Seminar Calendar
for events the week of Thursday, November 20, 2014.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, November 17, 2014

Symplectic & Poisson Seminar
3:00 pm   in 341 Altgeld Hall,  Monday, November 17, 2014
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Submitted by jawatts.
Camilo Arias Abad (U Toronto Math)
Flat connections and loop spaces
Abstract: If $E\rightarrow X$ is a flat vector bundle, and $\pi: LX \rightarrow X$ is the map given by evaluation at $1 \in S^1$, then the pull back bundle $\pi^*E$ is a flat bundle equipped with a canonical automorphism given by the holonomy. I will explain that this construction naturally generalizes to the case of flat $\mathbb{Z}$-graded connections on $X$. Moreover, the restriction of the holonomy automorphism to the based loop space provides a representation of the Pontryagin algebra $C_*(\Omega^{\mathsf{M}} X)$. I will describe how this construction fits into the general story of higher dimensional local systems. The talk is based on joint work in progress with Florian Sch\"atz.

Graduate Student Homotopy Theory Seminar
4:00 pm   in 243 Altgeld Hall,  Monday, November 17, 2014
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Submitted by pdnelso2.
Josh Wen (UIUC Math)
Operads and their Duality
Abstract: An operad can be viewed as a meta object that governs a class of algebraic objects, much like how a moduli space in some way governs a class of geometric objects. Once we've been given a suitable definition of such a thing and what it means for two such things to be (Koszul) dual, we can make precise an abstract statement like "commutative algebras are dual to Lie algebras". If time permits, I'll present some concrete consequences of our abstract hand-waving.

Nonacademic Career Search
4:00 pm   in 141 Altgeld Hall,  Monday, November 17, 2014
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Submitted by laugesen.
Jennifer Kim   [email] (Employer Outreach, Graduate College)
Strategies for a Successful Job Search
Abstract: Presentation and discussion on "Strategies for a Successful Job Search". All graduate students and postdocs are welcome. Preparation: read the overview of résumés at the Graduate College Career Development website (http://www.grad.illinois.edu/careerservices/resumes ), and examine samples of different types of résumé (http://www.grad.illinois.edu/careerservices/resumestructure ).

Tech Talks for Students
5:00 pm   in 245 Altgeld Hall,  Monday, November 17, 2014
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Submitted by seminar.
Nicholas Baier (AOL)
How internet companies make money, the start-up explosion, and how math majors fit into it all
Abstract: Please join Nick Baier to talk about how internet companies make money, the start-up explosion, and how math majors fit into it all. With 2.8 billion worldwide users spending 62 billion hours a month on the internet it is no longer the industry of the future but the industry of the present. Nick is the Business Manager of AOL Mail from the University of Illinois class of 2010 with a BA in Math and a BS in Econ and former President of MATRIX! Pizza will be provided!

Operator Algebra Learning Seminar
5:15 pm   in 141 Altgeld Hall,  Monday, November 17, 2014
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Submitted by mjunge.
Marius Junge (UIUC )
CB-entropy
Abstract: I will start late-and discuss quantum group channels and how to calculate their cb-entropy.

Tuesday, November 18, 2014

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Tuesday, November 18, 2014
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Submitted by astraub.
Huilin Zhu   [email] (Xiamen University)
On the generalized Lebesgue-Ramanujan-Nagell equation
Abstract: In this talk we will introduce the rich history and recent results of the generalized Lebesgue-Ramanujan-Nagell equation. We also point out the difficulty in studying it and give some problems.

Harmonic Analysis and Differential Equations (HADES)
1:00 pm   in 347 Altgeld Hall,  Tuesday, November 18, 2014
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Submitted by verahur.
Samuel Walsh (Missouri-Columbia)
Mathematical theory of wind-driven water waves
Abstract: It is easy to see that wind blowing over a body of water can create waves. But this simple observation leads to a more fundamental question: Under what conditions on the velocity profile of the wind will persistent surface water waves be generated? This problem has been studied intensively in the applied fluid dynamics community since the first efforts of Kelvin in 1871. In this talk, we will present a mathematical treatment of the predominant model for wind-wave generation, the so-called quasi-laminar model of J. Miles. Essentially, this entails determining the (linear) stability properties of the family of laminar flow solutions to the two-phase interface Euler equation. We give a rigorous derivation of the linearized evolution equations about an arbitrary steady solution, and, using this, a complete proof of the celebrated instability criterion of Miles. In particular, our analysis incorporates both the effects of surface tension and a vortex sheet on the air--sea interface. We are thus able to give a unified equation connecting the Kelvin--Helmholtz and quasi-laminar models of wave generation.

