# MSCS Seminar Calendar

Tuesday September 2, 2014

**Number Theory Seminar**

Elliptic curves with 2-torsion contained in the 3-torsion field

Nathan Jones (University of Illinois at Chicago)

11:00 AM in SEO 427

There is a modular curve X'(6) of level 6 defined over Q whose rational points correspond to j-invariants of elliptic curves E over Q for which Q(E[2]) is a subfield of Q(E[3]). In this talk I will characterize the j-invariants of elliptic curves with this property by exhibiting an explicit model of X'(6). The motivation is two-fold: on the one hand, X'(6) belongs to the list of modular curves which parametrize non-Serre curves (and is not well-known), and on the other hand, the set of rational points of X'(6) gives an infinite family of examples of elliptic curves with non-abelian ``entanglement fields,'' which is relevant to the systematic study of correction factors of various conjectural constants for elliptic curves over Q. This is based on joint work with J. Brau (Cambridge University, UK).

The seminar ends at 12:30.

**Quantum Topology / Hopf Algebra Seminar**

Quantum Link Invariants and Rotational Virtual Knot Theory

Louis H. Kauffman (UIC)

3:00 PM in SEO 612

This talk is self-contained. We define quantum link invariants via augmented solutions to the Yang-Baxter equation. We show how
the bracket polynomial model of the Jones polynomial fits into this framework and we show how many other invariants fit into this
framework. We also briefly discuss how quantum link invariants can be formulated in terms of Hopf algebras. Then we discuss how
classical knot theory extends to virtual knot theory and to rotational virtual knot theory. In rotational virtual knot theory one adds
virtual crossings and augments the Reidemeister moves by detour moves that are regular homotopies of the arc moved in the detour.
We then prove the Theorem: Every quantum link invariant of classical links extends to an invariant of rotational virtual knots and links.
This theorem shows that Rotational Virtual Knot Theory is the Proper Domain for the Study of Quantum Link Invariants. The talk
will consider many examples and questions that arise.

**Logic Seminar**

Tameness in Abstract Elementary Classes

Will Boney (UIC)

4:00 PM in SEO 427

Tameness is a locality property of Galois types in AECs. Since its isolation by Grossberg and VanDieren 10 years ago, it has been used to prove new results (upward categoricity transfer, stability transfer) and replace set-theoretic hypotheses (existence of independence notions). In this talk, we will outline the basic definitions, summarize some key results, and discuss some open questions related to tameness.

Wednesday September 3, 2014

**Graduate Algebraic Geometry Seminar**

Adjoint linear systems on algebraic surfaces I

Xudong Zheng (UIC)

2:00 PM in SEO 427

Let $X$ be a smooth projective surface and $L$ a big and nef line bundle. The pluricanonical $|nK_X|$ and adjoint linear systems $|K_X + L|$ have been well studied. The aim of this talk is to introduce the circle of ideas of Bombieri, Mumford, Van de Ven, Sommese, Reider, among others on the positivity and global generation of $|K_X + L|$ in the case that the base field has characteristic zero.

**Algebraic Geometry Seminar**

Ample divisors on moduli spaces of sheaves on the plane

Jack Huizenga (UIC)

4:00 PM in SEO 427

Let $v$ be the set of numerical invariants of a sheaf on $\mathbb{P}^2$. The moduli space $M(v)$ parameterizes isomorphism classes of semistable sheaves with Chern character $v$. In this talk, I will discuss recent work with Izzet Coskun computing the cone of ample divisors on $M(v)$ for many choices of the character $v$. Our results in particular cover the case where the rank and first Chern class of $v$ are coprime and the discriminant of $v$ is sufficiently large.

**Statistics Seminar**

Stat Wars Episode VI: Return of the Fiducialist

Keli Liu (Stanford University)

4:00 PM in SEO 636

Priors are the path to the dark side. Fisher developed the Fiducial argument to obtain prior free "posterior" inferences but at the
seeming cost of violating basic probability laws. Was Fisher crazy or did madness mask innovation? Fiducial calculations can be
easily understood through the missing-data perspective which illuminates for us that the Fiducial "posterior" is in fact a prior updated
not with the full data likelihood, but a

*partial*likelihood in the spirit of Cox regression. Just as Cox regression arose from a need to render inferences robust to an unknown hazard function, so Fiducial inferences are insensitive to the prior. While Statistics has fixated two extremes---fully conditional (but fragile) Bayesian inferences or unconditional (but robust) Frequentist inferences---a compromise via partial conditioning has gone ignored. Surely, the middle ground is more fiducial than either extreme.Thursday September 4, 2014

**Graduate Computational Algebraic Geometry Seminar**

the giftwrapping method in PHCpack

Jan Verschelde (UIC)

1:00 PM in SEO 1227

The giftwrapping method computes convex hull of polytopes in any dimension.
In this seminar, we apply the giftwrapping method to Newton polytopes,
polytopes spanned by points with integer coordinates.
The second part of the seminar will describe the implementation in PHCpack.

