaces Implementations

David Nicholls (University of Illinois at Chicago)

4:00 PM in 636 SEO

The faithful modeling of the propagation of linear waves in a layered,
periodic structure is of paramount importance in many branches of the
applied sciences, in particular, in the simulation and design of
multilayer plasmonic devices. In this talk we present a novel
numerical algorithm for the simulation of such problems which is free
of the artificial singularities present in related approaches. We
advocate for a non-overlapping domain decomposition method (DDM)
phrased in terms of Impedance-Impedance Operators that are immune to
the Dirichlet eigenvalues which plague the Dirichlet-Neumann Operators
that appear in classical formulations. We demonstrate a High-Order
Spectral algorithm to simulate these operators based upon a High-Order
Perturbation of Surfaces methodology which is rapid, robust, and
highly accurate. We demonstrate the validity and utility of our
approach with a sequence of numerical simulations.

Tuesday February 19, 2019

**AWM@UIC Event**

AWM@UIC Opening Event

AWM Executive Council (UIC)

3:00 PM in 636 SEO

Do you want to promote an inclusive and welcoming environment for women and gender minorities in mathematics? If so, you’re invited to a social mixer sponsored by the UIC Association for Women in Mathematics (AWM) student chapter. All members of our department (including students, faculty and staff, regardless of gender) who are interested in supporting the mission of the AWM are welcome to attend. Refreshments will be served.
Stop by if you’re interested in learning more about how you can get involved!

Refreshments will be served.

**Logic Seminar**

On strongly minimal Steiner systems: Zilber's Conjecture, Universal Algebra, and Combinatorics

John Baldwin (UIC )

3:30 PM in 427 SEO

Those who heard a version of this talk in early September will be interested to see unintelligible questions replaced by theorems.
With Gianluca Paolini (in preparation), we constructed, using a variant
on the Hrushovski dimension function,
for every $k \geq 3$, $2^\mu$ families of
strongly minimal Steiner $k$-systems. We study the mathematical properties
of these counterexamples to Zilber's trichotomy conjecture rather than thinking of them as merely exotic examples. In particular the long study of finite Steiner systems in reflected in results that depend on the block size $k$.
A quasigroup is a structure with a binary operation such that for each equation $xy=z$ the values of two of the variables determines a unique value for the third.
The
new Steiner $3$-systems are bi-interpretable with strongly
minimal Steiner quasigroups. For $k >3$, we show the pure $k$-Steiner systems have `essentially unary definable closure' and do not interpret a quasigroup. But we show that for $q$ a prime power the Steiner $q$-systems can be interpreted into specific sorts of quasigroups, block algebras.
We extend the notion of an $(a,b)$-cycle graph arising in the study of finite and infinite Stein triple systems (e.g Cameron-Webb) by introducing what we call the $(a,b)$-path graph of a block algebra. We exhibit theories of strongly minimal block algebras where all $(a,b)$-paths are infinite and others in which all are finite only in the prime model. We show how to obtain combinatorial properties (e.g. 2-transitivity) by either varying the basic collection of finite partial Steiner systems or modifying the $\mu$ function which ensures strong minimality.

Wednesday February 20, 2019

**Mathematics Education Colloquium**

The Importance of Social Interactions in Mathematics Education

Aida Alibek (UIC)

10:45 AM in 612 SEO

This week we will build our discussion on the excerpt "The importance of social interaction" from a book by Constance Kazuko Kamii.
The discussion will strive to challenge the beliefs we hold about the role of social interaction in the teaching of mathematics in general, as well as undergraduate math teaching at UIC in particular. We will brainstorm and discuss ways we can incorporate more meaningful social interactions into our classrooms.
Prior reading is not required, everyone is welcome! If interested in the reading, please email aalibe2@uic.edu for the pdf.

