Analysis

The Analysis seminar meets on Wednesdays at 12:00 at room 70 in the Ross Building.
2019 Feb 20

Analysis Seminar: Itay Londner (UBC) "Interpolation sets and arithmetic progressions"

12:00pm to 1:00pm

Location: 

Ross 70
Title: Interpolation sets and arithmetic progressions Abstract: Given a set S of positive measure on the unit circle, a set of integers K is an interpolation set (IS) for S if for any data {c(k)} in l^2(K) there exists a function f in L^2(S) such that its Fourier coefficients satisfy f^(k)=c(k) for all k in K. In the talk I will discuss the relationship between the concept of IS and the existence arithmetic structure in the set K, I will focus primarily on the case where K contains arbitrarily long arithmetic progressions with specified lengths and step sizes.
2018 Oct 24

Analysis Seminar: Boaz Slomka (WIS) "An improved bound for Hadwiger’s covering problem via thin shell inequalities for the convolution square"

12:00pm to 1:00pm

Location: 

Room 70, Ross building
Title: An improved bound for Hadwiger’s covering problem via thin shell inequalities for the convolution square. Abstract: A long-standing open problem, known as Hadwiger’s covering problem, asks what is the smallest natural number N(n) such that every convex body in {\mathbb R}^n can be covered by a union of the interiors of at most N(n) of its translates. Despite continuous efforts, the best-known general upper bound for this number remain as it was more than half a decade ago, and is of the order of \binom{2n}{n}n\ln n.
2018 Nov 18

Special Analysis Seminar: Sergey Denisov (Wisconsin) "Szego theorem for measures on the real line: optimal results and applications"

12:00pm to 1:00pm

Location: 

Manchester building, room 209
Title: Szego theorem for measures on the real line: optimal results and applications. Abstract: Measures on the unit circle for which the logarithmic integral converges can be characterized in many different ways: e.g., through their Schur parameters or through the predictability of the future from the past in Gaussian stationary stochastic process. In this talk, we consider measures on the real line for which logarithmic integral exists and give their complete characterization in terms of the Hamiltonian in De Branges canonical system. This provides a generalization of the
2018 Dec 19

Analysis Seminar: Dmitry Ryabogin (Kent) "On a local version of the fifth Busemann-Petty Problem"

12:00pm to 1:00pm

Location: 

Ross Building, Room 70
Title: On a local version of the fifth Busemann-Petty Problem Abstract: In 1956, Busemann and Petty posed a series of questions about symmetric convex bodies, of which only the first one has been solved. Their fifth problem asks the following. Let K be an origin symmetric convex body in the n-dimensional Euclidean space and let H_x be a hyperplane passing through the origin orthogonal to a unit direction x. Consider a hyperplane G parallel to H_x and supporting to K and let C(K,x)=vol(K\cap H_x)dist (0, G).

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