# MSCS Seminar Calendar

Monday October 27, 2014

**Geometry, Topology and Dynamics Seminar**

Horseshoe-like maps of plane and symbolic dynamics

Sonja Stimac (University of Zagreb and IUPUI)

3:00 PM in SEO 636

I will present a possible approach to coding of attractors of horseshoe-like maps of plane (such as the H\'enon and Lozi maps). I will also discuss
some techniques which can be used if an attractor is characterized by an appropriate countable collection of sequences of 0s and 1s (which play role
of ``kneading sequences'' of ``critical points''). I will show necessary and sufficient conditions for a sequence of 0s and 1s to be an itinerary
of a point which belongs to the unstable manifold of a fixed point.

**Combinatorics Seminar**

The number of maximal sum-free subsets of integers

Maryam Sharifzadeh (UIUC)

3:00 PM in SEO 427

Abstract: Cameron and Erdos raised the question of how many maximal sum-free sets there are in $\{1, \dots , n\}$,
giving a lower bound of $2^{\lfloor n/4 \rfloor }$. In this paper we prove that there are in fact at most $2^{(1/4+o(1))n}$ maximal
sum-free sets in $\{1, \dots , n\}$.
Our proof makes use of container and removal lemmas of Green as well as a result of
Deshouillers, Freiman, S\'os and Temkin on the structure of sum-free sets.
Joint work with: Jozsef Balogh, Hong Liu and Andrew Treglown

**Graduate Number Theory Seminar**

Remarks on the distribution of Frobenius for elliptic modules

Abel Castillo (UIC)

3:00 PM in SEO 712

In this talk we will state conjectures regarding the distribution of the trace of Frobenius for elliptic curves, including the the Lang-Trotter conjectures and the Koblitz conjecture, and point out how these are "higher-dimensional analogues" of familiar statements about primes in arithmetic progressions. We will then discuss heuristics that are used to make precise predictions about the constants appearing in the statements. As time permits, we will close by discussing analogues of these conjectures for Drinfeld modules in the global function field setting.

**Geometry, Topology and Dynamics Seminar**

Open-closed string maps and circle actions in symplectic topology

Sheel Ganatra (Stanford University)

4:00 PM in SEO 612

Floer (or pseudoholomorphic curve) theory associates
homological invariants to a symplectic manifold via a (semi-)infinite
form of Morse homology. The resulting structures come in a "closed
string" flavor generalizing quantum cohomology and an "open string"
one known as the Fukaya category.
In this talk, we describe a general program in Floer theory to recover
closed string invariants from open string invariants via "open-closed
string maps", with focus on an extra geometric structure present in
both theories: a chain-level circle action. There is motivation for
understanding such a circle action from both topological field theory
and mirror symmetry, where it is related to the Hodge-to-de Rham
spectral sequence.

Tuesday October 28, 2014

**Graduate Analysis Seminar**

Derivation of Nonlinear Schrödinger equation from many-body systems

Zhihui Xie (UIC)

4:00 PM in SEO 1227

The nonlinear Schrödinger equations have attracted a lot of attention from the mathematical community, which emphasizes the importance of making their derivation rigorous. In this talk, we look at the derivation of a certain type of NLS from many-body interactions of bosonic particles with many-body interactions.

Wednesday October 29, 2014

**Graduate Algebraic Geometry Seminar**

Elliptic Surfaces or: Not So Good Fibrations

Yang Shuhang (UIC)

2:00 PM in SEO 712

I will talk about basics of elliptic surfaces. An elliptic surface is, by definition, an elliptic fibration over an algebraic curve. We can regard it as an elliptic curve over the function field of the curve. I will talk about the singular fibres, especially Kodaira's classification of singular fibres. Also we will see that algebraic equivalence and numerical equivalence are the same for elliptic surfaces with a section.

