Seminar Calendar
for events the week of Tuesday, September 27, 2016.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, September 26, 2016

Topology Seminar
11:00 am   in 141 Altgeld Hall,  Monday, September 26, 2016
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Submitted by jbheller.
David Gepner (Purdue)
Excisive bivariant theories
Abstract: We construct stabilizations of infinity-topoi via bivariant theories which are excisive in the sense that they admit twisted Thom isomorphisms. This can be used to recover global forms of cohomology theories such as TMF and variants thereof. This is joint work with Thomas Nikolaus.

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Monday, September 26, 2016
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Submitted by laugesen.
Jozsef Balogh (Department of Mathematics, University of Illinois)
Some applications of the container method in discrete geometry
Abstract: The container method proved to be applicable in several areas of combinatorics. I will discuss some new applications. 1. We consider a problem of Erdos about point sets in the plane in (almost) general position. 2. We discuss epsilon-nets, where the underlying set is a subset of points in the plane, and the ranges are collinear point tuples. Though we have not completely solved any of the problems, maybe our improvements are of some interests. It is joint work with Jozsef Solymosi.

Operator Algebra Learning Seminar
5:00 pm   in 241 Altgeld Hall,  Monday, September 26, 2016
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Submitted by mjunge.
Marius Junge (UIUC)
Quantum value of classical games
Abstract: Following Scpara and Dailleux we will prove a parallel repetition for the quantum value of free games.

Tuesday, September 27, 2016

Topology Seminar
11:00 am   in 345 Altgeld Hall,  Tuesday, September 27, 2016
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Submitted by vesna.
Dondi Ellis (University of Michigan)
Motivic analogues of MO, MSO, and MR
Abstract: I will begin by briefly reviewing the foundations of stable motivic homotopy theory. In the non-equivariant stable motivic homotopy category, I will construct a k-spectrum MGLO whose topological realization over the field k=C is MO. I will give a complete description of the coefficient ring of MGLO up to knowledge of the coefficients of motivic HZ/2. Next I will discuss how MGLO is related to the Z/2-equivariant k-spectrum MGLR. MGLR is a motivic analogue of Landweber's real oriented cobordism MR. Just as taking fixed points of MR at the pre-spectrum level gives MO, taking fixed points MGLR at the pre-spectrum level gives MGLO. Restricting attention to the field k=C, I will discuss new research relating to MGLR. Finally, I will construct a k-spectrum MGLSO whose topological realization over the field k=C is MSO. Restricting to k=C, and completing at p an odd prime, MGLSO splits as a wedge sum of suspensions of motivic Brown-Peterson spectra BPGL. Restricting to k=C, and completing at p=2, MGLSO splits as a wedge sum of suspensions of motivic HZ and HZ/2.

Geometry, Groups, and Dynamics/GEAR
12:00 pm   in 243 Altgeld Hall,  Tuesday, September 27, 2016
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Submitted by bradlow.
Jordan Watts (University of Colorado Bolder)
Treating Limits as Colimits and Colimits as Limits ... with Applications!
Abstract: Actually, in this talk, we will restrict ourselves to treating subspaces as quotient spaces and quotient spaces as subspaces ... with applications. To elaborate, consider a manifold. Typically it is defined to be a certain gluing of open subsets of Euclidean space (a quotient space), although we know we can embed any manifold into some large Euclidean space (a subspace). Conversely, the level set of a regular value of a smooth real-valued function (a subspace) is a manifold (a quotient space). This is all elementary, but when one starts treating singular spaces in this fashion, interesting math occurs! We will first focus on orbifolds, and review how this point-of-view leads to an essentially injective functor between orbifolds and differentiable (local) semi-algebraic varieties. As an application, we use this to prove that a symplectic reduced space of a Hamiltonian circle action is never diffeomorphic to an orbit space of a Lie group action, unless it is an orbifold. Moreover, it is only ever an orbifold if its dimension is at most 2, or if the reduction is performed at a regular value of the momentum map.

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, September 27, 2016
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Submitted by anush.
Gabriel Conant (Notre Dame Math)
On tame expansions of the group of integers
Abstract: We discuss some recent work concerning expansions of the group $\mathbb{Z}$ of integers, which are tame with respect to model theoretic dp-rank. Our focus is on the ordered group of integers (also called Presburger arithmetic), which is a well-known example of a dp-minimal expansion of $\mathbb{Z}$. It was asked by Dolich et. al. whether every dp-minimal expansion of $\mathbb{Z}$ is a reduct of Presburger. We present a result in the opposite direction: there are no intermediate structures strictly between the group of integers and Presburger arithmetic. The proof of this result uses Cluckers' cell decomposition for Presburger sets, as well as work of Kadets on the geometry of convex polyhedra.

