Workshop III: The Kakeya Problem, Restriction Problem, and Sum-product Theory

Part of the Long Program Algebraic Techniques for Combinatorial and Computational Geometry
May 5 - 9, 2014

Schedule

All times in this Schedule are Pacific Time (PT)

Monday, May 5, 2014

Morning Session
8:00 - 8:55 Check-In/Breakfast (Hosted by IPAM)
8:55 - 9:00 Welcome and Opening Remarks (Illumination Room)
9:00 - 9:50
Ana Vargas (Autonomous University of Madrid)

Restriction Theorems for Some surfaces of Finite Type

 
10:00 - 10:30 Break
10:30 - 11:20
Larry Guth (Massachusetts Institute of Technology)

From incidence geometry of lines towards incidence geometry of tubes.

 
11:30 - 1:30 Lunch (on your own)

Afternoon Session
1:30 - 2:20
Michael Christ (University of California, Berkeley (UC Berkeley))

A Sharpened Hausdorff-Young Inequality
PDF Presentation

 
2:30 - 2:45 Break
2:45 - 3:35
Betsy Stovall (University of Wisconsin-Madison)

Uniform estimates for Fourier restriction to polynomial curves

 
3:45 - 4:00 Break
4:00 - 4:50
Tuomas Orponen (University of Edinburgh)

On restricted families of projections
PDF Presentation

 
5:00 - 6:30 Poster Session & Reception (Hosted by IPAM)

Tuesday, May 6, 2014

Morning Session
8:00 - 9:00 Continental Breakfast
9:00 - 9:50
Ciprian Demeter (Indiana University)

Proof of the $l^2$ decoupling conjecture

 
10:00 - 10:30 Break
10:30 - 11:20
Alexei Poltoratski (Texas A&M University - College Station)

Gaps and Oscillations in Fourier Analysis

 
11:30 - 1:30 Lunch (on your own)

Afternoon Session
1:30 - 2:20
Terence Tao (University of California, Los Angeles (UCLA))

Stickiness, graininess, planiness, and a sum-product approach to the Kakeya problem

 
2:30 - 2:45 Break
2:45 - 3:35
 
3:45 - 4:00 Break
4:00 - 4:50
Malabika Pramanik (University of British Columbia)

Lacunarity, Kakeya-type sets and directional maximal operators

 

Wednesday, May 7, 2014

Morning Session
8:00 - 9:00 Continental Breakfast
9:00 - 9:50
Andreas Seeger (University of Wisconsin-Madison)

Problems related to the Stein-Tomas theorem
PDF Presentation

 
10:00 - 10:30 Break
10:30 - 11:20
Jonathan Pakianathan (University of Rochester)

Group actions and Geometric Combinatorics in Finite Fields

 
11:30 - 1:30 Lunch (on your own)

Thursday, May 8, 2014

Morning Session
8:00 - 9:00 Continental Breakfast
9:00 - 9:50 Problem Session
10:00 - 10:30 Break
10:30 - 11:20
Richard Oberlin (Florida State University)

Unit Distance Problems

 
11:30 - 1:30 Lunch (on your own)

Afternoon Session
1:30 - 2:20
Joshua Zahl (Massachusetts Institute of Technology)

Visibility and discretized projection theorems

 
2:30 - 2:45 Break
2:45 - 3:35
 
3:45 - 4:00 Break
4:00 - 4:50
Jonathan Bennett (University of Birmingham)

Flow monotonicity and Strichartz inequalities

 

Friday, May 9, 2014

Morning Session
8:00 - 9:00 Continental Breakfast
9:00 - 9:50
Zeev Dvir (Princeton University)

Factors of sparse polynomials are sparse

10:00 - 10:30 Break
10:30 - 11:20
Michael Bateman (University of Cambridge)

Inverse 2D Kakeya theorems

 
11:30 - 1:30 Lunch (on your own)

Afternoon Session
1:30 - 2:20
Pertti Mattila (University of Helsinki)

Projection and slicing theorems in Heisenberg groups

 
2:30 - 2:45 Break
2:45 - 3:35
Tony Carbery (University of Edinburgh)

Colouring multijoints
PDF Presentation

 
3:45 - 4:00 Break
4:00 - 4:50
Misha Rudnev (University of Bristol)

Some new sum-product inequalities, over C