**Graduate Theoretical Computer Science Seminar**

Finding the K best synthesis plans

Rojin Kianian (University of Southern Denmark)

2:00 PM in SEO 427

Synthetic Chemistry has developed sophisticated tools in order to create new compounds. However, current algorithmic approaches to find optimal synthesis plans are limited to determining optimal bond sets. Noting that each bond set represents a possibly very large set of different synthesis plans for the target compound, there is a need for methods for choosing among these. We attack this problem by modeling synthesis plans for a given bond set as hyperpaths in a hypergraph. As a consequence, a polynomial time algorithm to find the K shortest hyperpaths can be adapted to computing the K best synthesis plans for the bond set. We use classical objective functions for synthesis plans, such as overall yield or convergence of the plan. The 4-bond disconnections of decaline are used as an illustrative example.

**Algebraic Geometry Seminar**

Normality of Secant Varieties

Brooke Ullery (University of Michigan)

4:00 PM in SEO 427

If X is a smooth variety embedded in projective space, we can form a new variety by looking at the closure of the union of all the lines through 2 points on X. This is called the secant variety to X. Similarly, the Hilbert scheme of 2 points on X parametrizes all length 2 zero-dimensional subschemes. I will talk about how these two constructions are related. More specifically, I will show how we can use certain tautological vector bundles on the Hilbert scheme to help us understand the geometry of the secant variety, leading to a proof that for sufficiently positive embeddings of X, the secant variety is a normal variety.

**Statistics Seminar**

Some important statistical considerations in biomarker discovery from high-dimensional data

V. Devanarayan (AbbVie)

4:00 PM in SEO 636

Biomarkers such as those based on genomic, proteomic and imaging
modalities play a vital role in biopharmaceutical R&D. Examples include
the discovery of novel genes/targets related to various diseases based on
which a suitable therapeutic can be developed, diagnostics for different
disease subtypes, identification of patients that are more likely to
progress in disease or benefit from a particular therapeutic, etc. The
discovery of such biomarkers are typically based on the evaluation of
high-dimensional datasets that require a strong combination of
bioinformatic and statistical considerations. This seminar will provide
a practical overview and intuitive explanation of some important concepts
and considerations around the analyses of such high-dimensional data.

Thursday October 30, 2014

Friday October 31, 2014

**Algebraic Topology Seminar**

Homotopy groups of spheres and the strong Kervaire invariant problem in dimension 62.

Zhouli Xu (University of Chicago)

1:00 PM in SEO 1227

Computing and understanding the homotopy groups of spheres is one of the most important and interesting questions in algebraic topology. In this talk, I will first review the known stemwise computations at the prime 2. In particular, I will briefly discuss recent work of Isaksen using motivic methods. Then I will discuss joint work with Beaudry that relates stemwise and chromatic computations. Finally, I will talk about the current status of the strong Kervaire invariant problem in dimension 62, including a sketch of the proof that twice theta five is zero.

**Departmental Colloquium**

The Role of Entanglement in DNA Structure and Function

De Witt Sumners (Florida State University)

3:00 PM in SEO 636

This talk will survey some of the results on properties of random
knots in 3-space and in confined volumes, with applications to enzyme action on
duplex DNA and the structure and dynamics of duplex DNA confined to viral
capsids. This talk is intended for a general mathematical audience.

Monday November 3, 2014

**Computer Science Seminar**

On Coloring Resilient Graphs

Jeremy Kun (UIC)

3:00 PM in SEO 427

We introduce a new notion of resilience for constraint satisfaction problems, with the goal of more precisely determining the boundary between NP-hardness and the existence of efficient algorithms for resilient instances. In
particular, we study $r$-resiliently $k$-colorable graphs, which are those
$k$-colorable graphs that remain $k$-colorable even after the addition of any
$r$ new edges. We prove lower bounds on the NP-hardness of coloring
resiliently colorable graphs, and provide an algorithm that colors sufficiently
resilient graphs. We also analyze the corresponding notion of resilience for $k$-SAT.
This notion of resilience suggests an array of open
questions for graph coloring and other combinatorial problems.
This work appeared in Mathematical Foundations of Computer Science, 2014 and is joint with Lev Reyzin

