| 7 (Friday) | Probability Seminar
Does the Brownian sheet have multiple points?
Carl Mueller, UR
3 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 algebras
Fatima 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 Seminar
On 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 Seminar
Zeros of the derivatives of the Riemann zeta function
YOONBOK 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 transform
Eli 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 Colloquium
On Arithmetic Progressions and Sharp Affine-Invariant Inequalities
Michael Christ, University of California, Berkeley
2 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 Seminar
About thinning invariant partition structures
Shannon Starr, University of Alabama
3:00 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 Talk
Uniqueness of Stochastic Differential Equations
Alejandro Gomez
2:00 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 Seminar
J-flow in Kahler geometry
Mijia 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 Seminar
The Bogomolov property and equidistribution
Paul 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 Seminar
Random graphs and complex networks
Zhuang Hou, Rochester
3:00 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.
|
![[Edit Mode]](/images/edit.gif)
![[Home]](/images/home.gif)
![[Previous]](/images/prev.gif)
![[Next]](/images/next.gif)