Stefan Steinerberger, Yale University
“Mysterious New Interactions between Analysis and Number Theory”
I will discuss three different topics that connect classical analysis with number theory in an unex- pected way (insightful remarks/comments are very much appreciated!). (1) A new type of Poincare inequality on the Torus that is optimal in all sort of ways, scales, exponents, . . . . (2a) If the Hardy- Littlewood maximal function of a function f(x) is easy to compute, the function is f(x) = sin(x) or, equivalently, (2b) if f(x) is periodic and the trapezoidal rule is sharp on all intervals of length 1, then the function is trigonometric. This statement is clearly very elementary but the only proof I could find has to use some transcendental number theory and I am not sure why! (3) Strange, unexplained (and pretty!) patterns that appear in an old integer sequence of Stanislaw Ulam from the 1960s [Prize Money: $200 dollars for an explanation/proof].
MC 5501
Refreshments will be served in MC 5501 at 3:30 pm. Everyone is welcome to attend.