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, November 18, 2014
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Submitted by ssolecki.
Anush Tserunyan (UIUC)
Equivalence relations and the Borel reducibility hierarchy
Abstract: For the past twenty years, a major focus of descriptive set theory has been the study of equivalence relations on Polish spaces that are definable (Borel, analytic, etc.) when viewed as sets of pairs; e.g. orbit equivalence relations induced by continuous actions of Polish groups are analytic. This study provides appropriate framework and tools for understanding the nature of classification of mathematical objects (measure-preserving transformations, unitary operators, Riemann surfaces, etc.) up to some notion of equivalence (isomorphism, conjugacy, conformal equivalence, etc.), and measuring the complexity of such classification problems. Due to its broad scope, it has natural interactions with other areas of mathematics, such as ergodic theory and topological dynamics, functional analysis and operator algebras. In this talk, I will give an introduction to this fascinating subject.

Probability Seminar
2:00 pm   in 347 Altgeld Hall,  Tuesday, November 18, 2014
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Submitted by psdey.
Sivaguru S. Sritharan   [email] (DRCSI, Naval Postgraduate School)
Stochastic Navier-Stokes Equation with Levy noise
Abstract: The subject of stochastic Navier-Stokes equation has grown in to a rich area in the past couple of decades with topics of research ranging from martingale solutions, invariant measures, large deviations, Malliavin calculus and control theory. There is also a natural connections to PDEs in infinite dimensions. In this talk we will give an introduction to this subject, touch upon some of the research areas, and indicate some open problems.

Graph Theory and Combinatorics Seminar
3:00 pm   in 241 Altgeld Hall,  Tuesday, November 18, 2014
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Submitted by molla.
Maryam Sharifzadeh (UIUC Math)
Subdivisions of a large clique in C_6-free graphs
Abstract: Mader conjectured that every $C_{4}$-free graph has a subdivision of a clique of order linear in its average degree. We show that every $C_{6}$-free graph has such a subdivision of a large clique. We also prove the dense case of Mader's conjecture in a stronger sense, i.e., for every $c$, there is a $c'$ such that every $C_{4}$-free graph with average degree $cn^{1/2}$ has a subdivision of a clique $K_{\ell}$ with $\ell=\lfloor c'n^{1/2}\rfloor$ where every edge is subdivided exactly $3$ times. Joint work with József Balogh and Hong Liu.

Wednesday, November 19, 2014

Graduate Student Algebraic Geometry Seminar
2:00 pm   in 441 Altgeld Hall,  Wednesday, November 19, 2014
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Submitted by fieldst2.
Matthew Mastroeni (UIUC Math)
A Primer on Reductions and Integral Closure of Ideals
Abstract: The aim of this talk is to give a basic introduction to reductions and the integral closure of ideals, two important tools in the study of Hilbert-Samuel multiplicity. I will explain how both topics arise naturally from the integral closure of a Rees ring $R[It]$, and then I will focus on what can be said when $R$ is Noetherian local ring with infinite residue field.

Integrability and Representation Theory
3:00 pm   in 347 Altgeld Hall,  Wednesday, November 19, 2014
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Submitted by rinat.
Tom Nevins (UIUC Math)
Representations of complex semisimple Lie algebras via geometry
Abstract: Following up on my IRT talk from earlier this semester, I’ll give an introduction to the realization of representations of a complex semisimple Lie algebra g via the associated flag variety. The goal will be to explain the Beilinson-Bernstein localization theorem, that offers precise control over the realization of representations. The talk will assume a bit of background on Lie algebras but will not assume attendance at the prior talk.

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Wednesday, November 19, 2014
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Submitted by laugesen.
Timur Oikhberg (Department of Mathematics, University of Illinois at Urbana-Champaign)
Some problems involving matrices
Abstract: We discuss two families of problems involving matrices. (1) The "almost versus near" problem. Suppose a pair of matrices (A,B) almost satisfies a certain equation -- that is, p(A,B) has small norm, where p is a polynomial (for instance, we can take p(A,B) = AB-BA - then the pair (A,B) almost commutes). Can we approximate (A,B) by a pair (X,Y) so that p(X,Y) = 0? (2) The preserver problem. Suppose a map T on the space of n by n matrices preserves a certain property (such as invertibility, or rank). What can we deduce about the general form of T? Time permitting, other open questions will be mentioned.

Thursday, November 20, 2014

U of I Langlands Day
10:00 am   in 241 Altgeld Hall,  Thursday, November 20, 2014
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Submitted by seminar.
To Be Announced
Abstract: All talks will take place in 241 Altgeld Hall. Coffee and refreshments will be served in the common room, 321 AH, at 9:30 AM and 3:30 PM. Visit the U of I Langlands Day website http://www.math.illinois.edu/~mluu/conference.html for more information.

