# MSCS Seminar Calendar

Sunday November 23, 2014

Monday November 24, 2014

**Special Colloquium**

Gromov's surface subgroup question

Alden Walker (University of Chicago)

3:00 PM in SEO 636

Gromov asked whether every one-ended hyperbolic group contains a subgroup isomorphic to the fundamental group of a closed surface. This question is open in general, but the answer is known to be "yes" for several notable classes of hyperbolic groups. I'll give some background on the question and describe the construction of surface subgroups of random groups, including why one might care about the case of random groups. I'll also explain some (interestingly superficial) similarities with the construction of surface subgroups of closed hyperbolic 3-manifold groups due to Kahn and Markovic. This is joint work with Danny Calegari.

Meet and greet Tea afterwards in SEO 300.

**Applied Mathematics Seminar**

Discrete ABP estimate and rates of convergence of linear elliptic PDEs in non-divergence form

Wujun Zhang (University of Maryland)

4:00 PM in SEO 636

We design a finite element method (FEM) for linear elliptic equations
in non-divergence form, which hinges on an integro-differential
approximation of the PDE. We show the FEM satisfies the discrete
maximum principle (DMP) provided that the mesh is weakly acute. Thanks
to the DMP and consistency property of the FEM, we establish
convergence of the numerical solution to the viscosity solution.
We derive a discrete Alexandroff-Bakelman-Pucci (ABP) estimate for
finite element methods. Its proof relies on a geometric interpretation
of Alexandroff estimate and control of the measure of the
sub-differential of piecewise linear functions in terms of jumps, and
thus of the discrete PDE. The discrete ABP estimate leads to optimal
rates of convergence for the finite element method under suitable
regularity assumptions on the solution and coefficient matrix.

Tuesday November 25, 2014

**Logic Seminar**

Interactions of Set Theory with $L_{\omega_1,\omega}$

John Baldwin (UIC)

4:00 PM in SEO 427

I will discuss some aspects of continuing joint work with Friedman,
Koerwein, Larson, Laskowski, and Shelah. This work uses forcing
techniques to prove model theoretic results in ZFC. Force a model
theoretic result to be consistent by a tool such as Martin's axiom,
collapsing cardinals or a specific forcing with high model theoretic
content. Then use iterated elementary embeddings of the model of set
theory to show the model theoretic result is absolute between V and a
well-chosen model. Deduce it holds in ZFC. Applications include
various extensions of results for $L_{\omega_1,\omega}$ to
analytically presented AEC, a new proof of Harrington's theorem on
Scott rank of counterexamples to Vaught's conjecture and the
development of a new notion of algebraic closure for
$L_{\omega_1,\omega}$ that better explains $\aleph_1$-categoricity.
I will briefly contrast this with results about the characterization
of cardinals. The circle is closed by concluding (95\% now) from
arguments of the first sort that if a sentence of
$L{\omega_1,\omega}$ characterizes a cardinal below the continuum
then it has $2^{\aleph_1}$ models in $\aleph_1$.

**Graduate Analysis Seminar**

Time Independent Schrödinger Equation via a Variational Method, Part 1

Jack Arbunich (UIC)

4:00 PM in SEO 512

Part 1: (11/25) We define an energy functional associated to the time independent Schrödinger equation and prove the existence of a minimizer.
Part 2: (12/2) We show that the minimizer is a solution, and we prove uniqueness and regularity results.

Wednesday November 26, 2014

Monday December 1, 2014

**Geometry, Topology and Dynamics Seminar**

A new solution to the von Neumann-Day problem for finitely presented groups

Yash Lodha (Cornell University)

2:00 PM in SEO 636

In this talk, I will describe a finitely presented subgroup of Monod's group of piecewise projective homeomorphisms of the real line. This in particular provides a new example of a finitely presented group which is nonamenable and yet does not contain a nonabelian free subgroup. The example is moreover torsion free. A portion of this is joint work with Justin Moore. Recent work on the higher finiteness properties of this group will be discussed if time permits.

**Special Colloquium**

Monge-Ampere operators and applications

Mihai Paun (Korea Institute for Advanced Stduy )

3:00 PM in SEO 636

We will highlight a few properties of the Monge-Ampere operators which make them useful in the study of some global problems arising from complex algebraic geometry. At the end of our presentation, we will present the main ideas of the numerical characterization of the Kaehler cone of a compact complex manifold.

