Tue, 22 Oct 2024
16:00
L6

Simultaneous extreme values of zeta and L-functions

Winston Heap
(Max Planck Institute Bonn)
Abstract
I will discuss a recent joint work with Junxian Li which examines joint distributional properties of L-functions, in particular, their extreme values. Here, it is not clear if the analogy with random matrix theory persists, although I will discuss some speculations. Using a modification of the resonance method we demonstrate the simultaneous occurrence of extreme values of L-functions on the critical line. The method extends to other families and can be used to show both simultaneous large and small values.
 



 

Tue, 18 Jan 2022
15:30
Virtual

TBA

Stephan Stadler
(Max Planck Institute Bonn)
Abstract

TBA

Mon, 02 Mar 2020
15:45
L6

Obstructing isotopies between surfaces in four manifolds

Hannah Schwartz
(Max Planck Institute Bonn)
Abstract

We will first construct pairs of homotopic 2-spheres smoothly embedded in a 4-manifold that are smoothly equivalent (via an ambient diffeomorphism preserving homology) but not even topologically isotopic. Indeed, these examples show that Gabai's recent "4D Lightbulb Theorem" does not hold without the 2-torsion hypothesis. We will proceed to discuss two distinct ways of obstructing such an isotopy, as well as related invariants which can be used to obstruct an isotopy between pairs of properly embedded disks (rather than spheres) in a 4-manifold.

Mon, 19 May 2014

16:00 - 17:00
C5

Periods of Hodge structures and special values of the gamma function

Javier Fresán
(Max Planck Institute Bonn)
Abstract

At the end of the 70s, Gross and Deligne conjectured that periods of geometric Hodge structures with multiplication by an abelian number field are always products of values of the gamma function at rational numbers, with exponents determined by the Hodge decomposition. I will explain a proof of an alternating variant of this conjecture for the cohomology groups of smooth, projective varieties over the algebraic numbers acted upon by a finite order automorphism.

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