Tuesday November 4, 2014

Wednesday November 5, 2014

**Algebraic Geometry Seminar**

Non-Abelian Lefschetz Hyperplane Theorems

Daniel Litt (Stanford University)

4:00 PM in SEO 427

Work of Lefschetz (in 1924) and Grothendieck (in SGA II) provides many relationships between properties of a smooth projective variety X and an ample divisor D in X. For example, the singular or l-adic cohomology of X agrees with that of D in low degree; X and D have the same Picard group if X has dimension at least 4; and X and D have the same fundamental group if X has dimension at least 3. I’ll describe a general result which encompasses some of these Lefschetz hyperplane theorems and many new ones, comparing maps out of X to maps out of D. The case when the target of these maps is a moduli scheme or stack is of particular interest; for example, one may take the target to be Mg, and thus compare families of curves over X to families over D.

**Statistics Seminar**

Random graphs and networks: estimation and modeling challenges

Sonja Petrovic (IIT)

4:00 PM in SEO 636

The ubiquity of network data in the world around us does not imply that the
statistical modeling and fitting techniques have been able to catch up with
the demand. This talk will discuss some of the basic modeling questions
that every statistician knows are fundamental, some of the recent advances
toward answering them, and the challenges that remain. The specific focus of the talk will be on goodness of fit testing for
random graph models. Recent joint work with Despina Stasi and Elizabeth
Gross developed a new testing framework for graphs that is based on
combinatorics of hypergraphs and model geometry. I will summarize our work
by showing simulation results for the popular $p_1$ model for directed
random graphs.

Thursday November 6, 2014

Friday November 7, 2014

Monday November 10, 2014

**Applied Mathematics Seminar**

Derivation of NLS and uniqueness of solutions to the Gross-Pitaeskii hierarchy

Zhihui Xie (UIC)

4:00 PM in SEO 636

The derivation of NLS has been a hot topic in math physics during the past few decades. A lot of interesting results flourished this area in both physics side and mathematical side. We will introduce one of the successful methods - the BBGKY approach in this talk and describe how to use it to derive a certain type of NLS. As a main part in the derivation, the establishment of the uniqueness on solutions to the limiting hierarchy is essential. We will briefly review the different proofs on the uniqueness part and present a recent progress in this line on solutions of lower regularity.

Wednesday November 12, 2014

**Statistics Seminar**

Optimal Plate Designs in High Throughput Screening Experiments

Xianggui Qu (Oakland University)

4:00 PM in SEO 636

High-throughput screening (HTS) is a large-scale process that screens hundreds of thousands to millions of compounds in order to identify potentially leading candidates rapidly and accurately. There are many statistically challenging issues in HTS. In this talk, I will focus the spatial effect in primary HTS. I will discuss the consequences of spatial effects in selecting leading compounds and why the current experimental design fails to eliminate these spatial effects. A new class of designs will be proposed for elimination of spatial effects. The new designs have the advantages such as all compounds are comparable within each microplate in spite of the existence of spatial effects; the maximum number of compounds in each microplate is attained, etc. Optimal designs are recommended for HTS experiments with multiple controls.

**Algebraic Geometry Seminar**

Towards the MMP of moduli spaces of sheaves on Enriques surfaces via Bridgeland stability

Howard Nuer (Rutgers University)

4:00 PM in SEO 427

Since the work of Arcara, Bertram, Coskun, and Huizenga on the application of Bridgeland stability conditions to the study of the birational geometry of $\mathbb{P}^{2[n]}$, there has been much progress in applying similar ideas to a Hassett-Keel-type approach to the study of the birational geometry of more general moduli spaces of sheaves on other surfaces. In this talk, I will discuss previous and ongoing work on the application of Bridgeland stability techniques to running the MMP (minimal model program) on moduli spaces of stable sheaves on an Enriques surface. As an application of the tools I discuss, I will describe the nef cone of the Hilbert scheme of points on an Enriques surface explicitly in terms of the classical geometry of the Enriques surface as well as give a modular description of the first minimal model.