**Statistics Seminar**

Posterior Contraction and Credible Sets for Filaments of Regression Functions

Subhashis Ghoshal (North Carolina State University)

4:00 PM in 636 SEO

The filament of a smooth function f consists of local maximizers of f when moving in a certain direction. The filament is an important geometrical feature of the surface of the graph of a function. It is also considered as an important lower dimensional summary in analyzing multivariate data. There have been some recent theoretical studies on estimating filaments of a density function using a nonparametric kernel density estimator. In this talk, we consider a Bayesian approach and concentrate on the nonparametric regression problem. We study the posterior contraction rates for filaments using a finite random series of B-splines prior on the regression function. Compared with the kernel method, this has the advantage that the bias can be better controlled when the function is smoother, which allows obtaining better rates. Under an isotropic Holder smoothness condition, we obtain the posterior contraction rate for the filament under two different metrics --- a distance of separation along an integral curve, and the Hausdorff distance between sets. Moreover, we construct credible sets of optimal size for the filament with sufficient frequentist coverage. We study the performance of our proposed method through a simulation study and apply on a dataset on California earthquakes to assess the fault-line of the maximum local earthquake intensity.
Based on joint work with my former graduate student, Dr. Wei Li, Assistant Professor, Syracuse University, New York.

**Graduate Groups and Dynamics Seminar**

Introduction to Invariant Random Subgroups

Samuel Dodds (UIC)

4:00 PM in 612 SEO

An Invariant Random Subgroup (IRS for short) for a group $G$ is a probability measure
on the space ${\rm Sub}_G$ of all closed subgroups of $G$, invariant under the natural $G$-action by conjugation.
This concept is a simultaneous generalization of closed normal subgroups and of lattices.
In the lecture we will discuss the compact space ${\rm Sub}_G$, and IRS and give some basic properties of those.

**Graduate Student Colloquium**

Splittings of groups and actions on trees

Christopher Perez (UIC)

5:00 PM in 636 SEO

Infinite groups can be studied by looking at how they split, i.e. how they can be expressed as amalgamated free products and HNN extensions, and more generally as graphs of groups. Splittings arise in a very geometric way when considering fundamental groups of spaces, and they can be found by studying how groups act on trees. In this talk we will give an overview of Bass-Serre theory and briefly discuss some applications in group theory, geometry and topology, and logic.

Thursday February 21, 2019

**Special Colloquium**

Designing Fast and Robust Learning Algorithms Using Spectral Graph Theory

Yu Cheng (Duke)

3:00 PM in 636 SEO

Most people interact with machine learning systems on a daily basis. Such interactions often happen in strategic environments where people have incentives to manipulate the learning algorithms. As machine learning plays a more prominent role in our society, it is important to understand whether existing algorithms are vulnerable to adversarial attacks and, if so, design new algorithms that are robust in these strategic environments.
In recent years, there have been exciting developments in algorithmic spectral graph theory, including faster algorithms for solving Laplacian linear systems, graph sparsification, and maximum flow. In this talk, I will focus on two lines of my work on leveraging the recent advancements in spectral graph theory to design fast and provably robust learning algorithms: making non-convex matrix completion approaches robust against semi-random adversaries, and designing robust high-dimensional statistical estimators that can be computed almost as efficiently as their non-robust counterparts.

Colloquium tea to follow at 4pm in SEO 300.

Friday February 22, 2019

**Mathematical Careers**

Breaking Enigma the First Time

David Saltman (Center for Communications Research - IDA)

3:00 PM in 636 SEO

I have two goals in this talk. The first one is to give you some idea of what it is like
to work at my center and more generally in the community we are part of. The second
goal is to give you some idea about how useful and important our kind of work is.
Now both goals are obstructed because our work is classified. For the first, I will give some
idea of how we work, if not what we do. For the second, I will give a historical example
describing how the Poles in World War II broke the German Enigma machine, and some of the math involved. As part of this section of the talk, I will invite you to examine and operate a original Enigma machine.

