
Notices
 The conference will take place in Room 1503 (5th floor, Building 1).
 KIAS booked the rooms at the Plaza hotel for all speakers based on the registration forms.
A shuttle service between the Plaza Hotel and KIAS will be provided (at 8:45 AM on Monday and at 9 AM on other days).
 KIAS booked the rooms at Benikea Hotel KP for all NSF supported nonspeakers based on the registration forms.
 The conference banquet will take place the evening of May 9th at Korea House.
All international participants are invited.
 Wednesday afternoon, there will be the option to sign up for an excursion to
the Secret Garden (cost: 8K KRW per person) or have free time to explore the city.
Organizers
Contact Information:
pj2017@math.stonybrook.edu
Supported by
Samsung Science &
Technology Foundation

Korea Institute
for Advanced Study

National Science Foundation


Department of Mathematics
Yale University

Downloadable Materials:
Program and Abstracts,
Poster
Scope.
Over the last four decades Peter Jones has demonstrated the power of using ideas from real and harmonic analysis to solve difficult problems in complex and functional analysis, geometric measure theory, conformal dynamics, conformal probability and geometrically based applied mathematics.
Although much of this work is highly technical, it is usually motivated by simple geometric or analytic ideas.
The conference will explore the areas listed above from the perspectives of both established experts and younger researchers, with an emphasis on interactions between areas and the basic themes that recur in each of them.
Specific topics will include recent advances in harmonic measure, SchrammLoewner Evolutions (SLE), Gaussian Free Fields (GFF), rectifiability, and the analysis of big data.
Travel Information
 The Plaza Hotel
 KIAS booked the rooms at the Plaza hotel for all speakers based on the registration forms. A shuttle service between the Plaza Hotel and KIAS will be provided.
 Incheon International Airport  the Plaza Hotel
 By KAL (Korean Air Lines) Limousine Bus 6701
The journey takes about 7080 minutes. (Bus fare: 16K KRW).
Departs from Incheon airport's KAL limousine bus stop.
Located at Exit No. 4A or Exit No. 10B on the 1st floor.
You can pay the driver with cash.
(Bus Tickets are available at both Incheon airport's KAL desk and hotel's front desk / bell desk.)
Stops
Incheon International Airport → Koreana → The Plaza Hotel → …
Departing time at Exit No. 4A
04:50 05:18 06:07 06:51 07:22 07:45 08:09 08:32 09:01 09:23 09:50 10:09 10:31 10:50 11:11 11:31 11:50
12:11 12:30 12:57 13:17 13:36 13:53 14:18 14:43 15:11 15:36 16:00 16:23 16:45 17:11 17:29 17:51
18:12 18:37 18:56 19:23 19:51 20:22 20:52 21:24 22:04 22:49
 By Taxi
Deluxe Taxi: about an hour (approx. 100K KRW  toll fees included)
Normal Taxi: about an hour (approx. 70K KRW  toll fees included)
 Benikea Hotel KP
 KIAS booked the rooms at Benikea Hotel KP for all NSF supported nonspeakers based on the registration forms.
 Incheon International Airport  Benikea Hotel KP

By Limousine Bus 6002
The most convenient limousine bus to KIAS and BENIKEA Hotel KP is No. 6002, bound for Cheongnyangni.
The bus stops at the airport are "5B" and "12A".
The fare is 10K KRW, and the bus departs every 12 to 15 minutes.
The first bus departs from the airport at 05:30 and the last bus departs at 23:30.
You can get off at 'Cheongnyangni Station' bus stop, which will take about an hour and half.
Take a taxi to reach KIAS or BENIKEA Hotel KP.
 It takes about 15 minutes from BENIKEA Hotel KP to KIAS on foot.
 Holiday Inn
 Incheon International Airport  Holiday Inn
Please take an airport limousine bus from the Incheon int'l airport, which is one of the fastest and most convenient ways to the hotel.