Graduate Student Analysis Seminar
10:00 am   in 143 Altgeld Hall,  Thursday, November 20, 2014
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Submitted by ackrmnn2.
Byron Heersink (UIUC Math)
The central limit theorem for dynamical systems
Abstract: In this talk, we outline the Nagaev-Guivarc'h method of extending the central limit theorem to certain dynamical systems using results from analytic perturbation theory.

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Thursday, November 20, 2014
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Submitted by cmalkiew.
Aaron Mazel-Gee   [email] (UC Berkeley)
Goerss--Hopkins obstruction theory for $\infty$-categories
Abstract: Goerss--Hopkins obstruction theory is a tool for obtaining structured ring spectra from algebraic data. It was originally conceived as the main ingredient in the construction of tmf, although it's since become useful in a number of other settings, for instance in setting up a tractable theory of spectral algebraic geometry and in Rognes's Galois correspondence for commutative ring spectra. In this talk, I'll give some background, explain in broad strokes how the obstruction theory is built, and then indicate how one might go about generalizing it to an arbitrary (presentable) $\infty$-category. This last part relies on the notion of a model $\infty$-category -- that is, of an $\infty$-category equipped with a "model structure" -- which provides a theory of resolutions internal to $\infty$-categories and which will hopefully prove to be of independent interest.

Geometry, Groups and Dynamics/GEAR Seminar
1:00 pm   in Altgeld Hall 243,  Thursday, November 20, 2014
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Submitted by kapovich.
Martin Lustig (Université Aix-Marseille III)
Long turns and the index of irreducible free group automorphisms
Abstract: We will define the index of a free group automorphism \Phi as well as the index list of the corresponding outer automorphism \phi, and give a bit of a panorama. We will then explain how the index list of \phi can be computed from a train track representative of \phi. The main difficulty in a direct such calculation, so called INPs, can be controlled via studying "long turns", which is a new tool that has been invented and investigated in recent joint work with T. Coulbois. We will then present joint work with Coulbois and Pfaff which uses this tool crucially to show that any possible values for the index list can be achieved by some irreducible \phi. View talk at http://youtu.be/W3IVbxpzhkc

Graduate Student Number Theory Seminar
2:00 pm   in 007 Illini Hall,  Thursday, November 20, 2014
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Submitted by amalik10.
Hui Lin Zhu (Xiamen University, China)
Jesmanowicz-Terai-Cao-Le Conjecture and Pure Ternary Exponential Diophantine Equations
Abstract: In this talk we will introduce the Jesmanowicz-Terai-Cao-Le Conjecture and some results in pure ternary exponential Diophantine equations. We will discuss further research plan and ideas in this direction.

Analisis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, November 20, 2014
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Submitted by tumanov.
Guixiang Hong (Instituto de Ciencias Matematicas )
Noncommutative ergodic averages of balls and spheres, dimension free estimates
Abstract: In this talk, we would like to present some recent results on noncommutative ergodic theorems. Precisely, we establish the maximal ergodic theorem for the ergodic averages of balls and spheres in noncommutative $L_p$ spaces. As a consequence, we obtain noncommutative analogues of Wiener's and Jone's pointwise ergodic theorems. Moreover, using the noncommutative spherical maximal inequality, we prove that the bounds in the noncommutative Wiener's maximal inequalities are dimension free when the underlying von Neumann algebras are group measure spaces. If time is allowed, I will also present some results on the Heisenberg groups.

Commutative Ring Theory Seminar
3:00 pm   in 243 Altgeld Hall,  Thursday, November 20, 2014
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Submitted by mastroe2.
Michael DiPasquale (UIUC Math)
Associated Primes of Homologies arising from Approximation Theory
Abstract: Billera showed that the algebra of splines over a polytopal complex - of interest in approximation theory and geometric modelling - can be encoded as the top homology module of a certain chain complex. Schenck and Stillman introduced a variation of this chain complex whose homology modules are simpler. We show that the associated primes of the homology modules of this latter chain complex are all linear. This has consequences for computing the dimension of the vector space of splines of degree at most d on the underlying polytopal complex. In particular, we recover (in large degrees) a dimension formula for $C^1$ splines over a generic tetrahedral complex originally due to Alfeld, Schumaker, and Whiteley.

Mathematics in Science and Society (MSS)
4:00 pm   in 245 Altgeld Hall,  Thursday, November 20, 2014
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Submitted by seminar.
Catherine Meadows (Naval Research Laboratory)
Maude-NPA: Cryptographic Protocol Analysis Modulo Equational Properties
Abstract: Cryptographic protocols are the thread that knits together the security of the Internet. Thus it is important that they be correct. This is especially true for the design of the protocol. Although implementation errors are more common, design errors are harder to fix, especially for protocols, which must be both interoperable and widely deployed, making them difficult to redesign and redistribute on the fly. Indeed, even protocols with known flaws may remain deployed for a long time in order to support communication with legacy systems. For this reason, it is important to get a protocol right the first time. But since cryptographic protocols must be designed to operate in the face of an active attacker working to subvert their goals, this is not an easy problem.

