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Home » Polynomial Method

Summer Graduate School

Polynomial Method July 08, 2019 - July 19, 2019
Parent Program: --
Location: MSRI: Simons Auditorium, Atrium
Organizers Adam Sheffer (Bernard M. Baruch College, CUNY), LEAD Joshua Zahl (University of British Columbia)
Speaker(s)

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Description
Twolines3d
from distinct distances in the plane to line incidences in R^3

In the past eight years, a number of longstanding open problems in combinatorics were resolved using a new set of algebraic techniques. In this summer school, we will discuss these new techniques as well as some exciting recent developments.

Bibliography

For eligibility and how to apply, see the Summer Graduate Schools homepage

Keywords and Mathematics Subject Classification (MSC)
Tags/Keywords
  • discrete geometry

  • combinatorial geometry

  • incidence geometry

  • polynomial method

  • distinct distances

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
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Schedule, Notes/Handouts & Videos
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Jul 08, 2019
Monday
09:00 AM - 09:15 AM
  Introduction to MSRI
09:15 AM - 10:15 AM
  Introduction to the polynomial method
Joshua Zahl (University of British Columbia)
10:15 AM - 10:45 AM
  Break
10:45 AM - 12:00 PM
  The joints problem
Joshua Zahl (University of British Columbia)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Problem Session
03:00 PM - 03:30 PM
  Tea Break
03:30 PM - 04:30 PM
  Problem Session
Jul 09, 2019
Tuesday
09:00 AM - 10:15 AM
  Introduction to Incidences
Adam Sheffer (Bernard M. Baruch College, CUNY)
10:15 AM - 10:45 AM
  Break
10:45 AM - 12:00 PM
  The Polynomial Partitioning Theorem
Adam Sheffer (Bernard M. Baruch College, CUNY)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Problem Session
03:00 PM - 03:30 PM
  Tea Break
03:30 PM - 04:30 PM
  Problem Session
Jul 10, 2019
Wednesday
09:00 AM - 10:15 AM
  Incidences via Polynomial Partitioning
Adam Sheffer (Bernard M. Baruch College, CUNY)
10:15 AM - 10:30 AM
  Break
10:30 AM - 11:30 AM
  More Applications of Incidences
Adam Sheffer (Bernard M. Baruch College, CUNY)
11:30 AM - 02:00 PM
  BBQ Lunch at Tilden Park
Jul 11, 2019
Thursday
09:00 AM - 10:15 AM
  Distinct distances in the plane
Joshua Zahl (University of British Columbia)
10:15 AM - 10:45 AM
  Break
10:45 AM - 12:00 PM
  Distinct distances in the plane continued
Joshua Zahl (University of British Columbia)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Problem Session
03:00 PM - 03:30 PM
  Tea Break
03:30 PM - 04:30 PM
  Problem Session
Jul 12, 2019
Friday
09:00 AM - 10:15 AM
  Distinct distances in the plane continued
Joshua Zahl (University of British Columbia)
10:15 AM - 10:45 AM
  Break
10:45 AM - 12:00 PM
  Distinct distances in the plane continued
Joshua Zahl (University of British Columbia)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Problem Session
03:00 PM - 03:30 PM
  Tea Break
03:30 PM - 04:30 PM
  Problem Session
Jul 15, 2019
Monday
09:00 AM - 10:15 AM
  Distinct distances in the plane continued
Joshua Zahl (University of British Columbia)
10:15 AM - 10:45 AM
  Break
10:45 AM - 12:00 PM
  Finite Field Kakeya
Adam Sheffer (Bernard M. Baruch College, CUNY)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Problem Session
03:00 PM - 03:30 PM
  Tea Break
03:30 PM - 04:30 PM
  Problem Session
Jul 16, 2019
Tuesday
09:00 AM - 10:15 AM
  The Cap Set Problem
Adam Sheffer (Bernard M. Baruch College, CUNY)
10:15 AM - 10:45 AM
  Break
10:45 AM - 12:00 PM
  The Cap Set Problem continued
Adam Sheffer (Bernard M. Baruch College, CUNY)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Problem Session
Cosmin Pohoata (California Institute of Technology)
03:00 PM - 03:30 PM
  Tea Break
03:30 PM - 04:30 PM
  Problem Session
Jul 17, 2019
Wednesday
09:00 AM - 10:15 AM
  The restriction problem in R3
Joshua Zahl (University of British Columbia)
10:15 AM - 10:45 AM
  Break
10:45 AM - 12:00 PM
  The restriction problem in R3 continued
Joshua Zahl (University of British Columbia)
12:00 PM - 02:00 PM
  Lunch
Jul 18, 2019
Thursday
09:00 AM - 10:15 AM
  The restriction problem in R3 continued
Joshua Zahl (University of British Columbia)
10:15 AM - 10:45 AM
  Break
10:45 AM - 12:00 PM
  The restriction problem in R3 continued
Joshua Zahl (University of British Columbia)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Problem Session
Marina Iliopoulou (University of Kent)
03:00 PM - 03:30 PM
  Tea Break
03:30 PM - 04:30 PM
  Problem Session
Jul 19, 2019
Friday
09:00 AM - 10:15 AM
  Sum-product in finite fields
Adam Sheffer (Bernard M. Baruch College, CUNY)
10:15 AM - 10:45 AM
  Break
10:45 AM - 12:00 PM
  Sum-product in finite fields continued
Adam Sheffer (Bernard M. Baruch College, CUNY)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Problem Session
03:00 PM - 03:30 PM
  Tea Break
03:30 PM - 04:30 PM
  Problem Session