By Limousine Bus 6101
Buy limousine bus tickets at the ticket office, bound for Dobong/Seongbuk(Bus No. 6101)
 Tickets can be purchased both inside and outside of the airport.
Board a bus bound for Dobong/ Seongbuk at either bus stop 3B or 10A.
The fare is 15K KRW, and the bus departs every 15 to 25 minutes.
The first bus departs from the airport at 05:50 and the last bus departs at 23:00.
The journey takes about 8090 minutes.
Main stops : Incheon International Airport → Gimpo International Airport → Jeongneung → Gireum Station →
Holiday Inn Seoul Seongbuk.
Invited Speakers
Name  Home Institution  Visit Dates 
Jonas Azzam  University of Edinburgh  May 07  14 
Michael Benedicks  KTH  May 07  13 
Ilia Binder  University of Toronto  May 06  12 
Mario Bonk  UCLA  May 08  13 
Krzysztof Burdzy  University of Washington  May 07  11 
Bertrand Duplantier  IPhT, ParisSaclay Univ.  May 06  13 
John Garnett  UCLA  May 07  13 
Maria Jose Gonzalez  University of Cadiz  May 07  13 
Alexander Iosevich  University of Rochester  May 08  12 
Nets Hawk Katz  Caltech  May 06  13 
Aleksandr Logunov  Tel Aviv University  May 07  13 
Mauro Maggioni  Johns Hopkins University  May 06  14 
Nikolai Makarov  Caltech  May 05  13 
Svitlana Mayboroda  University of Minnesota  May 08  15 
Paul Müller  J. Kepler Universität Linz  May 05  14 
Maria Cristina Pereyra  University of New Mexico  May 07  13 
Alexei Poltoratski  Texas A&M University  May 07  13 
Luke Rogers  University of Connecticut  May 07  13 
Steffen Rohde  University of Washington  May 07  14 
Eero Saksman  University of Helsinki  May 06  13 
Wilhelm Schlag  University of Chicago  May 06  13 
Stanislav Smirnov  Geneva, St. Petersburg U.  May 06  11 
Misha Sodin  Tel Aviv University  May 07  13 
Stefan Steinerberger  Yale University  May 07  12 
Xavier Tolsa  U. Autonoma de Barcelona  May 07  13 
Lesley Ward  Univ. of South Australia  May 06  13 
Dapeng Zhan  Michigan State University  May 07  11 
Schedule
 Monday  Tuesday  Wednesday  Thursday  Friday 
09:45  10:00  Opening Remarks  
10:00  10:45 
Smirnov  Garnett  Burdzy  Katz  Bonk 
11:00  11:45 
Duplantier  Azzam  Gonzalez  Binder  Ward 
12:00  12:45  Lunch  Maggioni  Lunch 
13:00  13:55  Discussion and Poster Session  Lunch  Discussion and Poster Session 
14:00  14:45 
Makarov  Iosevich  Free Time  Steinerberger  Poltoratski 
14:50  15:35 
Rohde  Pereyra  Logunov  Rogers 
 Coffee Break and Discussion  Coffee Break and Discussion 
16:05  16:50 
Zhan  Benedicks  Mayboroda  Müller 
17:00  17:45 
Saksman  Sodin  Schlag  Tolsa 
19:00  21:30   Banquet  
Themes
Monday 
Tuesday/Friday 
Wednesday 
Thursday 
SLE/Math Physics 
Complex/Real/Harmonic Analysis 
Probability/Applied Math 
Harmonic Analysis/PDE 
Titles and Abstracts
Monday: SLE/Math Physics
Stanislav Smirnov (University of Geneva, St. Petersburg University): Clusters, loops and trees
We will report on our ongoing work with Antti Kemppainen aimed at describing geometrically the scaling limit of the critical Ising model.
Bertrand Duplantier (Institute for Theoretical Physics, ParisSaclay University): CLE Exteme Nesting and Liouville Quantum Gravity
We describe recent advances in the study of SchrammLoewner Evolution (SLE), a canonical model of noncrossing random paths in the plane, and of Liouville Quantum Gravity (LQG), a canonical model of random surfaces in 2D quantum gravity. The latter is expected to be the universal, conformally invariant, continuum limit of random planar maps, as weighted by critical statistical models. SLE multifractal spectra have natural analogues on random planar maps and in LQG. An example is extreme nesting in the Conformal Loop Ensemble (CLE), as derived by Miller, Watson and Wilson, and extreme nesting in the $O(n)$ loop model on a random planar map, as derived recently via combinatorial methods. Their respective large deviations functions are shown to be conjugate of each other, via a continuous KPZ transform inherent to LQG.
Joint work with Gaetan Borot and Jérémie Bouttier.
Nikolai Makarov (Caltech): Etudes for the inverse spectral problem
Steffen Rohde (University of Washington): Conformal laminations and trees
Conformal maps $f$ of the unit disc $D$ have a continuous extension to the circle if (and only if) the boundary of the image $f(D)$ is locally connected. This extension induces an equivalence relation on the circle by declaring that $x \sim y$ if $f(x)=f(y).$ Which equivalence relations on the circle arise in this way? After a brief discussion of the history and motivation, I will present a characterization under the additional assumption that $f(D)$ is a John domain whose complement has empty interior.
Dapeng Zhan (Michigan State University): SLE loop measures