Monday February 25, 2019

**Special Colloquium**

Theory and Practice of Fair Resource Allocation

Alex Psomas (CMU)

3:00 PM in 636 SEO

The Internet and the vast increase in the availability of data have transformed algorithm design, as well as computer science in general. Designing algorithms that, given an input, quickly produce an output is no longer sufficient. In a myriad of modern applications, considerations like fairness and users’ incentives must be taken into account, complicating how success is defined and achieved. In this talk I’ll demonstrate how to tackle such issues in the context of food waste. I'll present a full stack of results on fair allocation, from theoretical results in formal models, all the way down to an improved allocation of food.
In the first part of the talk we study, from a purely theoretical angle, the fundamental problem of allocating a set of indivisible goods that arrive over time. Specifically, we will design algorithms that make allocation decisions in a way that is fair, under a formal definition of fairness. In the second part of the talk, we adopt and further develop an emerging paradigm called virtual democracy. Virtual democracy is an approach to automating decisions, by learning models of the preferences of individual people from data, and, at runtime, aggregating the predicted preferences of those people on the dilemma at hand. We will take the virtual democracy approach all the way to practice, in a collaboration with a Pittsburgh-based food bank, 412 Food Rescue, that provides on-demand food donation distribution services. I will present my work on designing and deploying an algorithm that automatically makes the decisions they most frequently face: given an incoming food donation, which recipient organization (such as a housing authority or food pantry) should receive it? I will also discuss challenges and solutions we faced in the data collection, learning and aggregation steps of virtual democracy, as well as this work’s implications for algorithmic fairness in general. I will conclude the talk by surveying some of my current and future research in algorithmic economics in general.

Colloquium tea to follow at 4pm in SEO 300.

**Analysis and Applied Mathematics Seminar**

Fourier transforms of indicator functions, lattice point discrepancy problems, and related matters

Michael Greenblatt (University of Illinois at Chicago)

4:15 PM in 636 SEO

We describe some sharp estimates for Fourier transforms of indicator functions of bounded open sets in R^n with real analytic boundary. These estimates are closely connected to corresponding sharp estimates on Fourier transforms of hypersurface measures. The estimates have immediate number theoretical applications, providing nontrivial lattice point discrepancy results for a large class of domains. Unlike most previous results in this subject, no convexity condition is required on the domains.
These estimates also have applications to maximal averages in harmonic analysis and local stability theorems for integrals of negative powers of real-analytic functions, which will be described if time permits.

Tuesday February 26, 2019

**Logic Seminar**

Equivalence of generic reals.

Iian Smythe (Rutgers University)

1:00 PM in 427 SEO

Given a countable transitive model of set theory and a notion of forcing in it, there is a natural countable Borel equivalence relation on generic objects over the model; two generics are equivalent if they yield the same generic extension. We study generic reals arising from familiar notions of forcing, e.g., Cohen and random forcing, under this equivalence relation and describe their relative complexity using the techniques of invariant descriptive set theory.

**Special Colloquium**

Algorithmic Convexity in the Discrete World

Nima Anari (Stanford)

2:00 PM in 636 SEO

A central algorithmic question is when can we efficiently sample from probability distributions?
In the continuous setting, convex sets and more generally log-concave distributions are the
main objects from which we can efficiently produce samples. In this talk, I will define a
parallel theory of convexity for discrete distributions and show how to use it to obtain
efficient sampling, counting, and optimization algorithms.
The main tool behind this theory consists of polynomials that encode discrete objects and
distributions, and the study of their analytical properties. This allows us to associate a
``continuous geometry’’ to discrete objects, and relate notions of convexity in the discrete
and continuous worlds.
We resolve several long-standing problems. This include sampling uniformly from bases
or independent sets of matroids, determinantal point processes and fractional powers of
them, and the random cluster (or Potts) model in the ``negative dependence regime'’ of q<1.
We also resolve a structural conjecture of Mason on the number of independent sets in
matroids, and derive Van der Waerden-type inequalities for matroids.

Note the unusual time! A small Tea in SEO 636 will be at 3pm (right after the talk)

**Quantum Topology / Hopf Algebra Seminar**

Seifert surfaces and existence of vortex reconnections in quantum fluids.