One way of assuring correctness that has seen great success is the use of formal verification based on automated search techniques. One reason for this success has been the simple but powerful paradigm developed by Dolev and Yao in the late 70's and early 80's. In this paradigm messages are represented by symbolic terms constructed out of constants, function symbols, and variables. Furthermore, the network is controlled by an intruder who can intercept, destroy, and redirect traffic, and create and send messages of its own. Thus, we can think of the protocol as a distributed program for generating elements of a term algebra, defined by a set of rules that define actions executed by the intruder, and a set of rules describing actions executed by the honest principals.

Although the basic Dolev-Yao model is well-understood, it becomes more complex when we take into account the equational properties underlying the cryptoalgorithms used in the protocol, e.g. the axioms governing Abelian groups. However, it is necessary to do this, not only to faithfully represent the protocol, but in order to reason about the possible actions of an attacker. Thus, representation and reasoning about equational properties has been an active area of research. In this talk we will give an overview of research in this area, and present the approach used by a particular tool, the Maude-NRL Protocol Analyzer (Maude-NPA).

Friday, November 21, 2014

MoSAIC Festival
9:00 am   in Altgeld Hall and Illini Union,  Friday, November 21, 2014
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Submitted by seminar.
MoSAIC Festival
Abstract: A MoSAIC Festival will be held on the Illinois campus Friday, November 21 through Sunday, November 23. MoSAIC Festivals are art/math mini-conferences that incorporate lectures, hands-on workshops, an art exhibition, video screenings, and space for participants to display works which they bring. The festival is open to the public. High school teachers and students are encouraged to attend. Schedule of events is at http://www.math.illinois.edu/MOSAIC/

Algebra, Geometry and Combinatorics
4:00 pm   in 343 Altgeld Hall,  Friday, November 21, 2014
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Submitted by redavid2.
Elizabeth Drellich   [email] (University of Massachusetts Amherst)
Equivariant Cohomology of Flags and Partial Flags
Abstract: We start with a flag variety G/B and a partial flag variety G/P and examine the relationship between the T-equivariant cohomology of each of these spaces. This talk will present several descriptions of this relationship, including the GKM fiber bundle model of Guillemin-Sabatini-Zara and a recent combinatorial linear algebraic construction that is joint work with J. Tymoczko.

Graduate Geometry Topology Seminar
4:00 pm   in 243 Altgeld Hall,  Friday, November 21, 2014
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Submitted by penciak2.
Yang Song (UIUC Math)
Quasi-Hamiltonian G-Spaces
Abstract: Atiyah and Bott gave a way to describe the moduli space of flat connection as a symplectic manifolds by doing a Hamiltonian reduction to an infinitely dimensional space. Quasi-Hamiltonian G-space, on the other hand, can be used to attack the same problem without the infinite dimensional space. In this talk, we will introduce lie group valued moment map and quasi-Hamiltonian G-spaces. If times allows, we will briefly sketch the construction of moduli spaces of flat connection using quasi-Hamiltonian G-spaces.

Model Theory and Descriptive Set Theory Seminar
4:00 pm   in 345 Altgeld Hall,  Friday, November 21, 2014
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Submitted by ssolecki.
Anush Tserunyan (UIUC)
Treeable equivalence relations
Abstract: Given a Borel equivalence relation $E$ on a Polish space $X$, a useful way to present it is via a Borel graphing; that is, a Borel graph $\mathcal{G}$ (i.e. antireflexive symmetric Borel subset of $X^2$) such that $E$ is exactly the equivalence relation of being in the same connected component of $\mathcal{G}$. Of course, such a graphing always exists: take $\mathcal{G} := E \setminus \text{Diag}(X)$, but it contains redundant information (lots of cycles), not necessary for reconstructing $E$. A minimal graphing of $E$ would be an acyclic Borel graphing; in other words, each $E$-class is spanned by a tree. The Borel equivalence relations that admit such a graphing are called treeable. In this talk, we will discuss the class of treeable equivalence relations, focusing on a particular open question about a certain closure property of this class and its connections with Borel combinatorics, ergodic theory, and geometric group theory.

Saturday, November 22, 2014

MoSAIC Festival
9:00 am   in Altgeld Hall and Illini Union,  Saturday, November 22, 2014
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Submitted by seminar.
MoSAIC Festival
Abstract: A MoSAIC Festival will be held on the Illinois campus Friday, November 21 through Sunday, November 23. MoSAIC Festivals are art/math mini-conferences that incorporate lectures, hands-on workshops, an art exhibition, video screenings, and space for participants to display works which they bring. The festival is open to the public. High school teachers and students are encouraged to attend. For more information go to http://www.mosaicmathart.org/mosaic-plan/