Graduate Student Analysis Seminar
1:00 pm   in 7 Illini Hall,  Tuesday, September 27, 2016
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Submitted by compaan2.
Derek Jung   [email] (UIUC Math)
On the lack of density of Lipschitz mappings in Sobolev spaces with model filiform target
Abstract: In 2014, Dejarnette, Hajlasz, Lukyanenko, and Tyson published a paper with the same title, except replacing model filiform with Heisenberg. They prove Lipschitz mappings $\mathbb{D}\to \mathbb{H}^1$ are not dense in the Sobolev space $W^{1,p}(\mathbb{D},\mathbb{H}^1)$ when $1\le p<2$. In this talk, I will present my efforts in translating their result from the Heisenberg group to the model filiform groups, which can be realized as the class of jet spaces $J^k(\mathbb{R},\mathbb{R})$. I will begin by briefly describing the structure of the Heisenberg group and discussing the main parts of their proof. After introducing the model filiform groups, I will give an example of a biLipschitz embedding of $\mathbb{S}^1$ into $J^k(\mathbb{R},\mathbb{R})$ for each $k$. I will conclude by remarking on the main obstacle to proving the non-density result: the regularity problem for the Carnot-Caratheodory metric.

Graduate Student Number Theory Seminar
2:00 pm   in 241 Altgeld Hall,  Tuesday, September 27, 2016
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Submitted by jli135.
Byron Heersink   [email] (UIUC )
Distribution of the periodic points of the Farey map
Abstract: A result of Series established a cross section of the geodesic flow in the tangent space of the modular surface which provided a lucid explanation of the connection between the geodesics in the modular surface and continued fractions. Pollicott later utilized this connection to show the limiting distribution of the periodic points of the Gauss map, i.e., the periodic continued fractions, when ordered according to the length of corresponding closed geodesics. In this talk, we outline how to extend the work of Series and Pollicott to obtain results for the Farey map. In particular, we expand the cross section of Series so that the return map under the geodesic flow is a double cover of the Farey map's natural extension. We then show how to adapt the method of Pollicott, which uses the analysis of a certain nuclear operator on the disk algebra, to prove an equidistribution result for the periodic points of the Farey map.

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, September 27, 2016
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Submitted by rtramel.
Ben Davison (EPFL)
The integrality conjecture and the Kac positivity conjecture
Abstract: Without assuming knowledge of any incarnation of Donaldson-Thomas theory, I'll give an introduction to the categorified version of it. I'll also explain what this upgrade of DT theory has to do with proving positivity conjectures, via my favourite example: the Kac positivity conjecture (originally proved by Hausel Letellier and Villegas), stating that polynomials counting absolutely indecomposable representations of quivers over F_q have positive coefficients.

Graph Theory and Combinatorics Seminar
3:00 pm   in 241 Altgeld Hall,  Tuesday, September 27, 2016
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Submitted by molla.
Ruth Luo (Illinois Math)
Stability theorems for graphs without long cycles
Abstract: We show stability versions of two Turán-type theorems for graphs without long cycles. The first is a theorem of Erdős from 1962 which gives an upper bound for the number of edges in a nonhamiltonian graph with prescribed minimum degree. A sharpness example $H_{n,d}$ is provided. The second is a theorem by Erdős and Gallai from 1959 which gives an upper bound on the number of edges in a graph with circumference less than $k$ (for some fixed $k$). The strongest sharpening of the Erdős-Gallai theorem was due to Kopylov who also provided sharpness examples $H_{n,k,t}$ and $H_{n,k,a}$. We show that 1. any 2-connected nonhamiltonian graph with minimum degree at least $d$ and "close" to the maximum number edges is a subgraph of $H_{n,d}$, and 2. any 3-connected graph with circumference less than $k$ and "close" to the maximum number of edges is a subgraph of either $H_{n,k,t}$ or $H_{n,k,2}$. This is joint work with Zoltán Füredi, Alexandr Kostochka, and Jacques Verstraëte.

Mathematics Colloquium: Trjitzinsky Memorial Lectures
4:00 pm   in Altgeld Hall 314,  Tuesday, September 27, 2016
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Submitted by kapovich.
Vaughan Jones (Vanderbilt University)
Lecture 1. What is it about the plane?
Abstract: It is natural to think that combinatorial problems become simpler if the objects involved are supposed to be planar. The isomorphism problem for graphs for instance. But in fact the restriction of planarity can make problems harder. Much harder. Take Sudoku for instance. We will give a couple of problems about contracting tensors which are unsolvable in the planar version but relatively easy without the planar restriction. In the process we will develop a general framework for manipulating planar diagrams.