Daniel Peralta-Salas (Instituto de Ciencias Matematicas (ICMAT), Madrid)

2:00 PM in 427 SEO

The quantum vortices of a superfluid are described as nodal lines of a solution to the time-dependent Gross-Pitaevskii equation. Experiments in Lab and extensive numerical computations show that quantum vortices cross, each of them breaking into two parts and exchanging part of itself for part of the other. This phenomenon, known as quantum vortex reconnection, occurs even though the superfluid does not lose its smoothness. This usually leads to a change of topology of the quantum vortices. In this talk I will show that, given any initial and final congurations of quantum vortices (i.e. closed curves, possibly knotted and linked), and any way of transforming one into the other through a generic Seifert surface embedded in spacetime, there is an initial condition whose associated solution realizes this specific vortex reconnection scenario. This allows us to track the vortex reconnection process at all times, both locally and globally. Moreover, just as in the physics literature, the distance between vortices near the reconnection time obeys the so called t^{1/2} law. This is based on joint work with Alberto Enciso.

**Distinguished Lecture Series (P. Sarnak)**

Super strong approximation for integer points on quadrics

Peter Sarnak (Institute for Advanced Study, Princeton)

3:30 PM in SES 130

Thanks to works of Minkowski, Hasse, Siegel and others integer
points on quadrics are largely understood. We review these briefly and then discuss
recent developments concerning the existence of solutions in small regions
and the computational complexity of finding them with applications
to quantum computing.

This is a public lecture.
Notice the location of the lecture - SES 130.
The lecture will be followed by a reception -SCE East Terrace 4:45-7:00.

Wednesday February 27, 2019

**Special Colloquium**

How to learn a quantum state

John Wright (MIT)

3:00 PM in 636 SEO

In the area of quantum state learning, one is given a small number of "samples" of a quantum state, and the goal is use them to determine a feature of the state. Examples include learning the entire state ("quantum state tomography"), determining whether it equals a target state ("quantum state certification"), or estimating its von Neumann entropy. These are problems which are not only of theoretical interest, but are also commonly used in current-day implementation and verification of quantum technologies. In this talk, I will describe my work giving efficient algorithms for a variety of these problems, including the first optimal algorithms for tomography and state certification. My results make use of a new connection between quantum state learning and longest increasing subsequences of random words, a famous topic in combinatorics dating back to a 1935 paper of Erdős and Szekeres. Motivated by this connection, I will show new and optimal bounds on the length of the longest increasing subsequence of a random word.

**Statistics Seminar**

Using Prior Information for Intelligent Factor Allocation and Design Selection

William Li (Shanghai Advanced Institute of Finance)

4:00 PM in 636 SEO

While literature on constructing efficient experimental designs has been plentiful, how best to incorporate prior information when assigning factors to the columns has received little attention. This talk summarizes a series of recent studies that focus on information of individual columns. For regular designs, we propose the individual word length pattern (iWLP) that can be used to rank columns. With prior information on how likely a factor is important, iWLP can be used to intelligently assign factors to columns, and select the best designs to accommodate such prior information. This criterion is then extended to study nonregular designs, which we denote as the individual generalized word length pattern (iGWLP). We illustrate how iGWLP helps to identify important differences in the aliasing that is likely otherwise missed. Given the complexity of characterizing partial aliasing, iGWLP will help practitioners make more informed assignment of factors to columns when utilizing nonregular fractions. The theoretical justifications of the proposed iGWLP are provided in terms of statistical model and projection properties. In the third part, we consider clear effects involving an individual column (iCE). Motivated by a real application, we introduce the clear effects pattern, derived from iCE, and propose a class of designs called maximized clear effects pattern (MCEP) designs. We compare MCEP designs with commonly used minimum aberration designs and MaxC2 designs that maximize the number of clear two-factor interaction. We also extend the definition of iCE and MCEP designs by considering blocking schemes.

