# MSCS Seminar Calendar

Saturday November 11, 2017

**RTG Workshop Talk**

A tour of the Hitchin moduli space

Laura Fredrickson (Stanford University)

3:00 PM in 430

We'll tour the rich geometric structure of the Hitchin moduli space. Two avatars of the Hitchin moduli space are the Higgs bundle moduli space and the moduli space of flat connections. We'll describe the nonabelian Hodge correspondence which connects these two. We'll also consider some of the structure that comes from the Higgs bundle side, including the Hitchin fibration and Hitchin section. For completeness, we'll describe the U(1) action and its utility.

The talk is part of the 2-day meeting "
RTG Workshop on the Geometry and Physics of Higgs bundles II
"

**RTG Workshop Talk**

Introduction to geometric structures on manifolds

Daniele Alessandrini (University of Heidelberg)

4:30 PM in 430

This will be an introduction to the theory of geometric structures on manifolds, their developing maps and holonomy representations, and their associated bundles endowed with a flat connection and a transverse section.

The talk is part of the 2-day meeting "
RTG Workshop on the Geometry and Physics of Higgs bundles II
"

Sunday November 12, 2017

**RTG Workshop Talk.**

How to use Higgs bundles?

Daniele Alessandrini

9:30 AM in 430

We will show how in some simple examples Higgs bundles can be used to construct geometric structures on manifolds. The flat connection can be expressed in terms of solutions of Hitchin, equations and the transverse section can be constructed from studying the holomorphic structure of the Higgs bundle.

The talk is part of the 2-day meeting "
RTG Workshop on the Geometry and Physics of Higgs bundles II
"

**RTG Workshop Talk**

The hyperkahler stucture of the Hitchin moduli space

Laura Fredrickson (Stanford University)

11:00 AM in 430

The Hitchin moduli space is hyperkahler. I'll give an introduction to hyperkahler geometry geared towards the Hitchin moduli space. We'll define the hyperkahler metric on the Hitchin moduli space.

**RTG Workshop Talk**

Higgs bundles and projective structures

Daniele Alessandrini (University of Heidelberg)

1:30 PM in 430

Hitchin and quasi-Hitchin representations act on real and complex projective space admitting a co-compact domain of discontinuity (Guichard-Wienhard). The holomorphic structure of the Higgs bundles and the solutions of Hitchin equations help us to describe the geometry of this domain. This is joint work with Qiongling Li.

**RTG Workshop Talk.**

Spectral data and limits in the Hitchin moduli space

Laura Fredrickson (Stanford University)

3:00 PM in 430

Given a Higgs bundle, Hitchin's equations are equations for a distinguihed hermitian metric---the so-called harmonic metric. We'll describe the asymptotic "abelianization" of Hitchin's equations near the ends of the Hitchin moduli space. We'll mention a few other limits in the Hitchin moduli space.

Monday November 13, 2017

**Conference talk.**

Interplay between Higgs bundles and opers.

Olivia Dumitrescu (Central Michigan University)

9:30 AM in SEO 636

We construct filtered extensions to explain the quantum deformation parameter, originated in physics as the Planck constant, as a deformation parameter of vector bundles and connections. The key concept is $SL(r,\mathbb{C})$- opers of Beilinson-Drinfeld (arbitrary $r$). We construct $SL(r,\mathbb{C})$-opers geometrically to prove that the quantization process is a biholomorphic map from the moduli space of Hitchin spectral curves to the moduli space of opers. We prove that the semiclasical limit of the family of opers is the spectral curve associated to the Higgs bundle. This talk is based on joint work with Motohico Mulase contained in arXiv:1702.00511, arXiv:1705.05969, and arXiv:1701.00155v2

The talk is part of the 2-day meeting "Current trends on spectral data for Higgs bundles III"

**Conference Talk.**

On cyclic Higgs bundles

Qiongling Li (QGM-Aarhus University and Caltech)

11:00 AM in SEO 636

The non-abelian Hodge theory gives a correspondence between the moduli space of representations of the fundamental group of a surface into a Lie group G with the moduli space of G-Higgs bundles over the Riemann surface. The correspondence is through looking for an equivariant harmonic map to the symmetric space associated to G, to a given representation or a given Higgs bundle. We discover some geometric properties of such harmonic maps associated to cyclic Higgs bundles.