Friday November 14, 2014

**Departmental Colloquium**

On the detection of non-independence

Jun Liu (Harvard)

3:00 PM in SEO 636

I will discuss a few recent results from my group aiming to the detection
of non-linear dependence between two random variables. Our approach is
based on an optimal slicing (discretization) of one or both variables to
optimize a score function derived from a likelihood-ratio test formulation.
Our approaches are compared with some well-known methods such as Distance
Correlation, Pearson Correlation, Maximal Information Criterion, etc., on
many simulated examples, and found superior for highly nonlinear and
non-smooth relationships between the two variables. We will also show how
these methods are applied to bioinformatics problems such as gene-set
enrichment analysis, transcription regulation analysis, etc.

Monday November 17, 2014

**Graduate Applied Math Seminar**

From quantum many body systems to nonlinear dispersive PDE, and back

Natasa Pavlovic (UT Austin)

3:00 PM in SEO 1227

Recently significant progress has been achieved in the mathematically rigorous derivation of the nonlinear dispersive equations from quantum systems of interacting bosons. This topic has been approached by many authors in a variety of ways, one of which is via the Gross-Pitaevskii (GP) hierarchy. The GP hierarchy is a coupled system of linear non-homogeneous PDE that describes the dynamics of a gas of infinitely many interacting bosons, while at the same time retains some of the features of a dispersive PDE.
In this talk we will discuss the process of going from a quantum many body system of bosons to the nonlinear Schroedinger equation (NLS) via the GP. Also we will look into what the nonlinear PDE such as the NLS can teach us about the GP hierarchy and quantum many body systems.
The talk is based on joint works with T. Chen and N. Tzirakis.

**Applied Mathematics Seminar**

Unconditional uniqueness for the cubic Gross-Pitaevskii hierarchy via quantum de Finetti

Natasa Pavlovic (University of Texas at Austin)

4:00 PM in SEO 636

The derivation of nonlinear dispersive PDE, such as the nonlinear Schroedinger (NLS) or nonlinear Hartree equations, from many body quantum dynamics is a central topic in mathematical physics, which has been approached by many authors in a variety of ways. In particular, one way to derive NLS is via the Gross-Pitaevskii (GP) hierarchy, which is an infinite system of coupled linear non-homogeneous PDE. The most involved part in such a derivation of NLS consists in establishing uniqueness of solutions to the GP. Erdös-Schlein-Yau developed an approach for proving uniqueness based on use of Feynman graphs. A key ingredient in their proof is a powerful combinatorial method that resolves the problem of the factorial growth of number of terms in iterated Duhamel expansions.
Motivated by the idea that techniques from nonlinear PDE might be useful at the level of the GP, recently with T. Chen, C. Hainzl and R. Seiringer we obtained a new, simpler proof of the unconditional uniqueness of solutions to the cubic Gross-Pitaevskii hierarchy in ${\mathbb{R}}^3$. In our work, we employ the quantum de Finetti's theorem (which a quantum analogue of the Hewitt-Savage theorem in probability theory) as a direct link between the NLS and the GP hierarchy.
In the talk, we will present a brief review of the derivation of NLS
via the GP, describing the context in which the new uniqueness result
appears, and will then focus on the uniqueness result itself.
The talk is based on the joint work with T. Chen, C. Hainzl and R.
Seiringer.

Tuesday November 18, 2014

**Logic Seminar**

The noncommutative Gurarij space

Martino Lupini (York University)

4:00 PM in SEO 427

Working in the framework of Fraisse theory for metric structures developed by Ben Yaacov, we show that the noncommutative Gurarij space introduced by Oikhberg can be characterized as the Fraisse limit of the class of 1-exact finite-dimensional operator spaces. As a consequence we deduce that such an operator space is unique, homogeneous, and universal for separable 1-exact operator spaces.

Wednesday November 19, 2014

Monday November 24, 2014

**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.

Wednesday November 26, 2014

Tuesday December 2, 2014

**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

Monday February 2, 2015

Monday February 16, 2015

Friday February 27, 2015

Wednesday March 18, 2015

Wednesday April 1, 2015

Wednesday April 8, 2015

Friday April 10, 2015