September 2012
Su Mo Tu We Th Fr Sa
1
2 3 4 5 6 7 8
9 10 11 12 13 14 15
16 17 18 19 20 21 22
23 24 25 26 27 28 29
30

## Events for September 2012:

 7 (Friday) Probability SeminarDoes the Brownian sheet have multiple points? Carl Mueller, UR3 pm, Hylan 1106A A process $X$ has $k$-multiple points if there are (random) times $t_1,...,t_k$ for which $X(t_1)=...=X(t_k)$. This topic is a classical question in probability with many connections to the behavior of processes. The Brownian sheet is a generalization of Brownian motion which is a test bed for studying more general processes. Surprisingly, necessary and sufficient criteria for the Brownian sheet to have k-multiple points were not known. In this talk we will outline an answer to this question. 11 (Tuesday) Geometry Seminar Contact quotients, differential forms, and Jacobi algebrasFatima Mahmood (University of Rochester) 2 pm, Hylan 1106A Let M be a cooriented contact manifold and G a compact connected Lie group that acts smoothly on M preserving the cooriented contact structure. The contact quotient of M by G is in general a singular space, but it has a stratification into contact manifolds. In this talk, we will introduce a complex of differential forms on the total quotient space whose corresponding cohomology ring is isomorphic to its (Cech, singular) cohomology ring with real coefficients. We will also discuss how the 0-forms on the quotient form a Jacobi algebra. Number Theory Seminar''Questions in combinatorial number theory". Giorgis Petridis, U of Rochester 3:30 pm, Hylan 1106A Questions in combinatorial number theory GIORGIS PETRIDIS The objective of the talk is to introduce some interesting problems in additive and combinatorial number theory. The talk will be relatively light in mathematical content and will be aimed at a wide audience. It is hoped that it will provide a gentle introduction to the subject. We will discuss problems concerning sumsets. For a finite non-empty set A in a commutative group its sumset is defined by: A + A = {a + b : a, b ∈ A} . It is essential to assume that the size of A + A is given in terms of the size of A, as otherwise most questions become trivial. Our aim will be to get upper bounds on the size of the difference set A−A := A+(−A); and the iterated sumset hA := A+(h−1)A for a fixed positive integer h. The unifying factors of the problems is that the existing upper bounds are both easy to prove, are valuable in applications and are reasonably accurate. We will derive them, quickly describe some of the applications they have found and discuss what improvements may be possible. 14 (Friday) Topology Seminar Browder's work on the Kervaire invariant.Doug Ravenel (University of Rochester)4 pm, Hylan 1106A In 1969 Bill Browder proved what was for 40 years the best theorem about the Kervaire invariant problem. This talk will describe its historical setting and outline the proof. Some pictures from the conference in honor of his retirement last May in Princeton will be shown. 18 (Tuesday) Geometry SeminarOn volume growth of gradient steady Ricci solitons. Peng Wu (Cornell University) 2:00 pm, Hylan 1106A We prove that if the potential function of a gradient steady Ricci soliton satisfies a uniform condition, then the gradient steady Ricci soliton has at most Euclidean volume growth. Algebra/Number Theory SeminarZeros of the derivatives of the Riemann zeta functionYOONBOK LEE (U of R)3:30 pm, Hylan 1106A In this talk we discuss various properties of the zeros of the derivatives of the Riemann zeta function. For example, the Riemann hypothesis implies that ζ(k)(s) has only finitely many zeros in the vertical strip 0 < Rs < 1/2. We will show that the number of zeros of ζ(k)(s) in the region Rs < σ and T < Is < 2T is smaller than T1+c(σ−1/2)(logT)2 for σ < 1/2 − AlogloglogT/loglogT. Here k > 1, A > 1 and the constant c satisfies 0 < c < (1 − 1/A)/2. 20 (Thursday) Analysis Seminar Relations between the Fourier transform and the Hilbert transformEli Liflyand 3:30 pm, Hylan 1106A In this talk we discuss various conditions of the integrability of the Fourier transform of a function of bounded variation and their connections to the behavior of the Hilbert transform of a related function. 