The talk is part of the 2-day meeting "Current trends on spectral data for Higgs bundles III"

**Conference talk.**

The ends of the Hitchin moduli space

Laura Fredrickson (Stanford University)

1:30 PM in SEO 636

Hitchin's equations are a system of gauge theoretic equations on a Riemann surface that are of interest in many areas including representation theory, Teichm\"uller theory, and the geometric Langlands correspondence. In this talk, I'll describe what solutions of $SL(n,\mathbb{C})$-Hitchin's equations ``near the ends'' of the moduli space look like, and the resulting compactification of the Hitchin moduli space. Wild Hitchin moduli spaces are an important ingredient in this construction. This construction generalizes Mazzeo-Swoboda-Weiss-Witt's construction of $SL(2,\mathbb{C})$-solutions of Hitchin's equations where the Higgs field is ``simple.''

The talk is part of the 2-day meeting "Current trends on spectral data for Higgs bundles III"

**Geometry, Topology and Dynamics Seminar**

On the Hitchin fibration for algebraic surfaces

Ngo Bao Chau (University of Chicago)

3:00 PM in SEO 636

We will we explore the structure of the Hitchin map for higher dimensional varieties with emphasis on the case of algebraic surfaces.

The talk is part of the 2-day meeting "Current trends on spectral data for Higgs bundles III"

**Analysis and Applied Mathematics Seminar**

Osmotic water flow and solute diffusion in moving cells: mathematical model and numerical method

Lingxing Yao (Case Western Reserve University)

4:00 PM in SEO 636

Differences in solute concentration across a semipermeable membrane of cells generates
transmembrane osmotic water flow. The interaction of such flows with membrane and flow mechanics is a little explored
area despite its potential significance in many biological applications. Particularly, in recent studies,
experimental evidence suggests that membrane ion channels and aquaporins (water channels),
and thus, solute diffusion and osmosis, play an important role in cell movement.
To clarify the role of osmosis in cell movement, one needs to understand the interplay between solute diffusion, osmosis and mechanical forces.
In this presentation, we discuss a mathematical model that allows for studying the interplay between diffusive, osmotic
and mechanical effects, and the numerical method for solving the model system. An
osmotically active solute obeys a advection-diffusion equation in a region
demarcated by a deformable membrane. The interfacial membrane allows transmembrane water flow
which is determined by osmotic and mechanical pressure differences across the membrane.
The numerical method is based on an immersed boundary method for fluid-structure
interaction and a Cartesian grid embedded boundary method for the solute. We demonstrate our numerical algorithm
with the test case of an osmotic engine, a recently proposed mechanism for cell propulsion.
This is joint work with Yoichiro Mori at University of Minnesota.

**MATH Club**

Christofides the traveling salesperson: approximation algorithms

Ben Fish (UIC)

4:00 PM in SEO 300

While most intro talks to the computational complexity of algorithms start by introducing NP-hardness, I'll take a more optimistic approach by talking about the power of provably-correct approximation algorithms, using metric TSP as an example to show the power of approximate solutions over exact solutions, and to explain what all these words mean.