We use Minkowski content (i.e., natural parametrization) of SLE to construct several types of SLE$_\kappa$ loop measures for $\kappa\in(0,8)$. First, we construct rooted SLE$_\kappa$ loop measures in the Riemann sphere $\hat{\mathbb C}$, which satisfy Möbius covariance, conformal Markov property, reversibility, and spacetime homogeneity, when the loop is parameterized by its $(1+\frac \kappa 8)$dimensional Minkowski content. Second, by integrating rooted SLE$_\kappa$ loop measures, we construct the unrooted SLE$_\kappa$ loop measure in $\hat{\mathbb C}$, which satisfies Möbius invariance and reversibility. Third, we extend the SLE$_\kappa$ loop measures from $\hat{\mathbb C}$ to subdomains of $\hat{\mathbb C}$ and to two types of Riemann surfaces using Brownian loop measures, and obtain conformal invariance or covariance of these measures. Finally, using a similar approach, we construct SLE$_\kappa$ bubble measures in simply/multiply connected domains rooted at a boundary point. The work answers a question raised by Greg Lawler.
Eero Saksman (University of Helsinki): On Gaussian multiplicative chaos and the Riemann zeta function
We recall some basic properties of Gaussian multiplicative chaos and describe our recent results on its connection to the functional statistics of the Riemann zeta function on the critical line (and to that of random unitary matrices). The talk is based on joint work with Christian Webb (Aalto University).
Tuesday: Complex/Real/Harmonic Analysis
John Garnett (UCLA): Many Theorems and Few Stories
Jonas Azzam (University of Edinburgh): The Analyst's Traveling Salesman Theorem for large dimensional objects
The classical Analyst's Traveling Salesman Theorem of Peter Jones gives a condition for when a subset of Euclidean space can be contained in a curve of finite length (or in other words, when a "traveling salesman" can visit potentially infinitely many cities in space in a finite time). The length of this curve is given by a sum of quantities called betanumbers that measure how nonflat the set is at each scale and location. Conversely, given such a curve, the sum of its betanumbers is controlled by the total length of the curve, giving us quantitative information about how nonflat the curve is. This result and its subsequent variants have had applications to various subjects like harmonic analysis, complex analysis, and harmonic measure. In this talk, we will introduce a version of this theorem that holds for higher dimensional objects other than curves. This is joint work with Raanan Schul.
Alex Iosevich (University of Rochester): Group actions, Mattila integral and simplexes inside fractal sets
We will describe how a simple group action viewpoint can be used to derive the classical Mattila integral and to study the distribution of simplexes inside compact subsets of Euclidean space of a given Hausdorff dimension. More general configuration are studied as well where the various notions of rigidity come into play along with Sard's theorem. A variety of interesting model multilinear variants of generalized Radon transforms arise in this context and we shall discuss some steps towards the general theory of these objects.
Maria Cristina Pereyra (University of New Mexico): Weighted inequalities and dyadic harmonic analysis
In this talk we survey the interplay between dyadic techniques and weighted inequalities. This interplay has led, among others, to the solution of the A2 conjecture by Hytönen and the two weight problem for the Hilbert transform by Lacey, Sawyer, Shen, and UriarteTuero.
Michael Benedicks (KTH): Almost sure continuity along curves traversing the Mandelbrot set
We study continuity properties of dynamical quantities while crossing the Mandelbrot set through typical smooth curves. In particular, we prove that for almost every parameter $c_0$ in the boundary of the Mandelbrot set $M$ with respect of the harmonic measure and every smooth curve $\gamma:[1,1]\mapsto {\mathbb C}$ with the property that $c_0=\gamma(0)$ there exists a set ${\mathcal A_\gamma}$ having $0$ as a Lebesgue density point and such that that $\lim_{x\to 0} \mathrm{HDim}(J_{\gamma(x)}) = \mathrm{HDim}(J_{c_0})$ for the Julia sets $J_c$. This is joint work with Jacek Graczyk.
Mikhail Sodin (Tel Aviv University): Translationinvariant probability measures on entire functions
I shall speak about a somewhat unexpected and wild object: the probability measures on the space of entire functions (of one complex variable) which are (a) invariant with respect to the action of the complex plane by translations, and (b) do not charge the constant functions. The existence (and even an abundance) of such measure was discovered by Benjy Weiss.
The talk will be based on the joint work with Lev Buhovsky, Adi Glucksam, Alexander Logunov, arXiv:1703.08101.
Wednesday: Probability/Applied Math
Krzysztof Burdzy (University of Washington): On the number of collisions of billiard balls
