The conference will feature ten lectures delivered by Dr. Svitlana Mayboroda
Besides these lectures, we plan several 45minute long lectures. We also plan a poster session (with posters printed at FSU for free!).
The list of speakers includes:
Time  Monday  Tuesday  Wednesday  Thursday  Friday  

1010:45 
S.M. 
S.M. 
S.M. 
S.M. 
S.M. 

10:4511:00 
Questions 
Questions 
Questions 
Questions 
Questions 

11:0011:15 
Break 
Break 
Break 
Break 
Break 

11:1512:00 
S.M. 
S.M. 
S.M. 
S.M. 
S.M. 

12:0012:15 
Questions 
Questions 
Questions 
Questions 
Questions 

12:152:15 
Lunch 
Lunch 

Lunch 
Lunch 

2:153:00 
David 
Tolsa 

Badger 
Li 

3:003:15 
Questions 
Questions 

Questions 
Questions 

3:153:30 
Break 
Break 

Break 
Break 

3:304:15 
Engelstein 
Garnett 

Davey 
Feneuil 

4:154:30 
Questions 
Questions 

Questions 
Questions 

4:304:45 
Break 
Break 




4:455:30 
Barton 
Zhao 




6:00  Conference Dinner 
Some preliminary materials can be found here
Matthew Badger, University of Connecticut
Title: Bourgain's constants for harmonic and caloric measures
Abstract: Bourgain’s constant is the largest number b_{n} such that the dimension of harmonic measure on any ndimensional domain is at most n − b_{n}. Jones and Wolff (1988) proved that b_{2} = 1. When n ≥ 3, Bourgain (1987) proved that b_{n} > 0 and Wolff (1995) proved that b_{n} < 1. In recent work, joint with Alyssa Genschaw, we prove that Bourgain’s theorem on the dimension of harmonic measure persists in the setting of the heat equation. Further, refining Bourgain’s original outline, we prove asymptotic lower bounds on Bourgain’s constant in high dimensions and explicit lower bounds on Bourgain’s constant in dimensions 3 and 4.
Ariel Barton, University of Arkansas
Title: Higher order elliptic partial differential equations with lower order terms
Abstract: Operators of the form Lu = ∇ ⋅ (A∇u), that is, second order linear differential operators in divergence form, are by now very well understood. Two important generalizations are higher order operators Lu = ∇^{m} ⋅ (A∇^{m}u), for m ≥ 2 an integer, and operators with lower order terms Lu = ∇ ⋅ (A∇u) + ∇ ⋅ (Bu) + C ⋅ ∇u + Du. In this talk we discuss some first attempts to combine the two generalizations and study higher order operators with lower order terms.
Blair Davey, Montana State University
Title: Exponential Decay Estimates for Fundamental Matrices of Generalized Schrödinger Systems
Abstract: In this work, we consider the behavior of the fundamental matrices associated to systems of generalized Schrödinger operators. The Schrödinger operators that we deal with have leading coefficients that are bounded and uniformly elliptic, and they have zerothorder potentials that belong to certain reverse Hölder matrix classes. By exploring the properties of reverse H\"older matrices and building on the ideas of Shen, Mayboroda and Poggi, we establish the existence of fundamental matrices and prove upper and lower exponential decay estimates for them. This talk covers joint work with Josh Isralowitz.
Guy David, Université de Paris Sud
Title: An elliptic operator on the fourcorner Cantor set, with elliptic measure proportional to H^{1}
Abstract: The lecture is about the construction, with S. Mayboroda, of an elliptic operator L = − div(a(x)∇) on the complement of a onedimensional Cantor set E in the plane, so that the corresponding elliptic measure on E is the product of the length measure H^{1 }by a function which is bounded and bounded from below. The main idea is to build the Green function by hand, deduce the function a, and use the fractal invariance to prove it is elliptic. I’ll try to explain why we care about such examples.
Max Engelstein, University of Minnesota, TwinCities
Title: Harmonic analysis tools for free boundary problems
Joseph Feneuil, Université ParisSaclay
Title: Generalized Carleson perturbations of elliptic operators.
Abstract: Let L_{0}=div A_{0} ∇ be a uniformly elliptic operator on a domain Ω, and we assume that the elliptic measure ω_{L0} is A_{∞}absolutely continuous with respect to a doubling measure σ on the boundary ∂Ω. We are interested in perturbations L_{1} of L_{0} that preserve the A_{∞}absolute continuity of the elliptic measure w.r.t. σ.
We shall discuss the literature on “Carleson perturbations of elliptic operators”, from the initial work of Fefferman, Kenig and Pipher in 1991, to the recent article of Bruno Poggi and the speaker. In the later paper, we proposed an extended notion of Carleson perturbations, and we worked on a wide range of domains and elliptic operators by assuming only a suitable elliptic theory.
John Garnett, UCLA
Title: Carleson measure estimates for bounded harmonic functions, without Ahlfors regularity assumptions.
Linhan Li, University of Minnesota, TwinCities
Xavier Tolsa, ICREA  Universitat Autònoma de Barcelona  CRM
Title: The regularity problem for the Laplace equation and boundary Poincaré inequalities in rough domains
Abstract: Given a bounded domain Ω ⊂ ℝ^{n}, one says that the L^{p}regularity problem is solvable for the Laplace equation in Ω if, given any continuous function f defined in ∂Ω and the harmonic extension u of f to Ω, the nontangential maximal function of the gradient of u can be controlled in L^{p} norm by the tangential derivative of f in ∂Ω. Up to quite recently this was only known to hold for Lipschitz domains (in some range of p’s). In my talk I will explain a recent result with Mihalis Mourgoglou where we show that the L^{p}regularity is also solvable in more general domains, such as 2sided chordarc domains. In the solution of this problem, the Poincaré inequality in the boundary of the domain plays an important role. I will also discuss this issue and a related joint result with Olli Tapiola where we show that the boundaries of 2sided chordarc domains support 1Poincaré inequalities.
Zihuy Zhao, University of Chicago
The main part of the conference will be held at the HCB building.
There are several hotels within walking distance from campus. There are also plenty of Airbnb and Vrbo options.
The following hotels gave a discounted rate for the conference participants:
Aloft Tallahassee Downtown Reserve
Hampton Inn & Suites Reservation Link Reserve
Seminole Cafe and the Suwanee room, two buffetstyle cafeterias, are located on Campus at five to ten minutes walking distance from the Department of Mathematics. Both places offer very good pricing and choice of food (in particular, vegetarian), and serve Breakfast, Lunch, and Dinner. Moreover, there are many independent dining options within 1 mile from campus, serving a wide variety of food. We particularly encourage the participants to check out the restaurants located on and around Gaines Street.
Florida State University uses the eduroam network, and the participants will be able to join it. In addition, guest accounts for the FSU network will be created for the participants, which will provide highspeed internet access. Access to printers and computer lab will be provided as well, in case the participants will need to download, copy or print papers or other materials.
CBMS’22 is supported by
FLORIDA STATE UNIVERSITY
COLLEGE OF ARTS & SCIENCES