Tuesday November 14, 2017

**Conference Talk.**

The intersection cohomology of the moduli space of Higgs bundles on a smooth projective curve

Camilla Felisetti (University of Bologna)

9:30 AM in SEO 636

Let $X$ be a smooth projective curve of genus $g$ over $\mathbb{C}$. The

*character variety*$\mathcal{M}_B$ parametrizing conjugacy classes of representations from the fundamental group of X into $SL(2,\mathbb{C})$ is an affine irreducible singular projective variety. The*Non Abelian Hodge theorem*, states that there is a real analytic isomorphism between $\mathcal{M}_B$ and the quasi projective singular variety $\mathcal{M}_{Dol}$ which parametrizes semistable Higgs bundles of rank $2$ and degree $0$ on $X$. During the seminar I will present a desingularization of these moduli spaces and compute several informations about their intersection cohomology using the famous*Decomposition theorem*by Beilinson, Bernstein, Deligne and Gabber. Time permitting, I will explain some possible applications to the so called $P=W$ conjecture, stated and proved by De Cataldo, Hausel and Migliorini in the case of rank 2 and degree 1 Higgs bundles.The talk is part of the 2-day meeting "Current trends on spectral data for Higgs bundles III"

**Conference Talk.**

Lagrangian spectral curves

Eric Zaslow (Northwestern University)

11:00 AM in SEO 636

I will explain a symplectic analogue of the spectral curve construction in the moduli of Higgs bundles. More specifically, exact Lagrangian surfaces filling Legendrian knots which encode Stokes braiding at a singularity provide an abelian chart for the (non-abelian) wild character variety associated to the singularity. I will demonstrate this in several simple examples and then (time-premitting) describe the very different behavior one finds for Lagrangian threefolds filling Legendrian surfaces. This talk is based on joint works with Linhui Shen, Vivek Shende, David Treumann and Harold Williams.

The talk is part of the 2-day meeting "Current trends on spectral data for Higgs bundles III"

**Special Colloquium**

Stability in ordered configuration spaces

Jennifer Wilson (Stanford University)

3:00 PM in SEO 636

The ordered configuration space F_k(M) of a manifold M is the space of ordered k-tuples of distinct points in M. For a fixed manifold M, as k increases, we might expect the topology of these configuration spaces to become increasingly complicated. Church and others showed, however, that when M is connected and open, there is a representation-theoretic sense in which these spaces stabilize. In this talk I will explain these stability patterns, and describe higher-order stability phenomena established in recent work joint with Jeremy Miller. This project was inspired by work-in-progress of Galatius--Kupers--Randal-Williams.

Tea at 4pm in SEO 300

Wednesday November 15, 2017

**Algebraic K-Theory Seminar**

An action of the Grothendieck-Teichmüller group on stable curves of genus zero.

Marcy Robertson (University of Melbourne)

10:30 AM in SEO 1227

The Grothendieck-Teichmüller group is an explicitly defined group introduced by Drinfeld which is closely related to (and conjecturally equal to) the absolute Galois group. The idea was based on Grothendieck's suggestion that one should study the absolute Galois group by relating it to its action on the Teichmüller tower of fundamental groupoids of the moduli stacks of genus g curves with n marked points. In this talk, we give an reimagining of the genus zero Teichmüller tower in terms of a profinite completion of the framed little 2-discs operad. Using this reinterpretation, we show that the homotopy automorphisms of this model for the Teichmüller tower is isomorphic to the (profinite) Grothendieck-Teichmüller group. We then show a non-trivial action of the absolute Galois group on our tower. This talk will be aimed a general audience and will not assume any previous knowledge of the Grothendieck-Teichmüller group or operads. This is joint work with Pedro Boavida de Brito and Geoffroy Horel.

**Graduate Geometry, Topology and Dynamics Seminar**

Geometry and Dynamics of Groups acting on $\mathbb{R}$-trees

Samuel Dodds (UIC)

3:00 PM in SEO 612

We will first give a rough overview of groups acting on simplicial trees. We will then move on to $\mathbb{R}$-trees, charting our way towards the Morgan-Shalen compactification.

**Algebraic Geometry Seminar**

Dominating varieties by liftable ones

Remy van Dobben de Bruyn (Columbia University)

4:00 PM in SEO 427

Given a smooth projective variety over an algebraically closed field of positive characteristic, can we always dominate it by another smooth projective variety that lifts to characteristic 0? We give a negative answer to this question.

