Title: Venetian blinds, digital sundials, and efficient coverings

Abstract: Davies's efficient covering theorem states that we can cover any measurable set in the plane by lines without increasing the total measure. This result has a dual formulation, known as Falconer's digital sundial theorem, which states that we can construct a set in the plane to have any desired projections, up to null sets. The argument relies on a Venetian blind construction, a classical method in geometric measure theory. In joint work with Alex McDonald and Krystal Taylor, we study a variant of Davies's efficient covering theorem in which we replace lines with curves. This has a dual formulation in terms of nonlinear projections.

About the Speaker. Alan Chang is an Assistant Professor at Washington University in Saint Louis, MO. He received his PhD from Chicago University in 2020 under the direction of Professor Marianna Csörnyei. He was an Instructor at Princeton University (mentor: Prof. Assaf Naor) before joining WashU in 2023. Dr. Chang's primary mathematical interests are harmonic analysis and geometric measure theory. He is an NSF grant holder and was an NSF GRF recipient. He has published in premier journals such as Proc. Lond. Math. Soc., Analysis and PDE, Adv. Math, Rev. Mat. Iberoamericana, Math. Z., J. Number Theory. Dr. Chang has an extensive outreach footprint, currently he directs the WashU Math Circle (for K12 students), he has been mentor and faculty member of Canada/USA Math Camp and of Clubes de Ciencia in México, while a graduate student he mentored over 10+ undergraduate students in the U. Chicago DRP program. He received a bronze medal at the International Linguistics Olympiad in Sweden in 2010, and now he submits problems for North American Computational Linguistics Olympiad! One of his problems, "Warlpiri Kinship Groups," appeared in the second round of the 2013 NACLO and was later featured in Alex Bellos's puzzle column in The Guardian.