The default time for the analysis seminar this semester is Wednesday at 2:30-3:30pm in the Seminar Room (French Hall 4206).
If you are interested in giving a talk contact Gareth Speight (Gareth.Speight<at>uc.edu).
To find out more about our department click here.
Michal Wojciechowski (Mathematical Institute of the Polish Academy of Sciences)
Wednesday September 17 at 2:30-3:30pm in the Seminar Room
On the Mityagin-Mirkhil-DeLeeuw theorem with differential constraints
The classical result of the authors mentioned in the title says that the uniform norm of Q(D)f is bounded by the uniform norms of Q_j(D)f, j=1,2,...,k for functions f of compact support if and only if Q is in the span of Q_j's (here Q and Q_j's are homogeneous polynomials of the same degree). In the talk I will present the analogs of this result with additional constraint that the estimate holds only for f being a solution of the differential equation P(D)f=0.
This is joint work with Eduard Curca.
Michael Penrod (University of Cincinnati)
Wednesday September 24 at 2:30-3:30pm in the Seminar Room
The Christ-Goldberg Maximal Operator in Variable Lebesgue Spaces
Mike Roysdon (University of Cincinnati)
Wednesday October 1 at 2:30-3:30pm in the Seminar Room
Comparison Problems for Radon Transforms.
We will discuss comparison problems for L^p norms of pairs of functions based on information exhibited from their Radon transforms. We will discuss how these problems are connected to the celebrated Busmann-Petty problem and Bourgain slicing problem from convex geometry. Based on joint work with Koldobsky and Zvavitch.
Oleg Asipchuk (University of Cincinnati)
October 8 at 2:30-3:30pm in the Seminar Room
Methods of construction of exponential bases on planar domains
The problem of proving (or disproving) the existence of exponential bases on measurable sets of the plane is still largely unsolved. An exponential basis is a set of exponential functions in the form of $\{e^{2\pi i \langle\lambda,\vec x\rangle}\}_{\lambda\in\Lambda}$, where $\Lambda$ is a discrete set of $\mathbb{R}^2$. The main examples of domains where exponential bases exist are shapes that tile the plane by translations, polygons with central symmetry, and unions of rectangles with sides parallel to the axes. We still know nothing about the existence of exponential bases on triangles, irregular polygons, and disks. In my talk, I will introduce an approach for constructing exponential bases on specific types of polygons using approximation by dyadic squares. I will also discuss examples and explore generalizations of the results.
Mike Roysdon (University of Cincinnati)
Wednesday October 15 at 2:30-3:30pm in the Seminar Room
Functional Liftings of Restricted Geometric Inequalities
The equivalence between the dimenion free version of the celebrated Brunn-Minkowski inequality and its functional counterpart, the Prekopa-Leindler inequality, is well known in the literature. Among the applications of these inequalities is that the standard Guassian probability measure on \R^n is log-concave with respect to Minkowski summation and the Gaussian concentration phenomena. In 2010, it was conjectured by Gardner and Zvavitch that, by restricting one's considerations to origin symmetric convex sets rather than general Borel measurable sets, the Gaussian measure is, in fact, (1/n)-concave. This conjecture was verified in 2020 by Eskenazis and Moschidis.
Inspired by the above, in this talk, we consider the term "sup-convolutions," and show that functional inequalities (aka PL) that enjoy an interpretation as sup-convolution inequalities can be deduced from the special case of indicator functions corresponding to a geometric inequality (aka BM). As consequences of our discussion we derive a Borell-Brascamp Lieb inequality for the Gaussian Brunn-Minkowski inequality and give a functional analog of the log-Brunn-Minkowski conjecture (2010) if time permits.
Joint work with Malliaris, Melbourne and Roberto.
Dmitry Ryabogin (Kent State University)
Wednesday October 22 at 2:30-3:30pm in the Seminar Room
On the homothety conjecture with the homothety coefficient $1/2$.
Let $K=-K$ be an origin-symmetric plane convex body and let $1/2 K=K_{\delta}$ for some $\delta\in (0,1/2)$; $K_{\delta}$ is a body of flotation of $K$.
We will discuss a recent proof of Ayala-Figueroa, Jer\'onimo-Castro and Jimenez-Lopez, who showed that under the above conditions $K$ must be an ellipsoid.
Karl Liechty (DePaul University)
Wednesday October 29 at 2:30-3:30pm in the Seminar Room
The six-vertex model with domain wall and related boundary conditions via orthogonal polynomials.
The six-vertex model is a well-known model in 2d statistical mechanics which, for certain boundary conditions, admits a determinantal formula for its partition function. I’ll discuss recent and current work on the asymptotic analysis of orthogonal polynomials arising from these determinantal formulas to obtain limit theorems for the model. I’ll discuss joint work with Vadim Gorin, Jimmy He, and Umid Ahmadali.
Michael Goldberg (University of Cincinnati)
Tentative for November