
THEMATIC PROGRAMS 

June 30, 2016  
THEMATIC PROGRAM ON NEW TRENDS IN HARMONIC
ANALYSIS

Michael Bateman (IndianaBloomington) Vitaly Bergelson (Ohio State University) Jim Colliander (University of Toronto) Cirprian Demeter (IAS & Indiana) Burak Erdogan (University of Illinois at UrbanaChampaign) Sushrut Gautam (University of California, Los Angeles) Michael Goldberg (Johns Hopkins University) Loukas Grafakos ( University of Missouri at Columbia) Allan Greenleaf (University of Rochester) Derrick Hart (University of MissouriColumbia) Steve Hofmann (University of MissouriColumbia) Alexandru Ionescu (University of Wisconsin, Madison) Nets Katz (Indiana, Bloomington) Doowon Koh (University of MissouriColumbia) Izabella Laba (University of British Columbia) Michael Lacey (Georgia Tech) Xiaochun Li (University of Illinois, UrbanaChampaign) Victor Lie (University of California, Los Angeles) Neil Lyall (University of Georgia, Athens) Akos Magyar (University of Georgia, Athens) 
Vladimir Mazya (Ohio State University)
Detlef Muller (ChristianAlbrechtsUniversitt zu Kiel) Camil Muscalu (Cornell University) Alexander Nagel (University of Wisconsin, Madison) Richard Oberlin (University of California, Los Angeles) Carlos Perez (University of Seville) Lillian Pierce (Princeton University) Jill Pipher (Brown University) Keith Rogers (Universidad Autonoma de Madrid) Eric Sawyer (McMaster University) Raanan Schul (University of California, Los Angeles) Andreas Seeger (University of Wisconsin, Madison) Hart Smith (Washington, Seattle) Alexander Stokolos (DePaul University) Christoph Thiele (University of California, Los Angeles) Rodolfo Torres (University of Kansas) Ana Vargas (Universidad Autónoma de Madrid) Alexander Volberg (Michigan State University, East Lansing) Xiangjin Xu (Binghamton University) 
SCHEDULE:
(Speakers Abstracts)
Tuesday, February 19  
8:309:00

Morning Coffee/Welcoming remarks 
9:009:45

Christoph Thiele (University of California,
Los Angeles) A modulation invariant bilinear variant of the T(1) theorem 
9:4510:00

Coffee Break 
10:0010:45

Cirprian
Demeter (IAS and University of Indiana) Bounds for the two dimensional bilinear Hilbert transform 
11:0011:45

Xiaochun Li (University
of Illinois, UrbanaChampaign) Some problems on bilinear oscillatory integrals along curves 
11:451:00

Lunch break 
1:001:20

Alexander Stokolos
(DePaul University) On the Tauberian condition for geometric maximal operators 
1:301:50

Sushrut Gautam
(University of California, Los Angeles) A criticalexponent BalianLow theorem 
2:002:45

Rodolfo Torres
(University of Kansas) New maximal functions and commutator and weighted estimates for the multlinear CalderónZygmund theory 
2:453:00

Coffee Break 
3:003:45

Loukas Grafakos
(University of Missouri at Columbia) Rough and rougher singular integrals 
4:004:45

Richard Oberlin
(University of California, Los Angeles) Some estimates for the Xray transform 
5:156:15

Reception cash bar 
Wednesday, February 20  
8:309:00

Morning Coffee 
9:009:45

Vitaly
Bergelson (Ohio State University) 10 open problems on positive definite functions 
9:4510:00

Coffee Break 
10:0010:45

Neil Lyall
(University of Georgia, Athens) Polynomial configurations in difference sets 
11:0011:45

Akos Magyar (University
of Georgia, Athens) A coloring problem for squares 
11:451:00

Lunch break 
1:001:20

Lillian Pierce
(Princeton University) Discrete fractional integral operators 
1:301:50

Derrick Hart (University
of MissouriColumbia) SumProduct Theory in Finite Fields 
2:002:20

Doowon Koh (University
of MissouriColumbia) Extension theorems for paraboloids in the finite field setting 
2:30  3:15  Alexander Nagel
(University of Wisconsin, Madison) A covering lemma for certain monomial polyhedra 
3:153:30