**Algebraic Geometry Seminar**

Intermediate Jacobian fibration and wall crossing

Giulia Sacca (Columbia University)

4:00 PM in 427 SEO

A few years ago with Laza and Voisin we constructed a hyperkahler
compactification of the intermediate Jacobian fibration associated to
a *general* cubic fourfold. In this talk I will first show how a HK
compactification J(X) exists for *any* smooth cubic fourfold X and then
discuss how the birational geometry of the fibration is governed by
any extra algebraic cohomology classes on X.

Thursday February 28, 2019

**Distinguished Lecture Series (P. Sarnak)**

Integer points on affine cubic surfaces

Peter Sarnak (Institute for Advanced Study, Princeton)

3:30 PM in SES 130

A cubic polynomial equation in four or more variables tends to have many integer solutions,
while one in two variables has a limited number of such solutions.
There is a body of work establishing results along these lines.
On the other hand very little is known in the critical case of three variables.
For special such cubics, which we call Markoff surfaces, a theory can be developed.
We will review some of the tools used to deal with these and related problems.
Joint works with Bourgain/Gamburd and with Ghosh.

This is the second lecture in the Distinguished Lecture Series.

Friday March 1, 2019

**Distinguished Lecture Series/ Colloquium**

The topologies of random real algebraic hypersufaces

Peter Sarnak (Institute for Advanced Study, Princeton)

3:00 PM in BSB 250

The topology of a hyper-surface in P^n(R)
of high degree can be very complicated.
However if we choose the surface at random there is a universal law.
Little is known about this law and it appears
to be dramatically different for n=2 and n>2 .
There is a similar theory for zero sets of monochromatic
waves which model nodal sets.
Joint work with Y.Canzani and I.Wigman .

This is Lecture 3 of the series. Note the lecture location. The lecture will be followed by departmental tea.

Monday March 4, 2019

Wednesday March 6, 2019

**Algebraic Geometry Seminar**

Batyrev-Borisov construction for cluster varieties

Man-Wai (Mandy) Cheung (Harvard)

4:00 PM in 427 SEO

Cluster varieties are blow up of toric varieties. They come in pairs (A,X), with A and X built from dual tori. Compactifications of A, studied by Gross, Hacking, Keel, and Kontsevich, generalize the polytope construction of toric varieties while the compactifications of X, studied by Fock and Goncharov, generalize the fan construction. The conjecture is that the A and the X cluster varieties are mirrors to each other. Together with Tim Magee, we have shown that there exists a positive polytope for the type A cluster varieties which give us a hint to the Batyrev-Borisov construction.

Monday March 11, 2019

Wednesday March 13, 2019

**Graduate Algebraic Geometry Seminar**

On 'A Young Person's Guide to Canonical Singularities' by Miles Reid

Ben Gould (UIC)

3:00 PM in 712 SEO

We will cover Chapter I of Miles Reid's 'A Young Person's Guide to Canonical Singularities.' The paper begins with the motivation for the notion of a (complex quasiprojective) variety to have canonical singularities, and then surveys the general theory, most of which is valid in all dimensions, and some of which is valid only up to dimension 3. We will assume as known much of the material from Hartshorne's II.6 and will overlap somewhat with the ongoing seminar on resolution of singularities.

**Graduate Algebraic Geometry Seminar**

On 'A Young Person's Guide to Canonical Singularities' by Miles Reid

Ben Gould (UIC)

3:00 PM in 712 SEO

We will cover Chapter I of Miles Reid's 'A Young Person's Guide to Canonical Singularities.' The paper begins with the motivation for the notion of a (complex quasiprojective) variety to have canonical singularities, and then surveys the general theory, most of which is valid in all dimensions, and some of which is valid only up to dimension 3. We will assume as known much of the material from Hartshorne's II.6 and will overlap somewhat with the ongoing seminar on resolution of singularities.

