# MSCS Seminar Calendar

Monday October 20, 2014

**Model Theory Seminar**

Covers of the multiplicative group I

David Marker (UIC)

1:00 PM in SEO 427

We will prove Zilber's categoricity result for covers of the multiplicative group. The BHHKK Theorem greatly simplifies the proof as we need only show quasiminimality and need not worry about excellence.
For this version we can get by with a simplified version of the "Thumbtack Lemma" which we will also prove. The later proof is a special case of a result of Bays, Gavrilovich and Hils.

**Graduate Number Theory Seminar**

Subsets are Balanced in Finite Groups

Kevin Vissuet (UIC)

3:00 PM in SEO 712

The sumset is one of the most basic and central objects in additive number theory. Many of the most important problems (such as Goldbach's conjecture and Fermat's Last theorem) can be formulated in terms of the sumset $S + S = \{x+y : x,y\in S\}$ of a set of integers $S$. A finite set of integers $A$ is sum-dominated if $|A+A| > |A-A|$. Though it was believed that the percentage of subsets of $\{0,\dots,n\}$ that are sum-dominated tends to zero, in 2006 Martin and O'Bryant proved a very small positive percentage are sum-dominated if the sets are chosen uniformly at random (through work of Zhao we know this percentage is approximately $4.5 \cdot 10^{-4}$). While most sets are difference-dominated in the integer case, this is not the case when we take subsets of many finite groups. We show that if we take subsets of larger and larger finite groups uniformly at random, then not only does the probability of a set being sum-dominated tend to zero but the probability that $|A+A|=|A-A|$ tends to one, and hence a typical set is balanced in this case.

**Combinatorics Seminar**

Grid Ramsey problem and related questions

Choongbum Lee (MIT)

3:00 PM in SEO 427

The Hales--Jewett theorem is one of the pillars of Ramsey theory, from which many other results follow.
A celebrated theorem of Shelah says that Hales--Jewett numbers are primitive recursive. A key tool used in his proof, now known as the cube lemma, has become famous in its own right. In its simplest form, this lemma says that if we color the edges of the Cartesian product $K_n \times K_n$ in $r$ colors then, for $n$ sufficiently large, there is a rectangle with both pairs of opposite edges receiving the same color. Shelah's proof shows that $n = r^{{r+1\choose 2}} + 1$ suffices, and more than twenty years ago, Graham, Rothschild and Spencer asked whether this bound can be improved to a polynomial in $r$. We show that this is not possible by providing a superpolynomial lower bound in $r$. We will also discuss a deep connection between this problem and generalized Ramsey numbers, and present a solution to a problem of Erd\H{o}s and Gy\'arf\'as on the transition of asymptotics of generalized Ramsey numbers.
Joint work with David Conlon (Oxford), Jacob Fox (MIT), and Benny Sudakov (ETH Zurich)

**Geometry, Topology and Dynamics Seminar**

Commuting homeomorphisms with non-commuting lifts

Kiran Parkhe (Technion University, Israel)

3:00 PM in SEO 636

Let $M$ be a manifold, and $f, g: M \to M$ commuting homeomorphisms. We consider whether there exist lifts of $f$ and $g$ to the universal cover of $M$ that also commute. We especially focus on the case where $f$ and $g$ are homotopic to the identity, so there are distinguished homotopy lifts.
We will see that the only two-manifold admitting commuting homeomorphisms with non-commuting homotopy lifts is the open annulus, and examples among closed three-manifolds are also quite limited. The proof uses a dynamical tool called homological rotation vectors, and Thurston's Geometrization Theorem in the latter case. Time permitting, we will specialize to the open annulus, and study what these examples can look like.

**Applied Mathematics Seminar**

Fritz John's ellipsoid theorem in frame theory

Kasso Okoudjou (University of Maryland)

4:00 PM in SEO 636

In this talk I will introduce the notion of finite frames
and present some of their elementary properties. In particular, I will
focus on a class of optimally conditioned frames called tight frames.
A question that one could ask is wether one can perfectly precondition
a frame, i.e., one can modify it in such a way that it becomes
optimally conditioned. In the last part of the talk, I will show how
the Fritz John ellipsoid theorem can be used to settle this question.
I will conclude by giving various characterization of the class of
perfectly preconditioned frames.