Coffee Break 
3:304:15

Michael Lacey (Georgia
Tech) The Small Ball Inequality in all Dimensions 
4:305:15

Raanan Schul (University
of California, Los Angeles) Towards uniform rectifiability in a general metric space 
Thursday, February 21  
8:309:00

Morning Coffee 
9:009:45

Alexandru Ionescu
(University of Wisconsin, Madison) Semilinear Schrodinger flows on hyperbolic spaces: scattering in H^1 
9:4510:00

Coffee Break 
10:0010:45

Keith Rogers
(Universidad Autonoma de Madrid) Mixednorm estimates for the free Schrodinger equation 
11:0011:45

Burak Erdogan
(University of Illinois at UrbanaChampaign) Nearlinear evolution for 1D periodic NLS 
11:451:00

Lunch break 
1:001:45

Michael Goldberg
(Johns Hopkins University) Strichartz estimates in the presence of an oscillating electromagnetic field 
2:002:45

Alexander Volberg
(Michigan State University, East Lansing) Electrostatic field with finitely many charges: the sharp estimates of the size of the level sets 
2:453:00

Coffee Break 
3:003:45

Hart Smith
(University of Washington) L^p bounds for eigenfunctions for Lipschitz metrics 
4:004:45

Allan Greenleaf
(University of Rochester) Estimates for Fourier integral operators with both singular symbols and folds 
5:005:45

Carlos Perez (University
of Seville) Sharp weighted endpoint estimates for CalderonZygmund Singular Integral Operators 
Friday, February 22  
8:309:00

Morning Coffee 
9:009:45

Steve Hofmann
(University of Missouri, Columbia) Layer potentials for complex divergence form equations 
9:4510:00

Coffee Break 
10:0010:45

Jill Pipher (Brown
University) Some remarks on absolute continuity of elliptic measure 
11:0011:45

Vladimir Mazya
(Ohio State University) Higher order elliptic equations in general domains 
11:451:00

Lunch break 
1:001:30

TBA 
1:301:50

Xiangjin Xu
(Binghamton University) Upper and lower bounds for normal derivatives of spectral clusters of Dirichlet Laplacian 
2:002:45

Andreas Seeger
(University of Wisconsin, Madison) Radial Fourier multipliers and a local smoothing inequality 
2:453:00

Coffee Break 
3:003:45

Camil Muscalu
(Cornell University) On an interesting multiparameter structure in harmonic analysis and its connection to the theory of differential equations 
4:004:45

Ana Vargas (Universidad
Autónoma de Madrid) Null form estimates for the wave equation 
5:005:45

Michael Bateman
(Indiana UniversityBloomington) Maximal averages along onevariable vector fields 
Saturday, February 23  
8:309:00

Morning Coffee 
9:009:45

Detlef Muller
(ChristianAlbrechtsUniversitt zu Kiel) Sharp Lpestimates for maximal operators for p > 2 , oscillation indices and a Fourier restriction theorem associated to hypersurfaces in R3 
9:4510:00

Coffee Break 
10:0010:45

Izabella Laba
(University of British Columbia) Arithmetic progressions in sets of fractional dimension 
11:0011:45

Jim Colliander
(University of Toronto) Weak turbulence for cubic NLS on the two dimensional torus 
11:451:00

Lunch break 
1:001:45

Nets Katz (Indiana,
Bloomington) Sums, Products, and other things 
2:002:45

Eric Sawyer (McMaster
University) Nehari theorems for the Dirichlet space 
Apply to the Program: All scientific events are open to the mathematical sciences community. Visitors who are interested in office space or funding are requested to apply by filling out the application form . Additional support is available (pending NSF funding) to support junior US visitors to this program. Fields scientific programs are devoted to research in the mathematical sciences, and enhanced graduate and postdoctoral training opportunities. Part of the mandate of the Institute is to broaden and enlarge the community, and to encourage the participation of women and members of visible minority groups in our scientific programs.
For additional information contact harmonic@fields.utoronto.ca