Seminar Calendar
for events the week of Sunday, February 14, 2016.

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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, February 15, 2016

Workshop on Responsible Conduct of Research
4:00 pm   in 314 Altgeld Hall,  Monday, February 15, 2016
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Submitted by laugesen.
Matthew Ando (Professor and Chair, Department of Mathematics)
Workshop on Responsible Conduct of Research
Abstract: I will lead a one-hour workshop on the "Responsible Conduct of Research". This will be an introduction to best practices, enriched with some scenarios to generate discussion. All graduate students who are or will be supported by NSF or other federal grants are required to receive this training. Participants will sign in, so that we can report participation to the university. (The university requirement is a response to a federal requirement). All graduate students are welcome to participate. You are required to participate if
1. you have not yet participated in one of these workshops (the department has held one each year for the last few years), and
2. you want to be eligible to be supported by an NSF grant.

Operator Algebras Learning Seminar
5:00 pm   in 241 Altgeld Hall,  Monday, February 15, 2016
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Submitted by longfie2.
Stephen Longfield (UIUC Math)
Classification of Baumslag-Solitar group von Neumann algebras (Part II)
Abstract: Since the introduction of von Neumann algebras, a program to classify group von Neumann algebras has been underway. Though many questions in this direction remain open, new techniques developed in the last 15 years have yielded several interesting results. Following last week's seminar, this talk will follow the 2014 paper of Meesschaert and Vaes, in which the authors apply the powerful deformation/rigidity theory of Popa to partially classify the von Neumann algebras of the Baumslag-Solitar groups.

Tuesday, February 16, 2016

Geometry, Groups and Dynamics/GEAR Seminar
12:00 pm   in Altgeld Hall 243,  Tuesday, February 16, 2016
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Submitted by kapovich.
Steven Bradlow (UIUC Math)
Higgs bundles and flexibility of surface group representations
Abstract: Among their many virtues, Higgs bundles reveal features of surface group representations that can be difficult to detect by other means. This will be illustrated in situations where the image of a representation into a group G lies in a subgroup of G, with special attention given to the case where G is a non-compact real form such as U(p,q) or Sp(2n,R).

Graph Theory and Combinatorics Seminar
3:00 pm   in 241 Altgeld Hall,  Tuesday, February 16, 2016
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Submitted by molla.
Andrew McConvey (UIUC Math)
Strengthening theorems of Dirac and Erdös on disjoint cycles
Abstract: Let $k$ be a positive integer, $H_{k}(G)$ be the set of vertices of degree at least $2k$ in a graph $G$, and $L_{k}(G)$ be the set of vertices of degree at most $2k-2$ in $G$. A seminal result of Corrádi and Hajnal states that a graph $G$ with at least $3k$ vertices and minimum degree at least $2k$ contains $k$ disjoint cycles. In 1963, Dirac and Erdös considered the case that $\delta(G) < 2k$. In particular, they proved if $k \geq 3$ and $|H_{k}(G)| - |L_{k}(G)| \geq k^{2} + 2k - 4$, then $G$ contains $k$ disjoint cycles. In this talk, we prove the following stronger result. If $k \geq 2$ and $|H_{k}(G)| - |L_{k}(G)| \geq 3k$, then $G$ contains $k$ disjoint cycles. In the special case that $V(G) = H_{k}(G)$, this reduces to the theorem of Corrádi and Hajnal for $k \geq 2$. This is joint work with Hal Kierstead and Alexandr Kostochka.

Wednesday, February 17, 2016

Integrability and Representation Theory
3:00 pm   in 243 Altgeld,  Wednesday, February 17, 2016
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Submitted by nevins.
Joshua Wen (UIUC Math)
Nakajima's quiver varieties: moduli of representations, and framings
Abstract: This will follow Sections 2-3 of Victor Ginzburg's lectures on Nakajima quiver varieties: http://arxiv.org/pdf/0905.0686v2.pdf

Thursday, February 18, 2016

Topology Seminar
11:00 am   in 345 Altgeld Hall,  Thursday, February 18, 2016
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Submitted by cmalkiew.
John Lind (Regensburg)
T-duality and iterated algebraic K-theory
Abstract: T-duality arose in string theory as an equivalence between the physics of two different but suitable related spacetimes. By considering only the underlying topological quantities, T-duality can be distilled into a mathematical theorem which states that the twisted K-theories of certain pairs of circle bundles equipped with U(1)-gerbes are isomorphic via a Fourier-Mukai transform. In this talk, I will describe a generalization of T-duality to higher rank sphere bundles. I will construct twists of the iterated algebraic K-theory of connective complex K-theory by higher gerbes and describe a T-duality isomorphism between the twisted iterated K-theories of a pair of suitably related sphere bundles. (Joint with H. Sati and C. Westerland)

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Thursday, February 18, 2016
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Submitted by sahlgren.
Ciprian Demeter (Indiana University Bloomington)
The proof of Vinogradov's Mean Value Theorem
Abstract: I will present some history, implications to number theory and elements of our proof of VMVT. Joint work with Jean Bourgain and Larry Guth.

Mathematics Colloquium
4:00 pm   in 245 Altgeld Hall,  Thursday, February 18, 2016
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Submitted by seminar.
Stefan Steinerberger (Yale)
New Interactions between Analysis and Number Theory
Abstract: I will tell three unrelated stories describing new mysteries occurring somewhere inbetween Analysis and Number Theory. (1) The Poincare inequality is a cornerstone of mathematical physics (and related to the behavior of vibrating membranes/plates). I will present a curious improvement on the Torus that has a strong number theoretical flavor - even Fibonacci numbers appear. (2) If the Hardy-Littlewood maximal function of f(x) is “easy" to compute, then f(x)=sin(x). This weird definition of sin(x) has applications in delay-differential equations. One would think that any characterization of sin(x) would be straightforward to prove, and yet the only proof I could find of this one relies on a fantastic miracle to occur (and transcendental number theory). (3) An old integer sequence (1,2,3,4,6,8...) defined by Stanislaw Ulam in the 1960s turns out to have very strange properties, giving rise to surprising pictures.

Friday, February 19, 2016

Logic Seminar
4:00 pm   in 345 Altgeld Hall,  Friday, February 19, 2016
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Submitted by ssolecki.
David Fernandez Breton (University of Michigan)
To Be Announced