Seminar Calendar
for events the week of Friday, September 4, 2015.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, August 31, 2015

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Monday, August 31, 2015
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Submitted by laugesen.
Bruce Reznick (Department of Mathematics, University of Illinois)
Problem-solving, question-asking and knowledge-finding
Abstract: Three of the most important activities that researchers perform are listed in the title. I will talk about practical techniques for improving your skills in these areas, using specific examples of mathematics from my own work and the work of my graduate students. My intention that most members of the audience will see at least a few objects which resonate with their own mathematical interests.

Graduate Student Analysis Seminar
4:00 pm   in Altgeld 241,  Monday, August 31, 2015
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Submitted by ackrmnn2.
Planning Meeting
Abstract: We will be scheduling talks for the semester, and potentially moving the seminar so it does not conflict with Math 499. Come by if you are a grad student either interested in giving or listening to talks in any field involving analysis!

Graduate Algebraic Geometry Seminar
4:00 pm   in 143 Altgeld Hall,  Monday, August 31, 2015
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Submitted by jjwen2.
Organizational Meeting

Descriptive Set Theory Reading Seminar
4:00 pm   in 141 Altgeld Hall,  Monday, August 31, 2015
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Submitted by anush.
Organizational meeting

Literature Seminar in Operator Algebras
5:00 pm   in 241 Altgeld Hall,  Monday, August 31, 2015
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Submitted by fboca.
Mingyu Zhao (UIUC Math)
Some operator space version of the AGM inequality

Tuesday, September 1, 2015

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, September 1, 2015
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Submitted by cmalkiew.
Agnes Beaudry (U Chicago)
Chromatic splitting: the way things work at p=2
Abstract: Recent computations show that the decomposition of $L_1L_{K(2)}S$ predicted by the chromatic splitting conjecture does not hold at $p=2$. I will explain how the situation differs and propose a different decomposition for $L_1L_{K(2)}S$ in this case.

Geometry, Groups and Dynamics/GEAR Seminar
12:00 pm   in 345 Altgeld Hall,  Tuesday, September 1, 2015
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Submitted by kapovich.
Saul Schleimer (University of Warwick)
Recognizing three-manifolds
Abstract: To the eyes of a topologist manifolds have no local properties: every point has a small neighborhood that looks like euclidean space. Accordingly, as initiated by Poincaré, the classification of manifolds is one of the central problems in topology. The "homeomorphism problem" is somewhat easier: given a pair of manifolds, we are asked to decide if they are homeomorphic. These problems are solved for zero-, one-, and two-manifolds. Even better, the solutions are "effective": there are complete topological invariants that we can compute in polynomial time. On the other hand, in dimensions four and higher the homeomorphism problem is logically undecidable. This leaves the provocative third dimension. Work of Haken, Rubenstein, Casson, Manning, Perelman, and others shows that these problems are decidable. Sometimes we can do better: for example, if one of the manifolds is the three-sphere then the homeomorphism problem lies in the complexity class NP. In joint work with Marc Lackenby, we show that recognizing spherical space forms also lies in NP. If time permits, we'll discuss the standing of the other seven Thurston geometries. View talk at https://youtu.be/4nu_dSCZ5V8

Several Complex Variables and CR Geometry
1:00 pm   in 241 Altgeld Hall,  Tuesday, September 1, 2015
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Submitted by jpda.
Ming Xiao (UIUC Math)
Embeddability Problems for CR Hypersurfaces
Abstract: I will first review the history of embeddability problems for CR structures and then begin discussing new results.

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, September 1, 2015
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Submitted by anush.
Not scheduled

Probability Seminar
2:00 pm   in 347 Altgeld Hall,  Tuesday, September 1, 2015
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Submitted by psdey.
Janna Lierl   [email] (UIUC Math)
Parabolic Harnack inequality on fractal-like Dirichlet spaces
Abstract: I will present some recent results on extending the parabolic Moser iteration method to the setting of fractal-type local Dirichlet spaces satisfying appropriate geometric conditions. I will also discuss the case of non-symmetric perturbations of the Dirichlet form. This method yields a parabolic Harnack inequality. Consequently, upper and lower bounds for the associated heat propagator can be obtained.

Graph Theory and Combinatorics Seminar
3:00 pm   in 241 Altgeld Hall,  Tuesday, September 1, 2015
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Submitted by molla.
Theodore Molla   [email] (UIUC Math)
Triangle factors in graphs, directed graphs and weighted graphs
Abstract: In 1963 Corrádi and Hajnal proved that if G is a graph on n vertices, n is divisible by 3 and the minimum degree of G is at least 2n/3, then G contains a triangle factor, i.e. a collection of n/3 vertex disjoint triangles. Since every graph G on n vertices with independent number greater than n/3 does not have n/3 vertex disjoint triangles, this theorem is sharp. In this talk, we will describe several related theorems for graphs, directed graphs and weighted graphs. For example, we will discuss the following recent result: For every ε > 0 there exists γ > 0 such that if G is a graph on n vertices and the minimum degree of G is at least (1/2 + ε)n while the independence number of G is at most γn, then G has a triangle factor provided n is sufficiently large and divisible by 3.

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, September 1, 2015
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Submitted by katz.
Rebecca Tramel (UIUC Math)
Bridgeland stability on surfaces with curves of negative self-intersection
Abstract: Let X be a smooth projective surface. In 2002, Bridgeland defined a notion of stability for objects in the derived category of X, which can be thought of as a generalization of slope stability for vector bundles on curves. The work of Bayer-Macri and of Toda shows that there are nice connections between deformations in Stab(X), the space of all Bridgeland stability conditions on X and the birational geometry of X.  I will consider the case of a surface which contains a rational curve C of negative self-intersection, and consider objects whose class is that of the skyscraper sheaf of a point. There is a distinguished chamber in Stab(X) called the geometric chamber, in which all such objects are stable. I will show that there is a wall to the geometric chamber along which the points of C are destabilized, and describe the moduli space of stable objects across this wall.

