# MSCS Seminar Calendar

Monday September 22, 2014

**Computer Science Seminar**

Fuzzy operators for practical applications

Jozsef Dombi (University of Szeged)

3:00 PM in SEO 427

In the first part we study a certain class of strict monotone fuzzy operators which build the DeMorgan class with
infinitely many negations. We give a necessary and sufficient condition for an operator to belong to this class.
We give a new representation theorem of negation based on the generator function of the strict operator.
On the other hand our starting point is the study of the relationship for Dombi aggregative operators, uninorms, strict t-norms
and t-conorms. We present a new representation theorem of strong negations where two explicitly contain the neutral value.
Then relationships for aggregative operators and strong negations are verified as well as those for t-norm and t-conorm
using the Pan operator concept. We will study a certain class of aggregative operators which build a self-DeMorgan class
with infinitely many negation operators. We introduce the so-called Pliant concept and characterize it by necessary and
sufficient conditions.
In the second part we give a certain class of weighted aggregative operators (weighted representable uninorms).
After that, we focus on a specific form of the aggregative operator. Using Dombi's generator function, we show that
this form is the same as that for the aggregation of expert probability values, and we can get this operator via
Bayes' theorem. These two theorems shed new light on the class of aggregative operators.

**Geometry, Topology and Dynamics Seminar**

Transitivity degrees of countable groups.

Michael Hull (UIC)

3:00 PM in SEO 636

We introduce the transitivity degree of a countable group $G$, denoted $td(G)$, as the $\sup$ over all $k$ such that $G$ admits a faithful, $k$-transitive action on an set with at least k elements. We show that for many classes of infinite groups (e.g. hyperbolic groups, mapping class groups, 3-manifold groups, RAAGS, or any infinite subgroups of one of these), $td(G)\in\{1, \infty\}$. In particular, we show that if $G$ is acylindrically hyperbolic and $G$ has no finite normal subgroups, $G$ admits a faithful action which is highly transitive, that is $k$-transitive for all $k$. We will also mention some applications of this result to the universal theory of acylindrically hyperbolic groups.

**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

**Logic Seminar**

The complexity of the homeomorphism relation between compact metric spaces

Joseph Zielinski (UIC)

4:00 PM in SEO 427

We consider the analysis of classification problems in the context of Borel reducibility and outline a proof that the complexity of the homeomorphism relation between compact metric spaces coincides, in this way, with that of the complete orbit equivalence relation of Polish group actions.

Wednesday September 24, 2014

**Graduate Algebraic Geometry Seminar**

Singularities of Schubert varieties in Grassmannians

Seckin Adali

2:00 PM in SEO 712

Schubert varieties have well understood singularities, in particular an explicit description can be given using a number of different approaches. In this talk I will give a description of the singular loci of Schubert varieties in Grassmannians using two different arguments: One uses the Bott-Samelson resolution, the other gives a description of their tangent spaces.

**Graduate Combinatorics Seminar**

Roth's Theorem via the Szemeredi Regularity Lemma Part II

Caroline Terry (UIC)

4:00 PM in SEO 512

Roth's theorem states that any set of positive integers of positive upper density contains an arithmetic progression of length three. We will introduce the Szemeredi regularity lemma, then present a proof Roth's theorem which uses the regularity lemma.

**Algebraic Geometry Seminar**

Kernels of numerical pushforwards

Mihai Fulger (Princeton)

4:00 PM in SEO 427

If $\pi:X\to Y$ is a morphism of projective varieties over an algebraically closed field,
and $Z$ is an effective $k$-cycle on $X$, then $\pi_*Z=0$ iff $Z$ is a combination of subvarieties
of $X$ that are contracted by $\pi$.
When working not with cycles, but with cycle classes (modulo numerical equivalence),
it is natural to ask when can we expect a similar geometric conclusion given
the vanishing of a class $\pi_*\alpha$.
I will present progress on this question, in particular leading to new cases of two
conjectures essentially due to Debarre, Jiang, and Voisin. This is joint work with
B. Lehmann.

