Room: Van Vleck B107

Time: Fridays, 1:20--2:10pm

Organizers: Jake Fiedler, Shaoming Guo, Betsy Stovall

If you would like to be included in our mailing list, please send an email to shaomingguo@math.wisc.edu

One email will be sent every week to announce the talk of that week. 

Week One (Sep 8) 

Organizational meeting

Week Two (Sep 15)

Jacob Denson: Turing machines, universal Turing machines, etc. 

Week Three (Sep 22)

Jake Fiedler: Kolmogorov complexity, inequalities with Kolmogorov complexity

Week Four (Sep 29)

Terry Harris: Effictive dimensions, Martin-Lof randomness, possibly point to set principle 

Week Five (Oct 6)

Sam Craig: The proof of point to set principle, application to 1/3 Cantor sets, “Algorithmic Information, Plane Kakeya Sets, and Conditional Dimension” by Lutz and Lutz

Week Six (Oct 13)

Tyler Tan: Application to planar Kakeya sets, “Algorithmic Information, Plane Kakeya Sets, and Conditional Dimension” by Lutz and Lutz

Week Seven (Oct 20)

Kaiyi Huang: "Distance sets bounds for polyhedral norms via effective dimension "

Week Eight (Oct 27)

Sarah Tammen: “Fractal Intersections and Products via Algorithmic Dimension”, Lutz 

Week Nine (Nov 3)

Jiankun Li: Bounding the Dimension of Points on a Line, part I

Week Ten (Nov 10)

Bounding the Dimension of Points on a Line, part I

Week Eleven (Nov 17)

Amelia Stokolosa: Marstrand projection theorem 

Week Twelve (Nov 24)

Thanksgiving week

Week Thirteen (Dec 1)

Alejo Salvatore: Pinned distance problem, part I

Week Fourteen (Dec 8)

Ryan Bushlingm, University of Washington 

Some variational problems characterizing families of convex domains

We prove a singular integral identity for the surface measure of -rectifiable sets  satisfying the orientation cancellation condition. In particular, sets of finite perimeter enjoy this property, and from this observation follows a geometric inequality in which equality is attained precisely by the convex sets. More generally, the integral identity has anisotropic analogues whose corresponding inequalities characterize some geometrically simple subfamilies of the family of convex sets.

Week Fifteen (Dec 15) 

First exam day