Function Theory Study Seminar (Fall 2008) - Department of Mathematics

Function Theory Study Seminar (Fall 08)
Thursdays 3:30 - 4:20pm CW 120

Organizer: Pietro Poggi-Corradini
Previous semesters: F05, S06, F06, S07, F07, S08

The seminar where people are not allowed to speak about their own research, but instead relate on classic papers, or obscure old papers, or brand new preprints not yet checked ...

September 4 - Sharad Silwal
"Another Characterization of BMO" by Coifman and Rochberg (PAMS Vol 79 #2, 1980)
Special time and place: Burt 204 - 4pm

September 11 - Sharad Silwal
"Another Characterization of BLO" by Colin Bennett (PAMS Vol 85 #4, 1982)
Special time and place: Burt 204 - 4pm

September 25 - Pietro Poggi-Corradini
"Dynamics on the unit disk", by Curt McMullen
Abstract: We will discuss the paper "Dynamics on the unit disk: short geodesics and simple cycles" by Curt McMullen.

October 9 - Pietro Poggi-Corradini
"Dynamics on the unit disk: short geodesics and simple cycles" by Curt McMullen. Part II.
Abstract: We will discuss the paper "Dynamics on the unit disk: short geodesics and simple cycles" by Curt McMullen.

October 16 - Dan Volok
"Basic properties of discrete analytic functions" by R.J. Duffin, Duke Math. J. 23 (1956), 335--363.

October 30 - Ivan Blank
"Intro to topics on the p-Laplacian"

November 6 - Serban Costea, McMaster University
" Strong A-infinity weights and Sobolev capacities in metric measure spaces"
Abstract: Click here

November 13 - Ivan Blank
"Viscosity and weak solutions for the p-Laplacian, are they the same? "
Abstract: Ivan will speak of such things that will make it clear that although viscosity and weak solutions are different things in general, they are in fact not different in the case of the p-Laplacian. Fruits and vegetables will also be mentioned.

November 20 - Ivan Blank
"Viscosity and weak solutions for the p-Laplacian, are they the same? Part II"

December 4 - Mukta Bhandari
" A new proof of the Hardy-Littlewood maximal theorem"
Abstract: The author of this paper is Hasse Carlsson. In this paper he proves the weak (1,1) inequality of the classical maximal function without using the Vitali type covering lemma. The method used in the proof is due to Miguel De Guzman.

December 11 - Xiang Fang
" A density theorem of Aleksandrov in the Hardy space over the unit disk"
Abstract: The above mentioned theorem says that "disk algebra functions are always dense in coinvariant subspaces."
Here, disk algebra refers to those functions analytic in the unit disc, and continuous up to the boundary; Coinvariant subspaces are the orthogonal complements of invariant subspaces of the Hardy space over the unit disk.
It appears that, at least to me, this simple, elegant theorem did not receive enough attention in the past. On the other hand, the proof I know is quite complicated. A direct/short proof will be desirable.