Seminar Calendar
for events the week of Monday, May 4, 2015.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, May 4, 2015

Symplectic & Poisson Geometry Seminar
12:00 pm   in 341 AH,  Monday, May 4, 2015
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Submitted by jawatts.
Jordan Watts (UIUC Math)
The Differential Structure of an Orbifold
Abstract: There are many ways of viewing an (effective) orbifold besides the classical way: as a Lie groupoid, a stack, a diffeological space, a (Sikorski) differential space, a topological space... Not all of these are equivalent. In fact, in the categorical sense, all of the above categories are generally completely different. However, when restricting our attention to "quotients" of manifolds by proper Lie group actions, there is a chain of functors between the above categories, each of which forgets information along the way. If we ignore "maps between orbifolds" and focus only on a fixed orbifold, one may ask: how far along this chain of functors can one go before losing so much information that our orbifold cannot be recovered? (Going all the way to topological spaces, for example, would be too far.) In this talk I will answer this question with "differential spaces". This category generalises the category of manifolds, and includes as objects arbitrary sets equipped with special rings of functions. I will give a minimal set of invariants required to "remember" the orbifold, and show that these all live in the category of differential spaces. Going back to our chain of categories above, what I will be showing can be restated as follows: there is a functor from orbifolds (as effective proper étale Lie groupoids, say) to differential spaces that is essentially injective.

Operator Algebra Learning Seminar
5:00 pm   in 241 Altgeld Hall,  Monday, May 4, 2015
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Submitted by fboca.
Florin Boca (Math UIUC)
C*-algebras and Continued Fractions
Abstract: We will continue from last time.

Tuesday, May 5, 2015

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, May 5, 2015
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Submitted by cmalkiew.
Ayelet Lindenstrauss   [email] (IU Bloomington)
Calculations of Higher Topological Hochschild Homology
Abstract: T. Pirashvili defined the higher Hochschild homology groups of a commutative ring (with coefficients in the ring itself or more generally a bimodule) as the homotopy groups of the Loday construction of that ring (and module) evaluated on spheres. Having strictly associative and commutative ring spectra allows us to do the same for spectra, obtaining higher topological Hochschild homology. I would like to discuss some basic calculations (joint with I. Bobkova, K. Poirier, B. Richter, and I. Zakharevich) of higher Hochschild homology, namely of Z/p[x] and Z/p[x]/x^a when p divides a. I would then like to explain how these lead to a calculation (joint with B. Dundas and B. Richter) of higher topological Hochschild homology of number rings with coefficients in their residue fields, and to a re-calculation of higher topological Hochschild homology of finite fields (done originally by other methods by M. Basterra and M. Mandell).

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, May 5, 2015
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Submitted by ssolecki.
Maciej Malicki (Warsaw School of Economics and Caltech)
Polish groups with ample generics
Abstract: A Polish group G has ample generics if every diagonal conjugation action of G on its finite power has a comeager orbit. In recent years, this notion has drawn attention of many researchers, mainly because of its very interesting and strong consequences such as the automatic continuity property or the small index property. In this talk, I will give a brief overview of results on Polish groups with ample generics, and discuss my own contributions to this subject. For example, I will characterize Polish ultrametric spaces whose isometry groups have a neighborhood basis at the identity consisting of open subgroups with ample generics. I will formulate a condition that implies that the automorphism group of a Polish metric structure shares all the main consequences of the existence of ample generics. I will also present an example of a Polish group with ample generics that fails to be non-archimedean.

Probability Seminar
2:00 pm   in 347 Altgeld Hall,  Tuesday, May 5, 2015
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Submitted by psdey.
Samantha Xu (UIUC Math)
Diffusion Processes and Invariant Gibbs Measures
Abstract: In this talk, we discuss the connection between various diffusion processes and invariant Gibbs measures for Hamiltonian PDEs. We analyze various examples of this connection, and discuss some recent results.

