Spring 2024 Analysis Seminar

Organizer: Shaoming Guo

Email: shaomingguo (at) math (dot) wisc (dot) edu

Time: Wed 3:30--4:30

Room: B223

We can use B223 from 4:30 to 5:00 for discussions after talks.

All talks will be in-person unless otherwise specified.

In some cases the seminar may be scheduled at different time to accommodate speakers.

If you would like to subscribe to the Analysis seminar list, send a blank email to analysis+join (at) g-groups (dot) wisc (dot) edu

	Date	Speaker	Institution	Title	Host
1	We, Jan. 24, 2024
2	We, Jan. 31	Sunggeum Hong	Chosun University	The Hörmander multiplier theorem for n-linear operators and its applications	Andreas
3	We, Feb. 7	Donald Stull	University of Chicago	Dimensions of pinned distance sets in the plane	Betsy, Shaoming, and Jake F.
4	We, Feb. 14
	Fr, Feb. 16	Jack Lutz	Iowa State University		Shaoming	department colloquium, 4-5pm
5	We, Feb. 21	Andrei Martinez-Finkelshtein	Baylor	Zeros of polynomials and free probability	Sergey
6	We, Feb. 28	Alex Rutar	University of St. Andrews		Andreas
7	We, Mar. 6	Song-Ying Li	UC-Irvine		Xianghong
8	We, Mar. 13
9	We, Mar. 20
10	We, Mar. 27	Spring recess	spring recess		spring recess
11	We, Apr. 3
12	We, Apr. 10	Victor Bailey	University of Oklahoma		Betsy
13	We, Apr. 17	Jianhui (Franky) Li	Northwestern University		Betsy
14	We, Apr. 24
15	We, May 1

Abstracts

Jack Lutz

Title: Dimensions of pinned distance sets in the plane

Abstract: In this talk, we discuss recent work on the Hausdorff and packing dimension of pinned distance sets in the plane. Given a point x in the plane , and a subset E , the pinned distance set of E with respect to x is the set of all distances between x and the points of E . An important open problem is understanding the Hausdorff, and packing, dimensions of pinned distance sets. We will discuss ongoing progress on this problem, and present improved lower bounds for both the Hausdorff and packing dimensions of pinned distance sets. We also discuss the computability-theoretic methods used to achieve these bounds.

Donald Stull

Title: Dimensions of pinned distance sets in the plane Algorithmic fractal dimensions are computability theoretic versions of Hausdorff dimension and other fractal dimensions. This talk will introduce algorithmic fractal dimensions with particular focus on the Point-to-Set Principle. This principle has enabled several recent proofs of new theorems in geometric measure theory. These theorems, some solving long-standing open problems, are classical (meaning that their statements do not involve computability or logic), even though computability has played a central in their proofs.

Andrei Martinez-Finkelshtein

Title: Zeros of polynomials and free probability

Abstract: I will discuss briefly the connections of some problems from the geometric theory of polynomials to notions from free probability, such as free convolution. More specifically, I will illustrate it with two examples: - real zeros of some hypergeometric polynomials, their monotonicity, interlacing, and asymptotics; - flow of zeros of polynomials under iterated differentiation.