In lieu of an abstract I offer a problem. Consider three billiard balls of the same radius and mass, undergoing totally elastic reflections on a billiard table with no walls (the whole plane). All three balls can be given nonzero initial velocities. What is the maximum (supremum) possible number of collisions among the three balls? The supremum is taken over all initial positions and initial velocities. I will discuss this problem and its generalization to any finite family of balls in one, two and higher dimensions. Joint work with Mauricio Duarte.
Maria Jose Gonzalez (University of Cadiz): A limit theorem for random games
We will apply techniques which arise in the context of Fourier Analysis on Boolean functions to study the behavior of the iterates of a special kind of functions, called selectors, acting on random variables. Our main motivation comes from game theory, however selectors appear in many different contexts, such as elections or noisy computations. Joint work with F. Durango, J.L. Fernandez and P. Fernandez.
Mauro Maggioni (Johns Hopkins University): Multiscale Geometric Methods for high dimensional data near lowdimensional sets
We discuss a family of ideas, algorithms, and results for analyzing various new and classical problems in the analysis of highdimensional data sets. These methods we discuss perform well when data is sampled from a probability measure in highdimensions that is concentrated near a lowdimensional set. They rely on the idea of performing suitable multiscale geometric decompositions of the data, and exploiting such decompositions to perform a variety of tasks in signal processing and statistical learning. In particular we will discuss the problem of dictionary learning, of regression, of learning the probability measure generating the data, and efficiently computing optimal transportation plans between probability measures. These are joint works with W. Liao, S. Vigogna and S. Gerber.
Thursday: Harmonic Analysis/PDE
Nets Hawk Katz (Caltech): Improved Hausdorff dimension bounds for Kakeya sets in $\mathbb{R}^3$
We show that for a uniform $\epsilon>0,$ Kakeya sets have Hausdorff dimension $5/2 + \epsilon.$ This is joint work with J. Zahl.
Ilia Binder (University of Toronto): Uniqueness and almost periodicity in time of solutions of the KdV equation with certain almost periodic initial conditions
In 2008, P. Deift conjectured that the solution of KdV equation with almost periodic initial data is almost periodic in time. I will discuss the proof of this conjecture (as well as the uniqueness) in the case of the socalled SodinYuditskii type initial data, i.e. the initial data for which the associated Schroedinger operator has purely absolutely continuous spectrum which satisfies some regularity conditions. In particular, it applies to small analytic quasiperiodic initial data with Diophantine frequency vector. This is a joint work with D. Damanik (Rice), M. Goldstein (Toronto) and M. Lukic (Rice).
Stefan Steinerberger (Yale University): Brownian motion and PDEs
Classical Brownian motion sheds an interesting light on the theory of elliptic partial differential equations  I will discuss various recent new results that strenghten/simplify/improve some classical results and point towards new problems. The main point of the talk is that all the Brownian motion arguments are quite simple and flow naturally (Brownian motion helps you drift in the right direction).
Aleksandr Logunov (Tel Aviv University, Chebyshev Laboratory): $0.01\%$ improvement of the Liouville property for discrete harmonic functions on $\mathbb{Z}^2$
Let $u$ be a harmonic function on the plane. The Liouville theorem claims that if $u$ is bounded on the whole plane, then $u$ is identically constant. It appears that if $u$ is a discrete harmonic function on the lattice $\mathbb{Z}^2,$
and $u$ < $1$ on $99.99\%$ of $\mathbb{Z}^2,$ then $u$ is a constant function.
Based on a joint work (in progress) with L. Buhovsky, Eu. Malinnikova, and M. Sodin.
Svitlana Mayboroda (University of Minnesota): The hidden landscape of localization of eigenfunctions
Numerous manifestations of wave localization permeate acoustics, quantum physics, mechanical and energy engineering. It was used in construction of noise abatement walls, LEDs, optical devices, to mention just a few applications. Yet, no systematic methods could predict the exact spatial location and frequencies of the localized waves.
In this talk I will present recent results revealing a new criterion of localization, tuned to the aforementioned questions, and will illustrate our findings in the context of the boundary problems for the Laplacian and bilaplacian, $div A\nabla$, and (continuous) Anderson and AndersonBernoulli models on a bounded domain. Via a new notion of "landscape" we connect localization to a certain multiphase free boundary problem and identify location, shapes, and energies of localized eigenmodes. The landscape further provides estimates on the rate of decay of eigenfunctions and delivers accurate bounds for the corresponding eigenvalues, in the range where both classical Agmon estimates and Weyl law may fail.
