Calendar
Thursday, October 10, 2024
Time  Items 

All day 

3pm 

4pm 
10/10/2024  4:00pm Lots of problems in combinatorics and analysis are connected to incidences: given a set of points and tubes, how much can they intersect? Upper bounds for incidences have been extensively studied, but lower bounds for incidences havenâ€™t received as much attention, and we prove results in this direction. We prove that if you choose n points in the unit square and a line through each point, there is a nontrivial pointline pair with distance <= n^{2/3+o(1)}. It quickly follows that in any set of n points in the unit square, some three form a triangle of area <= n^{7/6+o(1)}, a new bound for this problem. The main work is proving a more general incidence lower bound result under a new regularity condition. Joint with Cosmin Pohoata and Dimitrii Zakharov. Location:
KT 207
