Seminar Calendar
for events the week of Saturday, November 1, 2014.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, October 27, 2014

Symplectic & Poisson Geometry Seminar
3:00 pm   in 341 Altgeld Hall,  Monday, October 27, 2014
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Submitted by jawatts.
Rajan Mehta (Smith College)
Linear groupoid structures and representations up to homotopy
Abstract: The notion of representation for a Lie groupoid has the annoying problem that it isn't generally possible to define a good adjoint representation. To fix this problem, Arias Abad and Crainic introduced the notion of "representation up to homotopy". In this talk, I will show how 2-term representations up to homotopy are related to linear groupoid structures, which play the role of semidirect products. There is a one-to-one correspondence at the level of isomorphism classes, but at the level of objects, the correspondence is noncanonical, so it is possible for certain constructions to be "natural" in one perspective but not the other. A key example that illustrates the value of linear groupoids is the adjoint representation. To define the adjoint representation up to homotopy of a Lie groupoid G, one needs to choose a distribution transverse to the source fibers. On the other hand, the linear groupoid that corresponds to the adjoint representation is canonical; it is simply the tangent bundle TG. This talk is based on joint work with Alfonso Gracia-Saz (arXiv:1007.3658).

Academic Careers Panel Discussion
4:00 pm   in 141 Altgeld Hall,  Monday, October 27, 2014
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Submitted by laugesen.
Prof. Olcay Akman (Illinois State U.), Prof. Stephanie Alexander (U. of Illinois), Asst. Prof. Daniel Roberts (Illinois Wesleyan U.)Academic Careers Panel Discussion
Abstract: All graduate students, postdocs and visiting faculty in Math are welcome at this informal panel discussion of academic careers at the different types of U.S. institutions. Bring your questions!

Graduate Student Homotopy Theory Seminar
4:00 pm   in 243 Altgeld Hall,  Monday, October 27, 2014
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Submitted by pdnelso2.
Nima Rasekh (UIUC Math)
Topos Theory: Sketches of an Elephant
Abstract: Although it's ideas and results are used in different branches of mathematics from set theory to differential and algebraic geometry, topos theory is still one of the more mysterious concepts of mathematics. In this talk I give a general introduction to the notion of a topos and some its applications. As it is the homotopy seminar, I will then move on to talk about topoi in the context of homotopy theory using the language of higher category theory. Finally, if time permits, I mention some unresolved issues regarding the connection between topoi and homotopy theory.

Job application review for graduating PhD students
5:00 pm   in 259 and 243 Altgeld Hall,  Monday, October 27, 2014
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Submitted by laugesen.
Abstract: Graduating Math PhD students are invited to bring their academic job application materials (cover letter, CV, research statement, teaching statement etc.) and get on-the-spot feedback and advice from Prof. Olcay Akman (Illinois State U.), Asst. Prof. Daniel Roberts (Illinois Wesleyan U.), and Prof. Laugesen.

Operator Algebra Learning Seminar
5:00 pm   in Altgeld Hall,  Monday, October 27, 2014
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Submitted by mjunge.
Alba Wafaa_Minyu Zhao (UIUC)
Introduction to free products
Abstract: We give an introduction to free products with amalgamation.

Tuesday, October 28, 2014

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, October 28, 2014
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Submitted by cmalkiew.
Jeremy Miller (Stanford University)
Representation stability for homotopy groups of configuration spaces
Abstract: In the 1970s, McDuff proved that configuration spaces of distinct unordered particles in an open manifold exhibit homological stability. That is, H_i(Conf_k(M)) is independent of k for k>>i. A natural follow up question is: Do the homotopy groups also stabilize? From explicit calculations, one can show that this is not the case. However, in joint work with Alexander Kupers, I have shown that the rational homotopy groups of configuration spaces of particles in simply connected manifolds of dimension at least 3 exhibit representation stability in the sense of Church and Farb. This follows from a more general theorem we prove relating the homotopy groups and cohomology groups of co-FI-spaces and from the work of Church on representation stability for the cohomology of ordered configuration spaces. This result on homotopy groups suggests that in situations with homological stability, one should not expect classical stability for homotopy groups. Instead, one should try to incorporate the fundamental group into one's definition of stability.