Wilhelm Schlag (University of Chicago): Long term dynamics of nonlinear wave equations
We will review some of the work over the past decade aiming at a complete description of the asymptotic structure of solutions with finite energy to certain semilinear wave equations. A goal of this talk is to demonstrate the interplay between dynamical system ideas and methods (invariant manifolds in infinite dimensions), calculus of variations, and the solution theory of dispersive equations based on classical harmonic analysis (restriction theory of the Fourier transform and Strichartz estimates). We will also present new work on a damped wave equation, but with damping that vanishes asymptotically. The latter is joint work with Nicolas Burq and Genevieve Raugel at Orsay, France.
Friday: Complex/Real/Harmonic Analysis
Mario Bonk (UCLA): Quasisymmetric rigidity for Sierpinki carpets
Sierpinski carpets exhibit surprising rigidity under quasisymmetric maps. This phenomenon appears in various contexts in geometric group theory and complex dynamics. In my talk I will give a survey of some recent results in this area.
Lesley Ward (University of South Australia): Product Hardy spaces associated to operators with heat kernel bounds on spaces of homogeneous type
Much effort has been devoted to generalizing the CalderónZygmund theory from Euclidean spaces to metric measure spaces, or spaces of homogeneous type. Here the underlying space $\mathbb{R}^n$ with Euclidean metric and Lebesgue measure is replaced by a set $X$ with a general metric or quasimetric and a doubling measure. Further, one can replace the Laplacian operator that underpins the CalderónZygmund theory by more general operators $L$ satisfying heat kernel estimates. I will present recent joint work with P. Chen, X.T. Duong, J. Li and L.X. Yan along these lines. We develop the theory of product Hardy spaces $H^p_{L_1,L_2}(X_1 \times X_2)$, for $1\leq p <\infty$, defined on products of spaces of homogeneous type, and associated to operators $L_1$, $L_2$ satisfying DaviesGaffney estimates. This theory includes definitions of Hardy spaces via appropriate square functions, an atomic Hardy space, a CalderónZygmund decomposition, interpolation theorems, and the boundedness of a class of Marcinkiewicztype spectral multiplier operators.
Alex Poltoratski (Texas A&M University): Spectral gaps and the size of uncertainty
I will talk about a recent solution to the socalled gap problem in Fourier analysis and its applications in complex analysis and spectral theory for differential operators.
Luke Rogers (University of Connecticut): Settings in which many Sobolev spaces are not algebras
Let $(X,\mu)$ be a measure space on which there is a nonnegative definite selfadjoint Markovian operator $\mathcal{L}$ with dense domain in $L^2(\mu)$. The cannonical example is the (nonnegative) Laplacian on Euclidean space, and in other contexts it is known that natural examples of such operators $\mathcal{L}$ can be used in place of the Laplacian to define differential equations for physical phenomena such as wave and heat propagation on the space $X$. The corresponding Sobolev spaces are $W^{\alpha,p}_{\mathcal{L}}=\{ f\in L^p: \mathcal{L}^{\alpha/2}\in L^p\}$.
In the Euclidean setting with $\mathcal{L}=\Delta$ it is wellknown that the space $W^{\alpha,p}_{\Delta}\cap L^\infty$ is an algebra when $p\in(1,\infty)$ and $\alpha > 0$. There are extensions of this result to Lie groups with polynomial volume growth and manifolds with positive injectivity radius and nonnegative Ricci curvature. In joint work with Thierry Coulhon we give bounds on the range of $p$ and $\alpha$ for which such results can be true in a general space $(X,\mu)$ by exhibiting a class of fractal spaces and operators for which the algebra property fails.
Paul F. X. Müller (J. Kepler Universität Linz): Davis and Garsia inequalities for Hardy martingales in Banach spaces
We present Davis decompositions for Hardy martingales with values in Banach spaces and use them to derive Davis and Garsia inequalities for vector valued Hardy martingales. We relate the underlying isomorphic invariants to the concept of $H^1$ uniform convexity.
Xavier Tolsa (ICREA  U. Autonoma de Barcelona): Harmonic measure, Riesz transforms, and uniform rectifiability
In this talk I will review some recent results on harmonic measure where the connection between Riesz transforms and rectifiability plays an essential role. In particular, I will recall a converse of the Riesz brothers theorem and the solution of the socalled two phase problem. I will also explain a more recent result on a characterization of uniform rectifiability in terms of Carleson estimates for bounded harmonic functions which is based on a corona decomposition involving harmonic measure. Some of these results are collaborations with J. Azzam, J. Garnett and M. Mourgoglou.
Photos
Will be updated after the conference.
Peter W. Jones' Photos
Peter and Calderon

