UIUC Dept. of Mathematics Seminar Calendar

     October 2011          November 2011          December 2011    
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Tuesday, November 29, 2011

Topology Seminar
11:00 am in 241 Altgeld Hall, Tuesday, November 29, 2011

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Submitted by franklan.

Angelica Osorno (University of Chicago)
Stable homotopy 1-types and symmetric Picard groupoids
Abstract: It is a classical result that groupoids model homotopy 1-types, in the sense that there is an equivalence between the homotopy categories, via the classifying space and fundamental groupoid functors. We extend this result to stable homotopy 1-types and symmetric Picard groupoids, that is, symmetric monoidal groupoids in which every object has a weak inverse. Using an algebraic description of symmetric Picard groupoids, we identify the Postnikov data associated to a stable 1-type; the abelian groups π₀ and π₁, and the unique k-invariant. We relate this data to the exact sequences of Picard groupoids developed by Vitale. Joint with Niles Johnson.

Logic Seminar
1:00 pm in 345 Altgeld Hall, Tuesday, November 29, 2011

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Submitted by phierony.

Donald Brower (Notre Dame)
Supersimple 1-based theories
Abstract: Simple theories are the class of theories where forking independence is a nice independence relation. This talk will look at a property of forking which holds in exactly the theories having the so-called weak elimination of hyperimaginaries (WEHI). The nice thing about this property is that it makes the fact that forking is controlled by imaginary elements explicit, allowing us to show that forking and thorn forking independence are identical under WEHI. The motivation behind this work was to prove a nice induction argument to build stable forking formulas between elements of low SU-rank, which will be presented.

Probability Seminar
2:00 pm in Altgeld Hall 347, Tuesday, November 29, 2011

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Submitted by zeng8.

Qiang Zeng (UIUC Math)
Noncommutative Bennett and Rosenthal inequalities
Abstract: In classical probability theory, Bennett's inequality and Rosenthal's inequality are well-known results for the sum of independent random variables. I will talk about the recent joint work with Prof. Marius Junge in this direction. We extend Bennett's inequality to the noncommutative setting and provide an improved version of the noncommutative Rosenthal inequality, essentially due to Nagaev, Pinelis, and Pinelis, Utev for commutative random variables. We obtain new best constants in Rosenthal's inequality. Applying these results to random Fourier projections, we recover and elaborate on fundamental results from compressed sensing, due to Candes, Romberg, and Tao. An application to large deviation inequalities and how noncommutative gaussian random variables may violate the classical equalities will also be discussed.

Algebra, Geometry and Combinatoric
2:00 pm in 345 Altgeld Hall, Tuesday, November 29, 2011

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Submitted by darayon2.

Erik Insko (University of Iowa)
Patch Ideals and Hessenberg varieties
Abstract: Patch ideals encode neighbourhoods of a variety in GLn /B. For the Peterson varieties we determine generators for these ideals and show they are complete intersections, and thus Cohen-Macaulay and Gorenstein. Consequently, we combinatorially describe the singular locus of the Peterson variety; give an explicit equivariant K-theory localization formula; and extend some results of [B. Kostant '96] and of D. Peterson to intersections of Peterson varieties with Schubert varieties. (This is joint work with Alexander Yong) I will also discuss my further work that explores generalizations to other Hessenberg varieties.

Graph Theory and Combinatorics
3:00 pm in 241 Altgeld Hall, Tuesday, November 29, 2011

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Submitted by west.

Jozsef Balogh (UIUC Math)
Counting sum-free sets in Abelian groups
Abstract: A subset of a finite Abelian group is sum-free if it contains no solution to the equation $x+y=z$. We prove a general transference theorem, which allows us to deduce structural results in the sparse setting from stability results in the dense setting. As a consequence, we determine the typical structure and asymptotic number of sum-free sets of size $m$ in Abelian groups $G$ whose order is divisible by a prime $q$ with $q \equiv 2 \pmod 3$, when $m \ge C(q) \sqrt{n \log n}$. This extends and refines a theorem of Green and Ruzsa. In particular, we prove that almost all sum-free subsets of size $m$ are contained in a largest sum-free subset of $G$. We also give a completely self-contained proof of this statement for Abelian groups of even order, which uses spectral methods and a new bound on the number of independent sets of size $m$ in an $(n,d,\lambda)$-graph. To understand the talk, no group theory background is needed beyond the basics. (Joint work with Alon, Morris, and Samotij.)

Mathematics in Science and Society (MSS)
4:00 pm in Altgeld Hall 245, Tuesday, November 29, 2011

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Submitted by kapovich.

David Spivak (MIT)
Categorical Information Theory
Abstract: Classical information theory, as developed by Claude Shannon in 1948, studies how to optimize the quantity of data that can be transmitted across a noisy channel, but it ignores what this information "means". It is clear that information is intended to mean or signify something -- this is its only purpose -- but how can such a thing as meaning be formalized? In this talk I'll discuss how category theory may be useful in this endeavor. Going further, we may postulate that information is always intended as a communication from one party to another (perhaps from an entity to a later version of itself). In this case we can ask, "what is the relationship between the structure of the information being transferred and the structure of the two communicating parties?" I will outline a possible answer to this question in the form of a category-theoretic communication protocol for transferring information between parties. No prior knowledge of category theory will be necessary to understand this talk.