Thursday November 16, 2017

**Algebraic Geometry Seminar**

Syzygies on low-dimensional abelian varieties

Alex Küronya (Goethe Universitat - Frankfurt am Main)

1:00 PM in SEO 427

In a joint work with Victor Lozovanu we study syzygies of ample line bundles on abelian varieties, more specifically when property $(N_p)$ of Green and Lazarsfeld are satisfied. We give an equivalent characterization in dimension two, and look into what happens on abelian threefolds.

Friday November 17, 2017

**Special Colloquium**

Dynamics, geometry, and the moduli space of Riemann surfaces

Alex Wright (Stanford)

3:00 PM in SEO 636

The moduli space of Riemann surfaces of fixed genus is one of the hubs of modern mathematics and physics. We will tell the story of how simple sounding problems about polygons, some of which arose as toy models in physics, became intertwined with problems about the geometry of moduli space, and how the study of these problems in Teichmuller dynamics lead to connections with homogeneous spaces, algebraic geometry, dynamics, and other areas. The talk will mention joint works with Alex Eskin, Simion Filip, Curtis McMullen, Maryam Mirzakhani, and Ronen Mukamel.

Monday November 20, 2017

**Geometry, Topology and Dynamics Seminar**

Weakly aperiodic SFT on lamplighters

David Cohen (University of Chicago)

3:00 PM in SEO 612

A subshift of finite type (SFT) is a symbolic dynamical system defined by a finite collection of ``local rules". For instance, for any natural number k and any group G equipped with a finite generating set S, the set of all valid k-colorings of the corresponding Cayley graph of G (colorings of the Cayley graph in which no two adjacent vertices have the same color) forms an SFT. It is clear that any SFT X over a group G carries a G-action, and X is said to be weakly aperiodic if it is nonempty and has no finite G-orbits. When G=Z, there are no weakly aperiodic SFTs over G, but when G=Z^2 such SFTs do exist, as was shown by Berger. Carroll and Penland conjectured that a group with no weakly aperiodic SFT must be virtually cyclic. We will discuss some known obstructions to a group G being a counterexample to this conjecture (meaning that G is not virtually cyclic, but still admits a weakly aperiodic SFT), and explain why lamplighter groups were the most natural candidate. Time permitting, we will briefly discuss our proof that a lamplighter group cannot actually be a counterexample.

**Analysis and Applied Mathematics Seminar**

Efficient high-order algorithms for drift-diffusion and electromagnetic systems

Misun Min (Argonne National Laboratory)

4:00 PM in SEO 612

Simulations of ion channels and metamaterial devices are of considerable technological importance and also present very interesting and challenging problems from the perspective of numerical algorithms for PDEs. Robust and rapidly convergent numerical methods are essential to solve these systems. I will discuss efficient high-order algorithms for solving drift-diffusion models that describe the transport of charge-carriers coupled with a Poisson equation for electric potential. The spatial discretization is based on a standard spectral-element formulation with body-fitted hexahedral elements. The temporal discretization is a mixed implicit-explicit method using kth-order backward-difference formulas and extralpolation as well as a pseudo-timestepping approach based on Jacobi-free Newton Krylov methods. The electric potential is governed by a Poisson equation to be solved at each timestep. This problem is solved with GMRES iteration, preconditions with spectral-element multigrid. Validation of the algorithms is demonstrated with convergence studies and computational results for potassium ion channels. A second problem of interest is the study of novel ultra-thin flat metalens and graphene-based two-dimensional materials, whose behavior is governed by the solutions to Maxwell's equations. I will discuss high-order spectral element discontinuous Galerkin schemes for solving these equations. High-order discretizations offer minimial numerical dispersion and dissipation while providing high performance to deliver fast, efficient, and accurate simulations on current and next-generation architectures. The discussion will include the aspects of high-performance algorithms and performance analysis on many-core and many-GPU cmputing platforms.

