Series: Other Talks
The Meeting on Applied Algebraic Geometry (MAAG 2018) is a regional gathering that attracts participants primarily from the South-East of the United States. Two previous meetings took place at Georgia Tech in 2015 and at Clemson in 2016. This time around we have invited several speakers from outside this region and are open to "longer distance" participants as well. There is even some funding available (see registration form, priority is given to students). The main event on Saturday April 7 will be followed by an informal Numerical Algebraic Geometry day on Sunday April 8, which participants are encouraged to attend.
Series: Analysis Seminar
It is a conjecture of Zygmund that the averages of a square integrable function over line segments oriented along a Lipschitz vector field on the plane converge pointwise almost everywhere. This statement is equivalent to the weak L^2 boundedness of the directional maximal operator along the vector field. A related conjecture, attributed to Stein, is the weak L^2 boundedness of the directional Hilbert transform taken along a Lipschitz vector field. In this talk, we will discuss recent partial progress towards Stein’s conjecture obtained in collaboration with I. Parissis, and separately with S. Guo, C. Thiele and P. Zorin-Kranich. In particular, I will discuss the recently obtained sharp bound for the Hilbert transform along finite order lacunary sets in all dimensions, the singular integral counterpart of the Parcet-Rogers characterization of L^p boundedness for the directional maximal function in higher dimensions.