Please notice the change in time: 1pm instead of 4pm.
The seminar room 1227 SEO is not yet confirmed.

Monday September 8, 2014

**Geometry, Topology and Dynamics Seminar**

von Neumann algebras of negatively curved groups

Thomas Sinclair (UCLA)

3:00 PM in SEO 636

Negatively curved groups have long been and continue to be one of the most intensely studied classes of discrete groups. These groups have also played an important role in functional analysis, notably via K-theory and the Baum-Connes conjecture. In this talk I will survey some recent results in the classification of von Neumann algebras generated by negatively curved groups and their measurable actions. I will explain how negative curvature is central to these results in terms of a broad, cohomogical-type property such groups possess. As an application, I will show how these techniques generalize some results on the measurable dynamics of hyperbolic groups. No knowledge of von Neumann algebras will be assumed.

**Applied Mathematics Seminar**

Modeling tuberculosis, from cells to populations

Leonid Chindelevitch (Harvard School of Public Health)

4:00 PM in SEO 636

Tuberculosis continues to afflict millions of people and causes over a million deaths a year worldwide. Multi-drug resistance is also on the rise, causing concern among public-health experts. This talk will give an overview of my work on modeling tuberculosis at various scales. On the cellular side I will describe models of the metabolism of M. tuberculosis, where insights from duality led to a consistent analysis of existing models, a systematic method for reconciling discrepant models, and the identification of putative drug targets. On the population side I will describe models of strain evolution, where a new metric combined with an optimization-based approach resulted in an accurate classification of complex infections as originating from mutation or mixed infection, as well as the identification of the strains composing these complex infections.

Tuesday September 9, 2014

**Number Theory Seminar**

Elliptic modules and Frobenius endomorphisms

A.C. Cojocaru (University of Illinois at Chicago)

11:00 AM in SEO 427

Given a finite Galois extension L/K of global fields and a conjugacy class C of Gal(L/K), a fundamental problem is that of describing the (unramified) primes p of K for which the conjugacy class of the Frobenius at p is C. The Chebotarev Density Theorem provides the density of these primes, while, in general, the characterization of the primes themselves is a finer and deeper question. We focus on unraveling this question for the division fields of a generic Drinfeld module. For Drinfeld modules of rank 2, we obtain an explicit global description of the Frobenius. We apply this description to derive a criterion for the splitting modulo primes of a class of non-solvable polynomials and to study the frequency with which the reductions of Drinfeld modules have small endomorphism rings. We also generalize some of these results to higher rank Drinfeld modules and prove CM-lifting theorems for Drinfeld modules. This is joint work with Mihran Papikian (Pennsylvania State University, USA).

The seminar ends at 12:30.

**Logic Seminar**

Existentially closed C*-algebras

Thomas Sinclair (UCLA)

4:00 PM in SEO 427

A C*-algebra A is said to be existentially closed if, roughly, every set of equations involving norms of noncommutative *-polynomials which has a solution in B(H) has a sequence of approximate solutions in A. A basic result in continuous logic shows that every separable C*-algebra is contained in a separable, existentially closed C*-algebra. In this talk I will survey some basic properties of existentially closed C*-algebras. In particular I will describe how existential closure is deeply connected to several open problems in C*-algebras such as Kirchberg's problem on whether every separable C*-algebra embeds in an ultrapower of the Cuntz algebra O_2, as well as Kirchberg's C*-algebraic reformulation of of Connes' embedding problem. This talk is based on joint work with Isaac Goldbring.

Wednesday September 10, 2014

**Graduate Algebraic Geometry Seminar**

Adjoint linear systems on algebraic surfaces II

Xudong Zheng (UIC)

2:00 PM in SEO 427

This is the second part of the talk on adjoint linear systems on surfaces, in characteristic $p > 0$. In circumventing the classical vanishing theorems and Bogomolov's inequality on rank 2 vector bundles in characteristic zero, we briefly introduce the construction of Ekedahl and Shepherd-Barron on purely inseparable degree $p$ coverings.

Monday September 15, 2014

**Applied Mathematics Seminar**

Nonexistence of small coherent structures for dispersive equations

David Ambrose (Drexel University)

4:00 PM in SEO 636

For dispersive PDE on spatially periodic domains, we formulate the time-periodic solutions problem as a fixed point problem. The operator in question is the composition of a linear operator and a nonlinear operator. The linear operator can be bounded with small divisor estimates, losing derivatives in the process. If the nonlinear operator can be shown to have smoothing properties, then the composition can be shown to be a local contraction. Thus, the nonexistence of nontrivial small-amplitude doubly periodic waves follows from dispersive smoothing estimates. We demonstrate that the smoothing estimate holds for several equations, including the Korteweg-de Vries equation. Extensions to nonlinear Schrodinger equations and to solitons may be discussed.

