Special year seminar - Math

Date:
Feb
07
2023

Special Year Research Seminar

Infinite Partial Sumsets in the Primes
2:00pm|Simonyi 101 and Remote Access

It is an open question as to whether the prime numbers contain the sum A+B of two infinite sets of natural numbers A, B (although results of this type are known assuming the Hardy-Littlewood prime tuples conjecture).  Using the Maynard sieve and the...

Feb
08
2023

Special Year Learning Seminar

A Useful Lemma about Intersections of Sets and Some Applications
10:30am|Simonyi 101 and Remote Access

The "intersectivity lemma" states that if a ∈ (0,1) and A_n, n ∈ N,  are measurable sets in a probability space (X,m) satisfying  m(A_n) ≥ a for all n, then there exist a subsequence n_k, k ∈ N, which has positive upper density and such that the...

Feb
22
2023

Special Year Learning Seminar

Automorphic Density Theorems
10:30am|Simonyi 101 and Remote Access

A density theorem for L-functions is quantitative measure of the possible failure of the Riemann Hypothesis. In his 1990 ICM talk, Sarnak introduced the notion of density theorems for families of automorphic forms, measuring the possible failure of...