Tony Carberry, Peter, John Garnett, Mike Wilson, Mike Frazier, Jill Pipher
(all John's students who were there)

Lennart Carleson and Peter, Fred Gehring behind Peter, Tony Carbery on right

Zygmund and Calderon (no Peter, but it is a famous pairing)

Workshop on Dynamics, Probability, and Conformal Invariance
Banff International Research Station

Workshop on Laplacians and Heat Kernels: Theory and Applications
Banff International Research Station

Videos
Will be updated after the conference.
Peter W. Jones' Videos
 CUNY Einstein Chair Mathematics Seminars
 Harmonic measure on curves and related topics, December 03, 1986
 Estimates of harmonic measures, traveling salesman problems and Julia sets, May 23, 1989
 Misiurewicz sets are removable, February 23, 1990
 BiLipschitz mappings and the theory of rectifiability in quasiconformal mappings, February 25, 1992
 When is the complement of a Julia set a John domain? November 17, 1992
 ICM Plenary Lecture, Eigenfunctions and coordinate systems on manifolds, August 26, 2010
 Norbert Wiener Colloquium, Product formulas for positive measures and applications, February 17, 2012
 Banff International Research Station, Eigenfunctions and heat kernels: An overview, March 27, 2015
Registration
Please submit the registration form if you are

an invited speaker or an organizer,
(We will book and cover 6 nights (May 07  May 13) but hope to be able to accommodate 7.
We will book additional nights for you based on your registration form.)

an invited posterpresenter or a general participant.
(If your hotel room is not being paid for by the conference, then you need to book the hotel yourself.
Ask for a "KIAS conference rate" when you book the room.
Most of our funds in this direction are from the NSF, restricted to people at US institutions with no NSF support of their own.)