Monday September 22, 2014

**Applied Mathematics Seminar**

Soft metrics for decision analysis under uncertainty

Michelle Quirk (National Intelligence University and National Geospatial-Intelligence Agency)

4:00 PM in SEO 636

Modern decision making challenges the human capacity to reason in an
environment of uncertainty, imprecision, and incompleteness of
information. Probability measures are not well-suited when the evidence
is scarce and unreliable. Built from fuzzy sets, possibility metrics
overcomes some of the restrictions and insufficiencies of probabilities,
in a complementary, yet not competitive manner. We show the theoretical
foundation and the interdisciplinary approach required to devise soft
metrics as attributes of decision criteria that cannot be expressed
numerically. This talk concludes with an example of soft metrics used in
real-world ranking exercises.

Tuesday September 23, 2014

Wednesday September 24, 2014

Friday September 26, 2014

Monday September 29, 2014

**Geometry, Topology and Dynamics Seminar**

Hausdorff dimension in graph matchbox manifolds

Olga Lukina (UIC)

3:00 PM in SEO 636

A lamination is a compact connected metric space, where each point has a neighborhood homeomorphic to the product of a Euclidean disc and a totally disconnected space. Given a lamination, one can ask if this lamination can be realised as a subset of a smooth foliated finite-dimensional manifold, so that the leaves of the lamination are contained in the leaves of the foliation of the manifold. More precisely, one asks if there exists a foliated embedding of a given lamination into a smooth foliated manifold by a bi-Lipschitz homeomorphism.
Hausdorff dimension provides an obstruction to the existence of such an embedding. In the talk, we study a specific class of laminations, called graph matchbox manifolds, obtained as suspensions of pseudogroup actions on the space of pointed trees. We give examples of such laminations which have infinite Hausdorff dimension of their transversals, and, therefore, cannot be embedded as a subset of a smooth foliation of a finite-dimensional manifold by a bi-Lipschitz homeomorphism.

Monday October 6, 2014

Wednesday October 8, 2014

Monday October 13, 2014

Wednesday October 15, 2014

**Distinguished Lecture Series**

The "P vs. NP" problem: efficient computation, Internet security, and the limits to human knowledge

Avi Wigderson (Institute for Advanced Study)

4:00 PM in TBA

The "P vs. NP" problem, formulated by computer theorists in the 1970s, quickly became a central outstanding problem
of science and mathematics. In this talk I will attempt to describe its mathematical, scientific and philosophical
content. I will discuss its status, and the implications of its resolution on science and technology (making clear
that the \$1M prize on solving it pales in comparison with these implications).
No special background will be assumed.

Thursday October 16, 2014

**Distinguished Lecture Series**

Randomness

Avi Wigderson (Institute for Advanced Study)

3:00 PM in SEO 636

Is the universe inherently deterministic or probabilistic? Perhaps more importantly - can we tell the difference
between the two?
Humanity has pondered the meaning and utility of randomness for millennia.
There is a remarkable variety of ways in which we utilize perfect coin tosses to our advantage:
in statistics, cryptography, game theory, algorithms, gambling... Indeed, randomness seems indispensable!
Which of these applications survive if the universe had no randomness in it at all? Which of them survive
if only poor quality randomness is available, e.g. that arises from "unpredictable" phenomena like the
weather or the stock market?
A computational theory of randomness, developed in the past three decades, reveals (perhaps counter-intuitively)
that very little is lost in such deterministic or weakly random worlds. In the talk I'll explain the main ideas
and results of this theory.
The talk is aimed at a general scientific audience.

Friday October 17, 2014

**Distinguished Lecture Series**

Permanent & Determinant: non-identical twins

Avi Wigderson (Institute for Advanced Study)

3:00 PM in SEO 636

The determinant is undoubtedly the most important polynomial function in mathematics.
Its lesser known sibling, the permanent, plays very important roles in
enumerative combinatorics, statistical and quantum physics, and the
theory of computation. In this lecture I plan to survey some of the
remarkable properties of the permanent, its applications and impact on
fundamental computational problems, its similarities to and apparent
differences from the determinant, and how these relate to the P vs. NP
prolem.
This lecture is intended to a general Math & CS audience.

Monday October 20, 2014

Monday October 27, 2014

Wednesday October 29, 2014

**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.

Wednesday November 5, 2014

Friday November 7, 2014

Monday November 10, 2014

Wednesday November 12, 2014

Wednesday November 19, 2014

Wednesday November 26, 2014

Wednesday December 3, 2014