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December 1st, 2009 (11:15am - 12:05pm)

Seminar: Combinatorics/Partitions Seminar
Title: Enumeration of the Distinct Shuffles of Permutations.
Speaker: Dr. Camillia Smith Barnes, Sweet Briar College
Location: MB106

A shuffle of two words is a word obtained by concatenating the two original words in either order and then sliding any letters from the second word back past letters of the first word, in such a way that the letters of each original word remain spelled out in their original relative order. Examples of shuffles of the words 1234 and 5678 are, for instance, 15236784 and 51236748. In this talk, I enumerate the distinct shuffles of two permutations of any two lengths, where the permutations are written as words in the letters 1,2,3,...,m and 1,2,3,...,n, respectively.

December 1st, 2009 (02:30pm - 03:45pm)

Seminar: Logic Seminar
Title: Mass problems and measure-theoretic regularity
Speaker: Stephen G. Simpson, Pennsylvania State University
Location: MB315
Abstract: http://www.math.psu.edu/simpson/papers/massmtr.pdf

According to Y. Medvedev and A. Muchnik, a mass problem is a set of Turing oracles which are regarded as the "solutions" of the problem. A mass problem is said to be weakly reducible to another mass problem if any "solution" of the second problem can be used as a Turing oracle to compute some "solution" of the first problem. For each recursive ordinal number alpha, we consider the problem B_alpha of regularizing sets at level alpha + 2 of the effective Borel hierarchy. Thus, to solve B_alpha means to find a countable union of closed sets included in a given set at level alpha + 2 which is of the same measure as the given set. We show that this problem is Sigma^0_3. From this it follows that this family of problems is embeddable in the lattice of weak degrees of mass problems associated with effectively closed sets in Euclidean space.

December 1st, 2009 (02:30pm - 03:30pm)

Seminar: GAP Seminar
Title: A Lefschetz number theorem for differential operators
Speaker: Ajay Ramadoss, Cornell University
Location: MB106

Let $X$ be a compact, complex manifold and let $E$ be a holomorphic vector bundle on $X$. Let $ Diff^{\bullet}(E)$ be the Dolbeault resolution of the sheaf of holomorphic differential operators on $E$. A construction due to Feigin, et. al , gives a linear functional on the $0$-th Hochschild homology of $Diff^{\bullet}(E)$. This functional "extends" to a linear functional on the "completed" $0$-th Hochschild homology of $Diff^{\bullet}(E)$ ,thereby giving a linear functional $I_E$ on the top cohomology $\text{H}^{2n} (X,\mathbb C)$ of $X$ with complex coefficients. The main result is that $I_E$ is just integration over $X$. As a consequence, one obtains a Lefschetz number formula for a global holomorphic differential operator on $E$.

December 1st, 2009 (03:30pm - 06:00pm)

Seminar: Working Seminar: Dynamics and its Working Tools
Title: Attractors, coding and reduction theory for new general classes of continued fractions, I.
Speaker: Svetlana Katok, Penn State
Location: MB216

December 2nd, 2009 (12:15pm - 01:15pm)

Seminar: Geometry Luncheon Seminar
Title: Geometry Lunch Seminar
Speaker: Shmuel Weinberger, University of Chicago
Location: MB114

December 3rd, 2009 (11:00am - 12:30pm)

Seminar: Teaching Seminar
Title: What worked... What Didn't
Speaker: Mary Erickson
Location: MB114

This Teaching Seminar will be an opportunity for sharing. Mary Erickson will host an open discussion of teaching techniques that worked... and those that fell flat. Please bring ideas to share from your own experiences this semester. Awards will be given for the best student excuses (from this semester... no fair digging back into the archives for golden oldies). We'll also take this opportunity to look forward to 2010. Discussion will continue over lunch.

December 3rd, 2009 (11:15am - 12:05pm)

Seminar: Algebra and Number Theory Seminar
Title: Geometric structure in the representation theory of p-adic SLN
Speaker: Roger Plymen, University of Manchester
Location: MB106

In the general theory of automorphic forms, a crucial role is played by representations of the local groups, one for each place. This will include p-adic groups G such as GL(n) or SL(n). It is sometimes assumed that the local Langlands conjectures will answer any question in the representation theory of G. On looking more closely, this turns out not to be the case. An alternative (conjectural) approach is outlined in [1]. This is based on the elementary concept of the extended quotient of an algebraic variety by a finite group. This will be a non-technical talk, in which I will attempt to explain our approach via two examples: SL(2) and SL(n) where n is a prime number. [1] Geometric structure in the representation theory of p-adic groups, Anne-Marie Aubert, Paul Baum, Roger Plymen, C.R. Acad. Sci. Paris 345 (2007) 573-578.

December 3rd, 2009 (02:30pm - 03:30pm)

Seminar: MASS Colloquium
Title: Topology and Social Choice
Speaker: S. Weinberger, University of Chicago
Location: MB114
Abstract: http://

Often one is in the situation when there are many agents or voters who each have an idea of what should be done, and we must find some way to combine their preferences and decide what "society wants". (This might even be what happens in an individual, where various subroutines in the brain each calculate a preference based on the function they are designed to "want" to optimize.) It turns out that this is rarely possible, but that one can have a lot of geometric and topological fun thinking about and manipulating such elections.