Thursday, September 3, 2015

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Thursday, September 3, 2015
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Submitted by sahlgren.
Patrick Allen (UIUC Math)
Finiteness of unramified deformation rings
Abstract: Class field theory allows one to precisely understand ramification in abelian extensions of number fields. A consequence is that infinite pro-p abelian extensions of a number field are infinitely ramified above p. Boston conjectured a nonabelian analogue of this fact, predicting that certain pro-p representations that are unramified at p act via a finite quotient, and this conjecture strengthens the unramified version of the Fontaine-Mazur conjecture. We show in many cases that one can deduce Boston's conjecture from the unramified Fontaine-Mazur conjecture, which allows us to deduce (unconditionally) Boston's conjecture in many two-dimensional cases. This is joint work with F. Calegari.

Geometry, Groups and Dynamics/GEAR Seminar
1:00 pm   in Altgeld Hall 243,  Thursday, September 3, 2015
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Submitted by kapovich.
Ilya Kapovich (UIUC Math)
On purely loxodromic actions
Abstract: Purely loxodromic isometric actions of finitely generated groups on Gromov-hyperbolic spaces (that is, actions where every element of infinite order in the group acts as a loxodromic isometry) appear naturally in many contexts, such as in the theories of hyperbolic, relatively hyperbolic and acylindrically hyperbolic groups, the study of convex cocompact subgroups of mapping class groups, etc. Often one needs to consider non-proper actions, and in that context the notion of an acylindrical action serves as an important substitute of being proper. We construct an example of an isometric action of the free group $F(a,b)$ on a $\delta$--hyperbolic graph $Y$, such that this action is acylindrical, free, purely loxodromic, has asymptotic translation lengths of nontrivial elements of $F(a,b)$ separated away from $0$, has quasiconvex orbits in $Y$, but such that the orbit map $F(a,b)\to Y$ is not a quasi-isometric embedding. View talk at https://youtu.be/y5eXM5Nst0U

Graduate Student Number Theroy Seminar
2:00 pm   in 241 Altgeld Hall,  Thursday, September 3, 2015
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Submitted by amalik10.
Ravi Kiran Donepudi (UIUC Math)
Asymptotics of relative cubic function fields
Abstract: Fix a function field $k$. By Galois theory, every cubic extension of $k$ with Galois group $S_3$ has a unique quadratic sub-extension. So we fix a quadratic extension $K_2/k$ and count the number of cubic extensions of $k$ whose Galois closure contains $K_2$ up to a bounded discriminant. Following a result for number fields by Cohen and Morra (2010), we have an asymptotic formula for this count. Our main tools are Kummer theory and a tauberian theorem. This is joint work with Stefan Erickson and Colin Weir.

Graduate Student Homotopy Seminar
2:00 pm   in 347 Altgeld Hall,  Thursday, September 3, 2015
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Submitted by rasekh2.
Organizational Meeting

Commutative Ring Theory Seminar
3:00 pm   in 243 Altgeld Hall,  Thursday, September 3, 2015
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Submitted by mastroe2.
Organizational Meeting

Special Departmental Presentation
4:00 pm   in 245 Altgeld Hall,  Thursday, September 3, 2015
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Submitted by seminar.
Kathy Dams (Office of Sponsored Programs and Research Administration)
Grant Proposal Submissions

Friday, September 4, 2015

Symplectic & Poisson Geometry Seminar
2:00 pm   in 143 Altgeld Hall,  Friday, September 4, 2015
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Submitted by lerman.
Eugene Lerman (UIUC Math)
A category of open systems and networks without graphs
Abstract: Many systems of interest in science and engineering are made up of interacting subsystems. These subsystems, in turn, could be made up of collections of smaller interacting subsystems and so on. In a series of papers David Spivak with collaborators formalize these kinds of structures as algebras over presentable colored operads. DeVille and Lerman, building on the groupoid formalism for coupled cell networks of Golubitsky, Stewart and collaborators, proposed an approach to the study of dynamics of complex systems which is based on graph fibrations. My goal is to describe an algebraic framework that encompasses both the operadic approache of Spivak et al. and fibrations of networks of manifolds of DeVille and Lerman.

Graduate Geometry Topology Seminar
4:00 pm   in 243 Altgeld Hall,  Friday, September 4, 2015
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Submitted by penciak2.
Matej Penciak (UIUC Math)
To Be Announced

Model Theory and Descriptive Set Theory Seminar
4:00 pm   in 345 Altgeld Hall,  Friday, September 4, 2015
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Submitted by anush.
Anton Bernshteyn (UIUC Math)
On "Baire measurable paradoxical decompositions via matchings" by A. Marks and S. Unger
Abstract: The Banach--Tarski paradox states that the unit ball in $\mathbb{R}^3$ is equidecomposable with two copies of itself. Of course, there can be no such equidecomposition where each piece is measurable. Thus a natural question (first asked by Marczewski) is whether there exists such an equidecomposition where each piece has the Baire property. The answer is positive, as demonstrated by an intricate construction due to Dougherty and Foreman. This paper provides an alternative (short) proof of this result. In fact, a more general result is established, namely if a group acting by Borel automorphisms on a Polish space has a paradoxical decomposition, then it admits a paradoxical decomposition using pieces having the Baire property. The key ingredient of the proof is a Borel analogue of Hall's celebrated marriage theorem from graph theory. In this series of talks we will go over the proofs and enjoy the elegant transition back and forth between the original problem and its combinatorial counterpart.