21 (Friday) Math ColloquiumOn Arithmetic Progressions and Sharp Affine-Invariant InequalitiesMichael Christ, University of California, Berkeley2 pm, Hylan 1106A Three classical inequalities in geometry and analysis are those of Brunn-Minkowski, Riesz-Sobolev, and Young. In each, the size of a set is quantified using Lebesgue measure. Each of these inequalities has the rare feature of invariance under the full group of all affine symmetries of Euclidean space. These inequalities and their long histories will be reviewed. Each inequality is known to be an exact equality only for sets with particular structure. For each, this is a class of sets which can (and should) be regarded as n-dimensional continuum analogues of finite arithmetic progressions of minimal rank. We will introduce recent results which characterize those sets that nearly achieve exact equality. These results rely on an interplay between analysis, the geometry of Euclidean space, and --- crucially --- structural input from additive combinatorics. Three fundamental results from additive combinatorics will be reviewed, and connections with analysis will be outlined. Probability SeminarAbout thinning invariant partition structuresShannon Starr, University of Alabama3:00 pm, Hylan 1106A A random partition structure is a random measure where you only care about the sizes of the atoms. Two examples of applications of this definition are: the fraction of the whole of various market participants in mathematical models of finance, as in work of Fernholz and Karatzas, or allele/phenotype populations in population genetics, as in work of Kingman. The simplest type of dynamics, called uncorrelated kick dynamics'' was studied by (1) Aizenman and Ruzmaikina, (2) Arguin, and (3) Shkolnikov. With Ang Wei and Brigitta Vermesi, we considered a different dynamics called thinning.'' In this certain market participants or subpopulations are deleted, entirely, rather than just being suppressed. I will describe this and our partial results. We have a main conjecture whose missing proof seems to turn on tightness. 24 (Monday) Defense TalkUniqueness of Stochastic Differential EquationsAlejandro Gomez2:00 pm, Hylan 1106A This is part of the work I did during my PhD studies. The presentation will consist of three parts. The first is a study of an equivalence relation of binary matrices ( matrices with 0-1 entries ), which is independent of the other two parts. The second and third are based on the study of uniqueness for two different stochastic differential equations, one of which is a non-linear stochastic partial differential equation and the other is a second order stochastic differential equation related to the wave equation. The presentation will range from elementary to relatively advanced, but several interesting concepts will be discussed in a non-technical and very intuitive way for the audience to enjoy. ------------------------------------ 25 (Tuesday) Geometry SeminarJ-flow in Kahler geometryMijia Lai (University of Rochester) 2:00 pm, Hylan 1106A In this talk, I will first survey general results for the J-flow studied in Kahler geometry, then discuss some convergence problems. Algebra/Number Theory SeminarThe Bogomolov property and equidistributionPaul Fili (Rochester)3:30 pm, Hylan 1106A Certain fields have "nicer" properties than others: for example, number fields satisfy the Northcott property, while fields defined by splitting conditions such as being totally real or totally p-adic satisfy weaker analogues like the Bogomolov property for the standard height. In this talk we'll discuss how the ideas of equidistribution of points of small height can help us detect when the Bogomolov property is present, and we'll use these same ideas to establish a new bound for the limit infimum of the height of all totally real numbers. This appears to be the first such bound on the entire field of totally real numbers since Schinzel's 1973 bound away from zero. (Joint work with Z. Miner.) 28 (Friday) Probability SeminarRandom graphs and complex networks Zhuang Hou, Rochester3:00 pm, Hylan 1106A The theory of random graphs was first studied by Erdos and Renyi in 1959-1960, and lies at the intersection of probability theory and graph theory. The study of complex networks plays an important role in science. Telephone network, social relations, World-Wide Web and internet are examples. From empirical work, we find that networks have fascinating properties, for instance, the small world property. In this talk, I will describe the small world phenomenon in random graphs.