Tea after the talk

Tuesday December 2, 2014

**Special Colloquium**

Stable logarithmic maps

Qile Chen (Columbia University)

3:00 PM in SEO 636

Gromov-Witten theory, motivated from string physics, is the virtual counting of stable maps from nodal Riemann Surfaces to a target projective variety. The method of degeneration provides a powerful tool in the calculation of Gromov-Witten invariant. This has led to the study of relative stable maps which are stable maps with prescribed tangency conditions along fixed boundary divisors.
In this talk, I will introduce the theory of stable logarithmic maps, which provides a natural compactification of the space of relative stable maps. This theory not only gives us more flexible ways of degeneration in Gromov-Witten theory, but also provides a useful tool in birational geometry.

There will be a Meet and Greet Tea (after the Colloquium) in SEO 300.

**Graduate Analysis Seminar**

Time Independent Schrödinger Equation via a Variational Method, Part 2

Trevor Leslie (UIC)

4:00 PM in SEO 512

Part 1: (11/25) We define an energy functional associated to the time independent Schrödinger equation and prove the existence of a minimizer.
Part 2: (12/2) We show that the minimizer is a solution, and we prove uniqueness and regularity results.

**Logic Seminar**

Gordon's Conjectures: Pontryagin-van Kampen Duality and Fourier Transform in Hyperfinite Ambience

Pavol Zlatos (Comenius University)

4:00 PM in SEO 427

Using the ideas of E. I. Gordon [Go1], [Go2] we present an approach, based on nonstan-
dard analysis (NSA), to simultaneous approximation of locally compact abelian (LCA)
groups and their duals by nite abelian groups, as well as to approximation of the Fourier
transforms on various functional spaces over them by the discrete Fourier transform. In
2012 we proved the three Gordon's Conjectures (GC1{3) which were open since 1991 and
are crucial both in the formulations and proofs of the LCA groups and Fourier transform
approximation theorems. The proofs of GC1 and GC2 combine some methods of NSA
with Fourier-analytic methods of additive combinatorics, stemming from the paper [GR]
by Green and Ruzsa and the book [TV] by Tao and Vu. The proof of GC3 relies on a
fairly general nonstandard version of the Smoothness-and-Decay Principle.
Depending on time, we will survey most of the above mentioned constructions and
results.

Wednesday December 3, 2014

**Statistics Seminar**

Computer Experiment with Qualitative and Quantitative Factors

Dr. Devon Lin (Queens University)

4:00 PM in SEO 636

Computer experiments with qualitative and quantitative factors occur frequently in various applications in science and engineering. Design and analysis of such experiments is not yet completely resolved. To address this issue, we propose a new class of designs and a flexible modeling approach. The proposed designs allow us to accommodate a large number of qualitative factors with economic run sizes. Properties of such designs will be discussed. Several construction methods will be given. The new modeling approach employs a flexible function to capture the correlation among qualitative and quantitative factors. Several examples are provided to demonstrate significant improvement in prediction.

Wednesday December 10, 2014

Wednesday January 14, 2015

Tuesday January 27, 2015

**Mathematics Education Colloquium**

Solving Problems and Developing Theory: The Case of Teaching Proof in School Mathematics

Dr. Michelle Cirillo (University of Delaware)

5:00 PM in SEO 636

Not only do students find the learning of proof to be challenging at all levels, but research has shown that school mathematics teachers also find the teaching of proof to be a difficult endeavor. The pivotal epistemological role that proof plays in mathematics makes it an important object of inquiry for mathematics education researchers. Thus, if the field wishes to better prepare teachers to address the goals of current standards and therefore change the nature of school mathematics, we must first address the factors that shape it. Past research has explored many of these factors, including: the role of proof in the school curriculum; teachers' conceptions of proof; students' difficulties with proof; students' proof schemes and categories of justification; and descriptions of what 'doing proof' looks like in high school geometry. There is a need, however, for studies that look into classrooms and examine the work of teachers in practice. This notion will be explored through the case of The Geometry Proof Project, a collaborative study with high school mathematics teachers, which investigated some challenges of introducing formal, deductive proof. Through this colloquium, I will provide insights into the work of teachers in practice, specifically some of the conditions, challenges, and issues related to teaching proof at the secondary level. In addition, potential solutions for addressing these challenges will be presented through data and findings from the three-year research project. These findings may also have implications for teaching reasoning that leads to proof at the middle school level and for teaching proof at the post-secondary level.

Monday February 2, 2015

Monday February 9, 2015

Wednesday February 11, 2015

Monday February 16, 2015

Monday February 23, 2015

Friday February 27, 2015

Wednesday March 4, 2015

Wednesday March 18, 2015

Wednesday April 1, 2015

Wednesday April 8, 2015

Friday April 10, 2015

Monday April 13, 2015

Friday April 17, 2015

Wednesday April 22, 2015

Friday April 24, 2015