Wednesday November 22, 2017

**Complex Analysis Seminar**

The 1-dimensional extension property in complex analysis

Mark Lawrence (Nazarbayev University)

3:00 PM in SEO 1227

A classical theorem states that if a function on the unit circle has
vanishing negative Fourier coefficients, then it extends to holomorphic
function on the unit disc. What happens when you are given a family of
curves, and a function which extends holomorphically from each of the
curves? This area of study is called the "1-dimensional extension
problem". Results for planar domains, and for holomorphic extension from
boundaries in C^n will be discussed. One application is the construction
of a completely new class of algebras of real analytic functions.
Various techniques of analytic extension in several variables are used
to prove these results.

**Statistics Seminar**

Causality in the joint analysis of longitudinal and survival data

Lei Liu (Washington University in St. Louis )

4:00 PM in SEO 636

In many biomedical studies, disease progress is monitored by a biomarker over time, e.g., repeated measures of CD4, hemoglobin level in end stage renal disease (ESRD) patients. The endpoint of interest, e.g., death or diagnosis of a specific disease, is correlated with the longitudinal biomarker. The causal relation between the longitudinal and time to event data is of interest. In this paper we examine the causality in the analysis of longitudinal and survival data. We consider four questions: (1) whether the longitudinal biomarker is a mediator between treatment and survival outcome; (2) whether the biomarker is a surrogate marker; (3) whether the relation between biomarker and survival outcome is purely due to an unknown confounder; (4) whether there is a mediator moderator for treatment. We illustrate our methods by data from two clinical trials: an AIDS study and a liver cirrhosis study.

Wednesday November 29, 2017

**Algebraic Geometry Seminar**

Reduction of manifolds with semi-negative holomorphic sectional curvature

Gordon HEIER (University of Houston)

4:00 PM in SEO 427

The interplay of various notions of hyperbolicity and the geometry and
structure of a projective manifold is an important topic in complex
geometry. In this spirit, we investigate a projective Kaehler manifold
$M$ of semi-negative holomorphic sectional curvature $H$. We will
begin with an overview of the recent progress on this topic. We will
then introduce a new differential geometric numerical rank invariant
which measures the number of linearly independent truly flat
directions of $H$ in the tangent spaces. This invariant turns out to
be bounded above by the nef dimension and bounded below by the
numerical Kodaira dimension of $M$. We will also discuss a splitting
theorem for $M$ in terms of the nef dimension and, under some
additional hypotheses, in terms of the new rank invariant. This is
joint work with S. Lu, B. Wong and F. Zheng.

Monday December 4, 2017

**Geometry, Topology and Dynamics Seminar**

Relatively hyperbolic groups vs 3-manifold groups.

Genevieve Walsh (Tufts University)

2:00 PM in SEO 636

Bowditch described the boundary of a relatively hyperbolic group pair $(G,P)$ as the boundary of any hyperbolic space that $G$ acts geometrically finitely upon, where the maximal parabolic subgroups are conjugates of the subgroups in $P$. For example, the fundamental group of a hyperbolic knot complement acts geometrically finitely on $\mathbb{H}^3$, where the maximal parabolic subgroups are the conjugates of $\mathbb{Z} \oplus \mathbb{Z}$. Here the Bowditch boundary is $S^2$. We show that torsion-free relatively hyperbolic groups whose Bowditch boundaries are $S^2$ are relative $PD(3)$ groups, and give some other applications of our techniques. This is joint work with Bena Tshishiku. If time permits, I'll show some examples of relatively hyperbolic group pairs with planar boundary which are not 3-manifold pairs, joint with Chris Hruska.

Wednesday December 6, 2017

Monday February 5, 2018

Friday February 16, 2018

Wednesday February 21, 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.

Friday March 2, 2018

Friday March 9, 2018

Friday March 23, 2018

Monday April 2, 2018

Wednesday April 4, 2018

Friday April 6, 2018

Wednesday April 11, 2018

Wednesday April 25, 2018