December 3rd, 2009 (02:30pm - 03:30pm)

Seminar: Noncommutative Geometry Seminar
Title: TBA
Speaker: Shmuel Weinberger, Chicago
Location: MB106

December 3rd, 2009 (02:30pm - 03:20pm)

Seminar: MASS Colloquium
Title: Topology and Social Choice
Speaker: S. Weinberger, University of Chocago
Location: MB113

Often one is in the situation when there are many agents or voters who each have an idea of what should be done, and we must find some way to combine their preferences and decide what "society wants". (This might even be what happens in an individual, where various subroutines in the brain each calculate a preference based on the function they are designed to "want" to optimize.) It turns out that this is rarely possible, but that one can have a lot of geometric and topological fun thinking about and manipulating such elections.

December 3rd, 2009 (04:00pm - 05:00pm)

Seminar: Department of Mathematics Colloquium
Title: Poincare duality and aspherical manifolds
Speaker: S. Weinberger, University of Chicago
Location: MB114

The key homological feature of manifolds is Poincare duality. More than forty years ago Wall had conjectured that when this property holds in group cohomology, there is a natural geometric reason: the group is the fundamental group of a manifold whose universal cover is contractible. Although this conjecture is neither proved nor disproved, there has been some recent progress that I will hope to explain.

December 4th, 2009 (03:35pm - 04:25pm)

Seminar: Computational and Applied Mathematics Colloquium
Title: TBA
Speaker: Antonio Sa Barreto, Department of Mathematics, Purdue University
Location: MB106

December 7th, 2009 (03:30pm - 05:30pm)

Seminar: Center for Dynamics and Geometry Seminar
Title: Monotonicity of topological entropy under normalised Ricci flow
Speaker: Dan Thompson, Penn State
Location: MB106

We prove that the topological entropy of the geodesic flow for a compact Riemannian manifold (M, g) decreases as the metric g evolves under the normalised Ricci flow provided that M admits a metric of constant negative sectional curvature, and g is in a sufficiently small C^2 neighbourhood of the constant curvature metric. More generally, the same phenomenon occurs if g satisfies a certain negative curvature pinching condition, where the pinching constant depends on both the dimension and the diameter of (M, g). This provides an affirmative answer to an open question posed in Manning's paper 'The volume entropy of a surface decreases along the Ricci flow' [Ergodic Theory Dynam. Systems, 24:171-76, 2004].

December 7th, 2009 (04:00pm - 05:00pm)

Seminar: Student Geometric Functional Analysis Seminar
Title: TBA
Speaker: TBA
Location: MB315
Abstract: http://

December 8th, 2009 (02:30pm - 03:30pm)

Seminar: GAP Seminar
Title: Algebraic structures connected with pairs of compatible associative algebras
Speaker: Alexander Odesski, Brock University
Location: MB106

We study associative multiplications in semi-simple associative algebras over C compatible with the usual one or, in other words, linear deformations of semi-simple associative algebras over C. It turns out that these deformations are in one-to-one correspondence with representations of certain algebraic structures, which we call M-structures in the matrix case and PM-structures in the case of direct sums of several matrix algebras. We also investigate various properties of PM-structures, provide numerous examples and describe an important class of PM-structures. The classification of these PM-structures naturally leads to affine Dynkin diagrams of A, D, E-type.

December 8th, 2009 (03:30pm - 06:00pm)

Seminar: Working Seminar: Dynamics and its Working Tools
Title: Attractors, coding and reduction theory for new general classes of continued fractions, II.
Speaker: Svetlana Katok, Penn State
Location: MB216

December 10th, 2009 (11:15am - 12:05pm)

Seminar: Algebra and Number Theory Seminar
Title: Statistics for the traces of cyclic p-covers of curves over finite fields
Speaker: Chantal David, IAS Princeton
Location: MB106

We study in this talk the variation of the trace of the Frobenius endomorphism associated to curves C which have a cyclic p-fold cover over F_q as the curves vary in an irreducible component of the moduli space of cyclic p-covers of a fixed genus g. We show that for q fixed and g increasing, the limiting distribution of the trace of the Frobenius endomorphism is equal to the sum of q+1 independent random variables taking the value 0 with probability (p-1)/(q+p-1) and each of the p-th roots of unity with equal probability q/(p(q+p-1)). This generalises the work of Kurlberg and Rudnick who considered the same limit for hyperelliptic curves (i.e. cyclic 2-fold covers). We also show that when both the genus and q go to infinity, the normalized trace has a standard complex Gaussian distribution. This is joint work with A. Bucur, B. Feigon and M. Lalin.

December 10th, 2009 (05:15pm - 06:15pm)

Seminar: Topology/Geometry Seminar
Title: The 1-nullity distribution on a sasakian manifold
Speaker: Philippe Rukimbira, FIU
Location: MB106

It is conjectured that the dimension of the 1-nullity distribution on a (2n+1)-dimensional, closed sasakian manifold is 1, 3 or (2n+1)-dimensional. In our talk, we show that its dimension is no more than $n$.

December 18th, 2009 (03:35pm - 04:25pm)

Seminar: Computational and Applied Mathematics Colloquium
Title: TBA
Speaker: James P. Kelliher, University of California, Riverside
Location: MB106

TBA