91²Ö¿â

KENT STATE INFORMAL ANALYSIS SEMINAR

Lecture Series in Analysis
November  16 - 18, 2012
Please e-mail Dmitry Ryabogin ryabogin@math.kent.edu
or Artem Zvavitch zvavitch@math.kent.edu
for more information.

Organizers: Analysis Group of 91²Ö¿â

Speakers:

(University of Michigan) will talk about "Moment curves and polytopes with many faces"

Abstract:  If one seeks to construct a d-dimensional polytope with N vertices and as many faces as possible, a classical argument going back to Caratheodory states that it might be a good idea to take the convex hull of N distinct points on the moment curve  (t, t^2, ... , t^d). For example, if d=4 one gets a polytope for which every pair of vertices spans an edge.  What if one wants, additionally, the polytope to be symmetric about the origin (such polytopes are needed, for example, for the "sparse signal reconstruction") ? There are many mysteries surrounding centrally symmetric polytopes with many faces. For example,  even in dimension 4 the maximum percentage of all pairs of vertices of a centrally symmetric polytope that can span an edge is not known  (it is somewhere between 75% and 93.75%). I plan to review the classical construction and then discuss results about the convex hull of the "symmetric moment curve" (sin t, cos t, sin 3t, cos 3t, ..., sin (2k-1)t, cos (2k-1)t) obtained by Seung Jin Lee, Isabella Novik and myself.

(University of Chicago) will talk about"Differentiability of Lipschitz functions and tangents of sets."

Abstract: We will show how elementary product decompositions ofmeasures can detect directionality in sets, and show how this can beused to describe non-differentiability sets of Lipschitz functions on R^n, and to understand the phenomena that occur because of behavior of Lipschitz functions around the points of null sets.

In order to prove this we will need to prove results about thegeometry of sets of small Lebesgue measure: we show that sets of small measureare always contained in a "small" collection of Lipschitz surfaces.

The talks are based on a joint work with G. Alberti, P. Jones and D. Preiss.

Schedule:

Friday, November 16 

•  TBA

Saturday, November 17 

• 11:00 - 11:30am Coffee
• 11:30 - 12:30am Marianna Csörnyei
• 12:30 - 1:30pm Lunch in the MSB Library
• 1:30 - 2:30pm Marianna Csörnyei
• 2:30 - 3:00pm  Break
• 3:00 - 4:00pm Alexander Barvinok
• 4:00 - 4:30pm Break
• 4:30 - 5:30pm Alexander Barvinok
• 6:00pm Dinner TBA

Sunday, November 18

• 9:00 - 9:30am Breakfast/Coffee
• 9:30 - 10:30am Marianna Csörnyei
• 10:30 - 11:00pm Break
• 11:00 - 12:00pm Marianna Csörnyei
• 12:00 - 1:00pm Lunch in the MSB Library
• 1:00 - 2:00pm Alexander Barvinok
• 2:00 - 2:30pm Break
• 2:30 - 3:30pm Alexander Barvinok

Transportation: For driving directions and maps of the university please and select the information needed. Let us know if you would need a parking pass.

The closest airports to Kent are Akron/Canton Airport (CAK) and Cleveland Hopkins International Airport (CLE). We will schedule pick-up from the airport if advance notice will be provided. We recommend  the hotel at Streetsboro, please contact them directly. Please, say that you are visiting the Department of Mathematical Sciences, 91²Ö¿â - they will provide you with a special discount. Please let us know if there are any problems.

Participants:(as of 11/1/2012):