Friday September 26, 2014

**Departmental Colloquium**

Weyl's asymptotic law for Lévy processes

Rodrigo Bañuelos (Purdue University)

3:00 PM in SEO 636

In October 1910 Hendrik Antoon Lorentz, 1902 Nobel Prize in Physics, delivered a series of six lectures (the Paul Wolfskehl Lectures) to the faculty of the University of Göttingen titled "old and new problems in physics." During the fourth lecture, with David Hilbert and his student Hermann Weyl present in the audience, he conjectured that the number of eigenvalues for the Laplacian for a region $D$ in three space not exceeding the positive number $\lambda$ is proportional to the volume of $D$ times $\lambda^{3/2}$, when $\lambda$ is large. (The problem had been raised a month earlier by Arnold Sommerfeld at a lecture in Könisberg.) Hilbert predicted that the conjecture would not be proved in his lifetime. He was wrong by several years. The conjecture was proved by Weyl in 1912.
Weyl's celebrated theorem, commonly referred to as

*Weyl's Law*, has been extended and refined in many directions with connections to many areas of mathematics and physics. In this talk we first give an overview of some of the classical results in the field and discuss the elegant connections to Brownian motion first explored by Mark Kac in the 50's and 60's. We will then discuss problems that arise when the Brownian motion, which "goes" with the classical Laplacian, is replaced by other Lévy processes. Such processes share many important properties with Brownian motion. We will look at a class of interesting examples that have been widely studied recently, the rotationally invariant stable processes that "go" with fractional powers of the Laplacian.Note: This is a general talk aimed at a general mathematical audience.

Monday September 29, 2014

**Graduate Applied Math Seminar**

Mean field limits of interacting Bose gases and nonlinear Schroedinger equations

Thomas Chen (UT Austin)

3:00 PM in TBA

In this talk, we survey some of the background and recent developments in the mathematical analysis of dilute Bose gases and Bose-Einstein condensation. In particular, we will address the rigorous derivation of nonlinear Schroedinger equations from manybody bosonic quantum systems in a suitable mean field limit. This presentation is geared towards a graduate student audience.

**Applied Mathematics Seminar**

Unconditional uniqueness for Gross-Pitaevskii hierarchies and the quantum de Finetti theorem

Thomas Chen (University of Texas at Austin)

4:00 PM in SEO 636

This talk addresses some recent results related to the Cauchy problem for the cubic Gross-Pitaevskii (GP) hierarchy, an infinite system of coupled linear PDE’s which emerges in the derivation of the cubic nonlinear Schroedinger equation from interacting Bose gases. In particular, a new proof of unconditional uniqueness of solutions is presented, as well as a proof of scattering in the defocusing 3D case. The techniques involved include an application of the quantum de Finetti theorem, combined with recursive Strichartz estimates and tree graph expansions. This is joint work with C. Hainzl, N. Pavlovic and R. Seiringer.

Friday October 3, 2014

**Departmental Colloquium**

Roots, Schottky semigroups, and a proof of Bandt's Conjecture

Danny Calegari (University of Chicago)

3:00 PM in SEO 636

In 1985, Barnsley and Harrington defined a "Mandelbrot Set" M for pairs of similarities - this is the set of complex numbers z with norm less than 1 for which the limit set of the semigroup generated by the similarities x → zx and x → z(x-1)+1 is connected. Equivalently, M is the closure of the set of roots of polynomials with coefficients in {-1,0,1}. Barnsley and Harrington already noted the (numerically apparent) existence of infinitely many small "holes" in M, and conjectured that these holes were genuine. These holes are very interesting, since they are "exotic" components of the space of (2 generator) Schottky semigroups. The existence of at least one hole was rigorously confirmed by Bandt in 2002, but his methods were not strong enough to show the existence of infinitely many holes; one difficulty with his approach was that he was not able to understand the interior points of M, and on the basis of numerical evidence he conjectured that the interior points are dense away from the real axis. We introduce the technique of *traps* to construct and certify interior points of M, and use them to prove Bandt's Conjecture. Furthermore, our techniques let us certify the existence of infinitely many holes in M. This is joint work with Sarah Koch and Alden Walker.

Monday October 6, 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.

Tuesday October 7, 2014

**Logic Seminar**

Regular cross-sections of Borel flows

Kostya Slutskyy (UIC)

4:00 PM in SEO 427

A cross-section of a Borel flow is a Borel set that has
countable intersection with each orbit of the flow. We shall be
interested in constructing cross-sections with a prescribed set of
possible distances between adjacent points within orbits. The main
result of the talk is that given any two rationally independent
positive reals and a free Borel flow one can always find a
cross-section with distances between adjacent points being only these
two real numbers.
We shall give an overview of the subject from both ergodic theoretical
and descriptive points of view and an application of the above result
to orbit equivalence of flows will be presented.