Wednesday, September 28, 2016

Mathematics Colloquium: Trjitzinsky Memorial Lectures
4:00 pm   in Altgeld Hall 245,  Wednesday, September 28, 2016
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Submitted by kapovich.
Vaughan Jones (Vanderbilt University)
Lecture 2. Subfactors and the plane
Abstract: Von Neumann developed a theory of vector spaces over certain algebras where the dimension of the vector space is a non-negative real number (or infinity). The algebras are called type II_1 factors and the vector spaces are Hilbert spaces. Applying the dimension to subrings of the rings in question one gets a notion of index of a subring or degree of a ring extension. This index turns out to NOT be any real number bigger than 1, but is in some sense "quantized". Thanks to theorems of Popa, the subfactors are actually classified by systems of planar diagrams and this knowledge has been exploited to actually enumerate all subfactors of index up to 5.25.

Thursday, September 29, 2016

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Thursday, September 29, 2016
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Submitted by sahlgren.
Bruce Berndt (Illinois Math)
Ramanujan's formula for $\zeta(2n+1)$
Abstract: Let $\zeta(s)$ denote the Riemann zeta function. If $n$ is a positive integer, a famous formula of Euler provides an elegant evaluation of $\zeta(2n)$. However, little is known about $\zeta(2n+1)$. In Ramanujan's earlier notebooks, we find a formula for $\zeta(2n+1)$ which is a natural analogue of Euler's formula. We provide its history, indicate why it is "interesting," and show its connections with other mathematical objects such as the Dedekind eta function, Eisenstein series, and period polynomials.

Math-Physics Seminar
12:30 pm   in 464 Loomis Laboratory,  Thursday, September 29, 2016
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Submitted by katz.
Dan Freed (University of Texas Math)
Deformation classes of unitary invertible field theories
Abstract: The phase, or deformation class, of a quantum mechanical system determines its large-scale features. If we can approximate the long-range properties by a field theory, then we can bring to bear the Axiom System for field theory initiated by Segal. In joint work with Mike Hopkins we carry this out for invertible field theories using techniques from (equivariant) stable homotopy theory. The results apply immediately to the classification of short range entangled lattice systems in condensed matter physics. The new conceptual ingredient is an extended notion of unitarity for invertible topological theories. The explicit computations are via the Adams spectral sequence.

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, September 29, 2016
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Submitted by tumanov.
A. Dali Nimer (University of Washington)
Characterization and construction of conical 3-uniform measures

Mathematics Colloquium: Trjitzinsky Memorial Lectures
4:00 pm   in Altgeld Hall 245,  Thursday, September 29, 2016
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Submitted by kapovich.
Vaughan Jones (Vanderbilt University)
Lecture 3. Subfactors, conformal field theory and the Thompson group
Abstract: Subfactors actually arise in conformal field theory as shown by Wassermann for theories where space-time is actually the circle. It is tempting to speculate that all subfactors arise in this way but the famous Haagerup factor has not yet been obtained. The Thompson groups are certain countable groups of homeomorphisms of the circle which can be thought of as approximations to the group of diffeomorphisms of the circle which is an essential ingredient of conformal field theory. In an attempt to get at CFT’s from subfactors like the Haagerup we obtain interesting unitary representations of the Thompson groups which allow us to show that this approach can never work! As a consolation prize we present a construction of all knots and links showing that a Thompson group is as good as the braid groups at constructing knots and links.

Friday, September 30, 2016

Model Theory and Descriptive Set Theory Seminar
4:00 pm   in 345 Altgeld Hall,  Friday, September 30, 2016
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Submitted by anush.
Erin Caulfield (UIUC Math)
Distality and Keisler measures
Abstract: In this talk, I will introduce distality and discuss the connection between distality and weak cell decompositions. The presentation follows Sergei Starchenko's notes on "NIP, Keisler Measures and Combinatorics."

Graduate Geometry/Topology Seminar
4:00 pm   in 241 Altgeld Hall,  Friday, September 30, 2016
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Submitted by dcarmod2.
Tsutomu Okano (UIUC Math)
Homotopy groups of the MU spectrum
Abstract: Thom's 1954 paper implies that there is an isomorphism of rings between the cobordism ring of almost complex manifolds and $\pi_*(MU)$, the coefficient ring of the $MU$ spectrum. A notable property of the $MU$ spectrum is that it is the universal complex oriented cohomology theory, which is related to the notion of formal group laws. Indeed, the universal formal group law defined over the Lazard ring $L$ can be identified with the canonical formal group law defined on $\pi_*(MU)$ via an isomorphism of these underlying rings. This isomorphism is the content of Milnor-Quillen theorem and the goal of this talk is to give a sketch of this last isomorphism $L \simeq \pi_*(MU)$.