**Graduate Algebraic Geometry Seminar**

On 'A Young Person's Guide to Canonical Singularities' by Miles Reid

Ben Gould (UIC)

3:00 PM in 712 SEO

We will cover Chapter I of Miles Reid's 'A Young Person's Guide to Canonical Singularities.' The paper begins with the motivation for the notion of a (complex quasiprojective) variety to have canonical singularities, and then surveys the general theory, most of which is valid in all dimensions, and some of which is valid only up to dimension 3. We will assume as known much of the material from Hartshorne's II.6 and will overlap somewhat with the ongoing seminar on resolution of singularities.

**Graduate Algebraic Geometry Seminar**

On 'A Young Person's Guide to Canonical Singularities' by Miles Reid

Ben Gould (UIC)

3:00 PM in 712 SEO

Friday March 15, 2019

Monday March 18, 2019

Thursday March 21, 2019

**AWM@UIC : Invited Speaker Series**

Conversation and Refreshments

Kasia Jankiewicz (University of Chicago)

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 March 22, 2019

**Departmental Colloquium**

Wasserstein-Fréchet Regression and Covariance for Samples of Densities

Hans Mueller (UC Davis)

3:00 PM in 636 SEO

Samples of random densities and other non-Euclidean data are increasingly encountered in data analysis and meaningful notions of mean, regression and covariance for such data are of statistical interest.
This motivates a general class of regression models that relate responses consisting of random objects in a metric space with Euclidean predictors. In extension of the classical concept of Fréchet means (Fréchet 1948), this leads to conditional Fréchet means, which can be estimated with generalized versions of both global least squares and local weighted least squares regression. These approaches will be illustrated for the special case where the random objects are one-dimensional densities and where one chooses the Wasserstein metric on the space of densities. When data consist of vectors of random densities, the notion of Wasserstein covariance,
defined as an expected inner product of optimal transports, can be used to quantify the dependence of the components of these vectors. Applications include data from demography and brain imaging.

Monday April 1, 2019

**Analysis and Applied Mathematics Seminar**

On a dissipative Gross-Pitaevskii-type model for exciton-polariton condensates

Ryan Obermeyer (University of Illinois at Chicago)

4:00 PM in 636 SEO

We study a generalized dissipative Gross-Pitaevskii-type model
arising in the description of exciton-polariton condensates. We derive rigorous
existence and uniqueness results for this model posed on the one dimensional
torus and derive various a-priori bounds on its solution. Then, we analyze
in detail the long time behavior of spatially homogenous solutions and their
respective steady states. In addition, we will present numerical simulations in
the case of more general initial data. We also study the corresponding adiabatic
regime which results in a single damped-driven Gross-Pitaveskii equation and
compare its dynamics to the one of the full coupled system.
Joint work with C. Sparber, P. Antonelli, P. Markowich, and J. Sierra

**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).

Friday April 5, 2019

Friday April 12, 2019

Monday April 15, 2019

Wednesday April 17, 2019

Friday April 19, 2019

**Algebraic Geometry Seminar**

Double ramification cycles for target varieties

Rahul Pandharipande (ETH)

2:00 PM in 427 SEO

A basic question in the theory of algebraic curves is whether a
divisor represents the zeros and poles of a rational function.
An explicit solution in terms of periods was given by the work of Abel
and Jacobi in the 19th century. In the past few years, a different
approach to the question has been pursued: what is the class
in the moduli of pointed curves of the locus of such divisors? The
answer in Gromov-Witten theory is given by Pixton's formula
for the double ramification cycle. I will discuss recent work
with F. Janda, A. Pixton, and D. Zvonkine which considers
double ramification cycles for target varieties X (where Pixton's
original question is viewed as the X=point case). I will also
discuss the associated relations studied by Y. Bae.

Monday April 22, 2019

Wednesday April 24, 2019

Friday April 26, 2019

Monday April 29, 2019

Tuesday April 30, 2019

Wednesday May 1, 2019

Monday May 6, 2019

Monday September 9, 2019

Wednesday October 23, 2019

Friday November 1, 2019