Wednesday October 8, 2014

Monday October 13, 2014

**Geometry, Topology and Dynamics Seminar**

Coarse entropy and transverse dimension

Steve Hurder (UIC)

3:00 PM in SEO 636

The notion of "coarse entropy" for complete metric spaces was introduced in the paper "Manifolds which cannot be leaves of foliations", Topology, 1996, by O. Attie and S. Hurder, where this invariant was used to construct examples of complete Riemannian manifolds of bounded geometry which are not quasi-isometric to a leaf of any $C^1$-foliation of a closed Riemannian manifold. In this talk, we relate the coarse entropy to the "complexity entropy" of trees of finite type. We also show how the coarse entropy is related to the Hausdorff dimension of graph matchbox manifolds formed from such trees, as studied by Lukina. This work is joint with Olga Lukina.

**Applied Mathematics Seminar**

Dimension reduction for anisotropic Bose-Einstein condensates in the strong interaction regime

Florian Mehats (University of Rennes)

4:00 PM in SEO 636

We study the problem of dimension reduction for the three dimensional Gross-Pitaevskii equation (GPE) describing a Bose-Einstein condensate confined in a strongly anisotropic harmonic trap. Since the gas is assumed to be in a strong interaction regime, we have to analyze two combined singular limits: a semi-classical limit in the transport direction and the strong partial confinement limit in the transversal direction. We prove that both limits commute together and we provide convergence rates. The by-products of this work are approximated models in reduced dimension for the GPE, with a priori estimates of the approximation errors. This is a joint work with Weizhu Bao and Loic Le Treust.

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.

**Logic Seminar**

Intersections of isogeny classes and varieties

James Freitag (UC Berkeley)

4:00 PM in SEO 427

Take $ \alpha \in GL_2$ and a complex number $a$. There are at most $36^7$ complex numbers $b$ such that the elliptic curves $E_a$ and $E_b$ are isogenous and $E_ {\alpha (a)}$ and $E_ {\alpha (b)} $ are isogenous. Proving this fact along with an effective form of a special case of the Zilber-Pink conjecture uses input from model theory, differential algebra, and diophantine geometry. We will describe the proof and partial generalizations to various moduli spaces of abelian varieties.

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.

Tuesday October 21, 2014

**Algebraic Geometry Seminar**

Cartan-Fubini type extension of holomorphic maps preserving webs of rational curves

Jun-Muk Hwang (Korea Institute for Advanced Study (KIAS))

4:00 PM in TBA

Let $X_1$ and $X_2$ with $\mathrm{dim} X_1 = \mathrm{dim} X_2$ be two projective manifolds of Picard number 1 in projective space.
Assume that both $X_1$ and $X_2$ are covered by lines. Let $\varphi: U_1 \to U_2$ be a biholomorphic map between two connected Euclidean
open subsets $U_1 \subset X_1$ and $U_2 \subset X_2$. Suppose that both $\varphi$ and $\varphi^{-1}$ send pieces of lines to pieces of lines.
We show that $\varphi$ can be extended to a biregular morphism $\Phi: X_1 \to X_2$. This was proved by Hwang-Mok in 2001
when the indices of $X_1$ and $X_2$ are bigger than 2 and the new result is when the indices are 2. In this case, the covering family
of lines form webs of rational curves. We exploit the monodromy of the webs of lines to extend the holomorphic map.

Friday October 24, 2014

**Algebraic Topology Seminar**

Duality and Tilting for Commutative DG Rings

Amnon Yekutieli (Ben Gurion University)

2:00 PM in SEO 1227

We study super-commutative nonpositive DG rings. An example is the Koszul complex associated to a sequence of elements in a commutative ring. More generally such DG rings arise as semi-free resolutions of rings. They are also the affine DG schemes in derived algebraic geometry. The theme of this talk is that in many ways a DG ring A resembles an infinitesimal extension, in the category of rings, of the ring H^0(A).
I first discuss localization of DG rings on Spec(H^0(A)) and the cohomological noetherian property. Then I introduce perfect, tilting and dualizing DG A-modules. Existence of dualizing DG modules is proved under quite general assumptions. The derived Picard group DPic(A) of A, whose objects are the tilting DG modules, classifies dualizing DG modules. It turns out that DPic(A) is canonically isomorphic to DPic(H^0(A)), and that latter group is known by earlier work. A consequence is that A and H^0(A) have the same (isomorphism classes of) dualizing DG modules.

Monday October 27, 2014

Tuesday October 28, 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.

Friday October 31, 2014

**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

Wednesday November 5, 2014

Friday November 7, 2014

Monday November 10, 2014

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.

Monday November 17, 2014

Wednesday November 19, 2014

Monday November 24, 2014

Wednesday November 26, 2014

Wednesday December 3, 2014

Wednesday April 1, 2015