# MSCS Seminar Calendar

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.

**Analysis and Applied Mathematics Seminar**

New Integrals of Motion and Singularities in 2D Fluid Dynamics with Free Surface

Sergey Dyachenko (UIUC)

4:00 PM in SEO 636

We study the problem of 2D incompressible fluid dynamics with free surface, we assume
the the fluid is ideal and the flow is potential. Following the conformal mapping
technique we reformulate the problem to surface variables and demonstrate the existence
of previously undiscovered constants of motion associated with singularities in the
analytic continuation of conformal map and complex potential. In numerical simulations
we recover the analytic structure of the surface shape and observe simple poles and
branch point singularities of the square-root type. We use the Alpert-Greengard-Hagstrom
method to recover the location, type and magnitude of the singularities. We show how
the approach of square-root type singularities may be responsible for the breaking of
waves in the ocean, following the nonlinear stage of modulational instability.

**Stat Lab Seminars**

Robust Methods in Small Area Estimation

Prof. Abhyuday Mandal (University of Georgia)

4:00 PM in SEO 612

Modern societies have an ever-increasing appetite for reliable and up to date data to make informed decisions in both public and private sectors alike. While censuses, usually conducted once in a decade, provide reliable information about the population across various geography and demography, such information quickly get outdated each passing year after a census. To obtain a current picture of a population under study, suitable surveys are conducted to collect data from only a fraction of the population. Due to budget constraints, these surveys are inherently limited in size. While information gained from such surveys may be adequate for the entire population, the same data is often inadequately small when it is sliced and diced across geographic and demographic sub-populations. These sub-populations are termed small areas.
National Statistical Offices around the world have been mandated for many years to produce reliable small area statistics for many important variables such as population, income, unemployment, health outcomes, etc. Statistical summaries based on traditional direct estimates, computed using only sample data from individual small areas, are usually very unreliable. In small area estimation, by borrowing strength from other data sources, appropriate statistical methodologies have been developed to improve on the traditional direct estimates.
In this talk, we propose new alternatives to some popular models in small area estimation. Model-based small area estimates are developed by shrinking direct estimates to suitable regression synthetic estimates, generated from the regression model for small area population means. Our new models are based on finite mixture of normal distributions. We implement our models using a hierarchical Bayesian approach.
This talk is based on collaboration with Gauri Sankar Datta and Adrijo Chakraborty.

Tea will be served at SEO 612.

Tuesday March 20, 2018

**Mathematics Education Colloquium**

"Studying students studying calculus"

Aida Alibek (UIC)

1:00 PM in SEO 612

We will have a discussion of Uri Treisman's article "Studying students studying calculus: a look at the lives of minority mathematics students in college", as well as the ESP program and minority student experiences at UIC.
Everyone is welcome to join the discussion. For a pdf of the paper, please contact aalibe2@uic.edu.
Note: Uri Treisman is the creator of the ESP program that is currently implemented at UIC.

Wednesday March 21, 2018

**Statistics Seminar**

Sampling for Conditional Inference on Network Data

Yuguo Chen (UIUC)

4:00 PM in SEO 636

Random graphs with given vertex degrees have been widely used as a model for many real-world complex networks. We describe a sequential sampling method for sampling networks with a given degree sequence. These samples can be used to approximate closely the null distributions of a number of test statistics involved in such networks, and provide an accurate estimate of the total number of networks with given vertex degrees. We apply our method to a range of examples to demonstrate its efficiency in real problems.

Thursday March 22, 2018

**Quantum Topology / Hopf Algebra Seminar**

New Mathematical Developments in Quantum Mechanics

Arkady L. Kholodenko (H. L. Hunter Laboratories, Clemson University, Clemson, SC)

3:00 PM in SEO 612

This talk discusses the structure of quantum mechanics in the context of more general complex scalar fields.

**Graduate Geometry, Topology and Dynamics Seminar**

Applications of constructible sheaves

Jānis Lazovskis (UIC)

4:00 PM in SEO 512

All we do is for this frightened thing we call Love, want and lack — fear that we aren’t the one whose body could be beloved of all the brides of Kansas City, kissed all over by every boy of Wichita — O but how many in their solitude weep aloud like me — On the bridge over Republican River almost in tears to know how to speak the right language — on the frosty broad road uphill between highway embankments I search for the language that is also yours.

Friday March 23, 2018

**Departmental Colloquium**

The Maximal Rank Theorem

Joe Harris (Harvard)

3:00 PM in Lecture Center A1

The Brill-Noether theorem establishes a fundamental link between the classical notion of a curve in projective space, given as the zero locus of polynomials, and the (relatively) modern notion of an abstract curve. Specifically, it tells us when and how a given general abstract curve can be embedded in $\mathbb{P}^r$.
But that's just the opening line of the story: having embedded our abstract curve in projective space, we can ask about the geometry and algebra of the image. In particular, we ask what sort of polynomial equations define the image -- what their degrees are, and how many of them there are.

*The Maximal Rank Conjecture*, recently proved by Eric Larson, gives the answer to this question. In this talk, I'll describe the ideas leading up to this theorem, give an overview of the proof, and discuss the questions that follow.This lecture will also serve as the first talk in the ``Workshop on Algebraic Geometry and its Broader Implications'' to be held over the following weekend March 23-25 at UIC, a conference in honor of Robin Hartshorne's 80th and the book's 40th. See http://kftucker.people.uic.edu/Hart80/ for further details.

Monday April 2, 2018

**Analysis and Applied Mathematics Seminar**

Orbital Stability of Vortex Solitary Waves for Dispersive Equations

Shijun Zheng (Georgia Southern University)

4:00 PM in SEO 636

Vortex type solitons exhibit remarkable and ubiquitous phenomena that arise in modeling quantum optics, plasma, superfluids and pseudo-relativistic boson stars.
I will discuss orbital stability and instability by providing certain sharp conditions for the governing equations including magnetic and fractional NLS with unbounded potentials.
This study is motivated by related open question in the area in oder to understand the asymptotic behavior and rates of wave-collapse for the solutions. Some numerical simulations are presented as well.

Wednesday April 4, 2018

Friday April 6, 2018

Monday April 9, 2018

Tuesday April 10, 2018

Wednesday April 11, 2018

Friday April 13, 2018

Monday April 16, 2018

**Analysis and Applied Mathematics Seminar**

Guaranteed-Accuracy Fast Algorithms for the Evaluation of Layer Potentials using `Quadrature by Expansion'

Andreas Kloeckner (UIUC)

4:00 PM in SEO 636

Quadrature by Expansion, or `QBX', is a systematic, high-order approach to singular quadrature that applies to layer potential integrals with general kernels on curves and surfaces. The efficient and accurate evaluation of layer potentials, in turn, is a key building block in the construction of solvers for elliptic PDEs based on integral equation methods.
I will present a new fast algorithm incorporating QBX that evaluates layer potentials on and near surfaces in two and three dimensions with user-specified accuracy, along with supporting theoretical and empirical results on complexity and accuracy. A series of examples on unstructured geometry across a variety of applications in two and three dimensions demonstrates the applicability of the method.

Monday April 23, 2018

Wednesday April 25, 2018

Monday April 30, 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.