Harmonic Analysis and Differential Equations
1:00 pm   in 347 Altgeld Hall,  Tuesday, October 28, 2014
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Submitted by verahur.
Chanwoo Kim (Wisconsin-Madison)
CANCELLED

Logic Seminar
1:00 pm   in Altgeld Hall,  Tuesday, October 28, 2014
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Submitted by ssolecki.
No seminar
Abstract: No seminar---Midwest Model Theory Day in Chicago

Geometry, Groups and Dynamics/GEAR Seminar
1:00 pm   in Altgeld Hall 243,  Tuesday, October 28, 2014
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Submitted by kapovich.
Grace Work (UIUC Math)
Gap distribution for saddle connections on the octagon
Abstract: We will describe the strategy used to explicitly compute the limiting gap distribution for slopes of saddle connections on the octagon. This is the first such computation where the Veech group of the translation surface has multiple cusps. This is joint work with Caglar Uyanik. View talk at http://youtu.be/9ui5dm5n5KU

Probability Seminar
2:00 pm   in 347 Altgeld Hall,  Tuesday, October 28, 2014
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Submitted by psdey.
Krishna Athreya (Iowa State University)
Coalescence in branching trees with application to branching random walks.
Abstract: Consider a single type Galton Watson branching tree that is super critical with no extinction. Pick two individuals at random by srswor from the nth generation and trace their lines of descent back in time till they meet.Call that generation number the coalescence time Xn. This talk will address the problem of determining the limit behavior of Xn as n goes to infinity for both supercritical and explosive cases. An application to branching random walks will also be discussed.

Graph Theory and Combinatorics Seminar
3:00 pm   in 241 Altgeld Hall,  Tuesday, October 28, 2014
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Submitted by molla.
Amin Bhamanian   [email] (Illinois State Math)
Extending factorizations of complete uniform hypergraphs
Abstract: We consider when a given $r$-factorization of the complete uniform hypergraph on $m$ vertices $K_m^h$ can be extended to an $s$-factorization of $K_n^h$. The case of $r=s=1$ was first posed by Cameron in terms of parallelisms, and solved by Häagkvist and Hellgren. We extend these results, which themselves can be seen as extensions of Baranyai's Theorem. For $r=s$, we show that the "obvious" necessary conditions, together with the condition that $\gcd(m,n,h)=\gcd(n,h)$ are sufficient. For $r < s$ we show that the obvious necessary conditions, augmented by $\gcd(m,n,h)=\gcd(n,h)$, $n\geq2m$, and $1 \leq \frac{s}{r} \leq \frac{m}{k} \left(1 -\binom{m-k}{h}/\binom{m}{h}\right)$ are sufficient, where $k=\gcd(m,n,h)$. Joint work with Mike Newman.

Wednesday, October 29, 2014

Graduate Student Algebraic Geometry Seminar
2:00 pm   in 441 Altgeld Hall,  Wednesday, October 29, 2014
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Submitted by fieldst2.
Anna Weigandt (UIUC Math )
The Geometry of Type A Quiver Representations
Abstract: A quiver is a finite directed graph. We will look at quiver representations, an assignment of a vector space to each vertex and a linear map to each arrow. A natural question is to study isomorphism classes of quiver representations. Equivalently, we may look at orbits of a group action on some associated affine space. Taking orbit closures, we obtain varieties called quiver loci. We will discuss the Zelevinsky map, which realizes each equioriented type A quiver locus as an open affine piece of a Schubert variety.

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Wednesday, October 29, 2014
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Submitted by laugesen.
Vadim Zharnitsky (Department of Mathematics, University of Illinois at Urbana-Champaign)
Cyclic evasion in the three bug problem.

Thursday, October 30, 2014

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Thursday, October 30, 2014
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Submitted by astraub.
Khang Tran   [email] (Truman State University)
The zero distribution of polynomials with a three-term recurrence
Abstract: For any fixed positive integer $n$, we study the zero distribution of a sequence of polynomials $H_{m}(z)$ satisfying the rational generating function \[ \sum_{m=0}^{\infty}H_{m}(z)t^{m}=\frac{1}{1+B(z)t+A(z)t^{n}} \] where $A(z)$ and $B(z)$ are any polynomials in $z$ with complex coefficients. We show that for all large $m$, the zeros of $H_{m}(z)$ which satisfy $A(z)\ne0$ lie on the fixed real algebraic curve given by \[ \Im\frac{B^{n}(z)}{A(z)}=0\qquad\mbox{and}\qquad0\le(-1)^{n}\Re\frac{B^{n}(z)}{A(z)}\le\frac{n^{n}}{(n-1)^{n-1}} \] and are dense there as $m\rightarrow\infty$.

