Calendar
Printer-friendly versionMonday, October 21, 2024
| Time | Items |
|---|---|
| All day |
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| 3pm |
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| 4pm |
10/21/2024 - 4:15pm We will discuss the following result. For every geometrically finite Kleinian group Γ < SL2(ℂ) there is εΓ such that for every g ∈ SL2(ℂ) the intersection gΓg-1 ∩ SL2(ℝ) is either a lattice or a has critical exponent δ(gΓg-1 ∩ SL2(ℝ)) ≤ 1-εΓ. This result extends Margulis-Mohammadi and Bader-Fisher-Milier-Strover. We will discuss some ideas of the proof. We will focus on the applications of a new ergodic component, of preservation of entropy in a direction. Location:
KT205
10/21/2024 - 4:30pm The period-index problem is a classical problem about finite-dimensional division algebras over a field. When the base field is the function field of a complex variety, there is a longstanding conjecture, which is wide open for function fields of threefolds and beyond. I will discuss recent perspectives on the conjecture from topology, Hodge theory, and moduli theory. Finally, I will explain a result showing that, roughly speaking, topological solutions to the conjecture exist for complex function fields of arbitrary dimension.
Location:
KT 801
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