Date: 30 September 2025
Speaker: Vasiliy Neckrasov
Title: Zero-one laws for uniform inhomogeneous Diophantine approximations
Abstract: In [Compositio Math. 155 (2019)] Kleinbock and Wadleigh proved a “zero-one law” for uniform Diophantine approximations to pairs (\Theta, \eta) of a matrix \Theta and vector \eta by using dynamics on the space of grids. We will show how the classical Diophantine transference principle provides an alternative approach to this problem and allows us to prove some generalizations. Namely, we will reduce the statement for pairs to the twisted (“fixed matrix”) case and show zero-one laws for twisted uniform approximations.
All the proofs are made in weighted case and, more generally, in the setup of approximations with arbitrary weight functions, which will also be discussed.
This talk is based on arXiv:2508.01912 and arXiv:2503.21180.
Date: 14 October 2025
Speaker: Chengyang Wu
Title: Simultaneously bounded and dense orbits for commuting Cartan actions
Abstract: With the goal to attack Uniform Littlewood’s Conjecture proposed in [BFK25], we introduced the concept of “fiberwise nondivergence” for the action of a cone inside the full diagonal subgroup of SL_3(R). Then it is proved in our paper that there exists a dense subset of SL_3(R)/SL_3(Z) in which each point has a fiberwise non-divergent orbit under a cone inside the full diagonal subgroup and an unbounded orbit under every diagonal flow. Our proof also presented the first instance of results concerning simultaneously bounded and dense orbits for commuting actions on noncompact spaces. This is a joint work with Dmitry Kleinbock.
Date: 21 October 2025
Speaker: Pratyush Sarkar
Title: TBA
Abstract: TBA