Math-Physics Seminar
12:30 pm   in 464 Loomis Laboratory,  Thursday, October 30, 2014
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Submitted by katz.
Anastasios Petkou (Aristotle University of Thessaloniki Physics)
Some aspects of large-N vector models and their higher-spin holography

Geometry, Groups and Dynamics/GEAR Seminar
1:00 pm   in Altgeld Hall 243,  Thursday, October 30, 2014
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Submitted by kapovich.
George Willis (Newcastle)
Totally Disconnected, Locally Compact Groups
Abstract: Locally compact groups in general and the structure of connected groups will be brie y surveyed in the rst part of the talk. The second part of the talk will review recent developments in the structure theory of totally disconnected, locally compact groups. There are three strands in this work: the scale function and related ideas; a theory of decomposition into simple pieces; and a local theory. These three strands promise to combine to produce a much richer understanding of totally disconnected groups than we have at present. View talk at http://youtu.be/Sr55vamxQdI

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, October 30, 2014
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Submitted by tumanov.
Claudio DiMarco (Syracuse University)
Two Fractal Metric Space Dimensions
Abstract: There are many ways to define dimension for metric spaces. Some dimensions measure size, others connectivity, and some consider both. Balka, Buczolich and Elekes (2011) modified the notion of Hausdorff dimension to include topological considerations (such as connectivity). We use that same strategy to modify the notion of conformal dimension. For a metric space X, this usually amounts to considering a basis for the topology on X, then determining the conformal dimension of the boundaries of the basis elements.

Commutative Ring Theory Seminar
3:00 pm   in 243 Altgeld Hall,  Thursday, October 30, 2014
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Submitted by mastroe2.
Sankar Dutta (UIUC Math)
On the Edge Homomorphism of a Spectral Sequence
Abstract: The purpose of these talks is to present a connection between the non-vanishing of a specific edge homomorphism of a spectral sequence originating from the associativity property of Hom and Tensor product and several homological conjectures. Ramifications of this observation will be discussed.

Mathematics Colloquium
4:00 pm   in 245 Altgeld Hall,  Thursday, October 30, 2014
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Submitted by seminar.
Gelasio Salazar (Instituto de Fisica, Universidad Autónoma de San Luis Potosí, Mexico)
Drawings of complete graphs
Abstract: Using the Jordan Curve Theorem, it is an easy exercise to show that if $n\ge 5$, then the complete graph $K_n$ on $n$ vertices cannot be drawn in the plane without edge crossings. It is natural to ask: what is the minimum number of crossings of edges in a drawing of $K_n$ in the plane? Using graph theory terminology, this question reads: what is the "crossing number" cr$(K_n)$ of $K_n$? In the late 1950s, the British artist Anthony Hill developed an interest in drawing $K_n$ with as few edge crossings as possible. He eventually came up with a general construction to draw $K_n$ with exactly $H(n):=(1/4)\lfloor{n/2}\rfloor \lfloor{(n-1)/2}\rfloor \lfloor{(n-2)/2}\rfloor \lfloor{(n-3)/2}\rfloor $ crossings. No drawings with fewer crossings have ever been found, and the widely believed Hill's Conjecture $cr(K_n) = H(n)$ has become one of the most important open problems in Topological Graph Theory. An important variant of this version is the {\em rectilinear crossing number}, in which we require that the edges be drawn as straight segments. In this talk we will review the history of these problems, and give some unexpected and important connections to problems in geometric probability and convex geometry. Finally, we will survey the state-of-the-art of these open problems, including some recent progress obtained for the crossing number of $K_n$ borrowing from classical techniques in discrete geometry.

Friday, October 31, 2014

Graduate Geometry Topology Seminar
4:00 pm   in 243 Altgeld Hall,  Friday, October 31, 2014
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Submitted by penciak2.
Joel Villatoro (UIUC Math)
Morita Equivalence and Picard Groups of Lie Groupoids
Abstract: In this talk I will briefly discuss a basic definition of Morita equivalence for unital associative algebras over a commutative ring. With that discussion as motivation, I will develop a notion of Morita equivalence for Lie Groupoids. Some work will be done to develop intuition for the geometric meaning behind two Lie groupoids being Morita equivalent. I will try to prove at least one thing.