Tuesday October 21, 2014

**Quantum Topology / Hopf Algebra Seminar**

Logical Question Theory

Roy Lisker (Institute Henri Poincare, Paris)

3:00 PM in SEO 612

This talk is the first of two talks. The second is entitled "Quantum Question Theory".
A mathematical formalism for the basic syntactic structure of a well-formed question is described as a pair of
schemas - the interrogation phase and the response phase. Errors arise from confusing the syntactic categories of a question.
A particular application of this framework to quantum experiments leads to a different way of treating questions, proper to
quantum theory alone, which the speaker calls quantum question theory.

**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 SEO 636

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.

**Graduate Analysis Seminar**

Applications of Fourier Series

Keaton Quinn (UIC)

4:00 PM in SEO 512

We'll continue our crash course in harmonic analysis today with an overview of some applications of Fourier series, such as the heat equation on a circle, the isoperimetric inequality and Weyl's equidistribution theorem.

Wednesday October 22, 2014

**Statistics Seminar**

Universally optimal designs for two interference models

Wei Zheng (IUPUI)

4:00 PM in SEO 636

A systematic study is carried out regarding universally optimal designs under the interference model, previously investigated by Kunert and Martin (2000) and Kunert and Mersmann (2011). Parallel results are also provided for the undirectional interference model, where the left and right neighbor effects are equal. It is further shown that the efficiency of any design under the latter model is at least its efficiency under the former model. Designs universally optimal for both models are also identified. Most importantly, this paper provides Kushner's type linear equations system as a necessary and sufficient condition for a design to be universally optimal. This result is novel for models with at least two sets of treatment-related nuisance parameters, which are left and right neighbor effects here. It sheds light on other models in deriving asymmetric optimal or efficient designs.

**Algebraic Geometry Seminar**

Kodaira vanishing for q-ample divisors

Alex Kuronya (Budapest University of Technology and Economics)

4:00 PM in SEO 427

Line bundles sharing some but not all the good properties of
ampleness have been investigated for quite some time, here we will focus on
the cohomological point of view. Building on earlier work of Sommese and
Demailly-Peternell-Schneider, Totaro came up with a very satisfactory theory
of line bundles with partially vanishing higher cohomology to which we will
refer as q-ample.
As it turns out, q-ampleness gives rise to interesting applications,
including a useful concept of ampleness for subvarieties, where among others,
one retains a Lefschetz hyperplane theorem (as showed by Ottem).
The main focus of this talk will be a generalization of Kodaira vanishing
to q-ample line bundles.

Thursday October 23, 2014

**Quantum Topology / Hopf Algebra Seminar**

Quantum Question Theory

Roy Lisker (Institute Henri Poincare, Paris)

3:00 PM in SEO 612

This talk is the second of two talks.
The first is entitled "Logical Question Theory". A mathematical formalism for the basic syntactic structure of a well-formed question is described as a pair of schemas - the interrogation phase and the response phase. Errors arise from confusing the syntactic categories of a question. A particular application of this framework to quantum experiments
leads to a different way of treating questions, proper to quantum theory alone, which the speaker calls quantum question theory.

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.

**Departmental Colloquium**

Survival Analysis and Some Recent Developments

Jianguo Sun (University of Missouri)

3:00 PM in SEO 636

Survival analysis is one of major and important fields
in statistics and this is especially true from the point of biological and medical
research. In addition, we also see the increasing of its applications
in many other fields including demography, economics finance,
political science, psychology and sociology. In this talk, we will first
give some basic and simple introduction of survival analysis and
then discuss several current research topics in the field related
to the analysis of interval-censored survival data, a special and
common type of survival data.

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 512

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 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.

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

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.

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.

Friday November 14, 2014

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.

Wednesday November 19, 2014

Monday November 24, 2014

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

Wednesday March 18, 2015

Wednesday April 1, 2015

Wednesday April 8, 2015

Friday April 10, 2015