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, May 5, 2015
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Submitted by katz.
Bruce Reznick (UIUC Math)
On the varying lengths of binary forms
Abstract: If the coefficients of a binary form p(x,y) of degree d are in a field F and $F \subset K \subset C$, one can ask for the minimal r such that $p = \sum_{i=1}^r c_i (a_i x + b_i y)^d$, with $a_i, b_i, c_i \in K$. I call this the K-length of p. Using two theorems of Sylvester, it is easy to show that K-length can vary with K. A few years ago, I gave an example of a real quintic which has lengths 3, 4 and 5 over various fields. In this talk, I'll show that such examples exist for all degrees $\ge 5$, and they are not particularly exotic: for even degree, $(xy)^k$ and for odd degree, $(xy)^k(x-y)$.

Graph Theory and Combinatorics Seminar
3:00 pm   in 241 Altgeld Hall,  Tuesday, May 5, 2015
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Submitted by molla.
Keivan Hassani Monfared   [email] (Western Illinois University Department of Mathematics)
Spectral characterization of graphs with a given matching number k
Abstract: We provide a characterization of graphs with a given matching number k, in terms of the spectra they can realize. Here, we allow the entries of the matrix corresponding to the edges of the graph to be any nonzero real number. This is a joint work with Sudipta Mallik.

Wednesday, May 6, 2015

Women in Mathematics (WIM) Seminar
1:00 pm   in 343 Altgeld Hall,  Wednesday, May 6, 2015
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Submitted by riveraq2.
Neriman Tokcan (UIUC Mathematics)
Lengths of Binary Forms
Abstract: The $K$-length of a form $f$ of degree $d$, $K \subseteq \mathbb{C}$, is the smallest number of $d$-th powers of linear forms of which $f$ is a $K$-linear combination. If $\mathbb{R}$-length of $f$ is d, then we say that $f$ has full length over $\mathbb{R}$. In this talk, we will show that a real binary quintic form $f$ has full length over $\mathbb{R}$ if and only if $f$ splits over $\mathbb{R}$. We will also give examples of binary forms with 3 different lengths over the subfields of $\mathbb{C}$.

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Wednesday, May 6, 2015
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Submitted by laugesen.
George Francis (Department of Mathematics, University of Illinois at Urbana-Champaign)
Computer Animation and Mathematical Visualization
Abstract: We present the geometrical principles of real-time interactive computer animation (RTICA) for mathematical visualization as it is practiced in the classroom, research seminar, and webpages but also in immersive virtual environments from head-mounted displays (Oculus Rift) to the CAVE at the Illinois Simulator Lab (ISL) of the Beckman Institute. Read more at http://new.math.uiuc.edu/595index.html

Thursday, May 7, 2015

Number theory seminar
10:00 am   in 241 Altgeld Hall,  Thursday, May 7, 2015
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Submitted by ford.
Kate Stange (University of Colorado)
The Apollonian structure of imaginary quadratic fields
Abstract: Let $K$ be an imaginary quadratic field with ring of integers OK. The Schmidt arrangement of $K$ is the orbit of the extended real line in the extended complex plane under the Bianchi group $PSL(2,OK)$ (realised as Mobius transformations). The arrangement takes the form of a dense collection of intricately nested circles. I'll explain how the number theory of $K$ influences the arrangement, and I'll use these arrangements to generalise Apollonian circle packings and define a new collection of thin groups of arithmetic interest.

Geometry, Groups and Dynamics/GEAR Seminar
1:00 pm   in Altgeld Hall 243,  Thursday, May 7, 2015
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Submitted by kapovich.
Jimmy Tseng (University of Bristol)
Simultaneous dense and nondense orbits
Abstract: We consider pairs of maps on (usually) the same phase space and, in particular, examine pairs for which many points have drastically different orbit structures. Our main example is a pair of commuting automorphisms of the d-torus, for which the set of points with dense orbit under one map and nondense orbit under the other has full Hausdorff dimension. Two other examples that we only very briefly mention are two linearly independent elements of the Cartan action on compact higher rank homogeneous spaces and the multiplication-by-n map on the circle and the geodesic flow under the induced map on the circle corresponding to the expanding horospherical subgroup. The last result is an example for which the phase spaces are not the same (because the geodesic flow acts on the space of unimodular lattices) but, nevertheless, it allows us to obtain a counterpart to a classical result of R. Kaufman in Diophantine approximation. This talk is based on my joint work with V. Bergelson and M. Einsiedler and my other recent joint work with R. Shi.