HeKKSaGOn Mathematics Meeting 2024

Nov 24, 2024, 9:00 AM → Nov 30, 2024, 8:00 PM Europe/Berlin

KIT & Göttingen Mathematics Departments

Philippe Kupper (KIT), Artem Nepechiy, Wilderich Tuschmann (KIT)

The Hekksagon Mathematics 2024 Meeting will take place from November 24 (arrival) to 30 (departure) and consist of two parts:

On November 25 and 26, all participating HeKKSaGOn group members are invited to shortly report on their current research and research interests at our kick-off meeting at Karlsruhe to foster further communication and future collaborations.

 

After traveling to Göttingen on November 27, November 28 and 29 will feature there the workshop 'Non-Euclidean spaces in Geometry, Optimization and Statistics' with topic-related longer research talks.

 

Confirmed Speakers include:

Shinpei BABA (Osaka University)
Benjamin ELTZNER (Max Planck Institute for Multidisciplinary Sciences)
Ryushi GOTO (Osaka University)
Stephan HUCKEMANN (University of Göttingen)
Hisashi KASUYA (Osaka University)
Tsuyoshi KATO (Kyoto University)
Peer KUNSTMANN (KIT)
Lars LAMMERS (University of Göttingen)
Jun MASAMUNE (Tohoku University)
Mahshidsadat MIRHASHEMI (University of Göttingen)
Kaori NAGATO-PLUM (KIT)
Artem NEPECHIY (KIT)
Shin-ichi OHTA (Osaka University)
Luke RUSSELL (University of Göttingen)
Takashi SHIOYA (Tohoku University)
Wilderich TUSCHMANN (KIT)

 

Scientific Committee

Stephan Huckemann
Wilderich Tuschmann
 

Local Organisers Karlsruhe                               

  Philippe Kupper
  Artem Nepechiy
  Wilderich Tuschmann

Local Organisers Göttingen

             Stephan Huckemann
             Lars Lammers
             Mahshidsadat Mirhashemi

Sunday, November 24

6:00 PM → 9:00 PM Reception

Monday, November 25

9:30 AM → 10:00 AM Registration

10:00 AM → 10:15 AM Survey Talk Takashi Shioya (Tohoku University)

10:25 AM → 10:40 AM Survey Talk Jun Masamune (Tohoku University)

10:45 AM → 11:30 AM Discussion & Coffee Break

11:30 AM → 11:45 AM Survey Talk Ryushi Goto (Osaka University)

11:55 AM → 12:10 PM Survey Talk Shinpei Baba (Osaka University)

12:15 PM → 3:00 PM Discussion & Lunch Break

3:00 PM → 3:15 PM Survey Talk Shin-ichi Ohta (Osaka University)

3:25 PM → 3:40 PM Survey Talk Hisashi Kasuya (Osaka University)

3:45 PM → 4:30 PM Discussion & Coffee Break

4:30 PM → 4:45 PM Survey Talk Stephan Huckemann (University of Göttingen)

4:55 PM → 5:10 PM Survey Talk Benjamin Eltzner (Max Planck Institute for Multidisciplinary Sciences)

Tuesday, November 26

10:00 AM → 10:15 AM Survey Talk Kaori Nagato-Plum (Karlsruhe Institute of Technology)

10:25 AM → 10:40 AM Survey Talk Peer Kunstmann (Karlsruhe Institute of Technology)

10:45 AM → 11:30 AM Discussion & Coffee Break

11:30 AM → 11:45 AM Survey Talk Mahshidsadat Mirhashemi (University of Göttingen)

11:55 AM → 12:10 PM Survey Talk Lars Lammers (University of Göttingen)

12:15 PM → 3:00 PM Discussion & Lunch Break

3:00 PM → 3:15 PM Survey Talk Artem Nepechiy (Karlsruhe Institute of Technology)

3:25 PM → 3:40 PM Survey Talk Wilderich Tuschmann (Karlsruhe Institute of Technology)

3:45 PM → 4:30 PM Discussion & Coffee Break

4:30 PM → 5:30 PM Open Discussion & Wrap-up

6:00 PM → 9:00 PM Conference Dinner

Wednesday, November 27

9:40 AM → 4:00 PM Train Ride to Göttingen and Hotel Check-in

4:30 PM → 6:30 PM City Tour through Göttingen

City tour with a viewpoint from mathematics and the natural sciences

7:30 PM → 8:30 PM Reception

Wine & Bretzels

Thursday, November 28

10:00 AM → 10:50 AM Research Talk Tsuyoshi Kato (Kyoto University)

Title: Homotopy type of finitely propagated unitary operators and its applications

Abstract:

I will explain our computational results of homotopy type of finitely propagated unitary operators. As an application, we induce qualitative properties on distributions of zeros of vector fields over amenable covering spaces of compact manifolds. I will also explain another application, if time allows. These researches are based on joint works with D. Kishimoto and M. Tsutaya.

11:00 AM → 11:30 AM Discussion & Coffee Break

11:30 AM → 12:20 PM Research Talk Luke Russell (University of Göttingen)

Title: Proximal Splitting Algorithms in Nonlinear Spaces

Abstract:

In the setting of CAT(κ ) spaces, common fixed point iterations built from prox
mappings (e.g. prox-prox, Krasnoselsky–Mann relaxations, nonlinear
projected-gradients) converge locally linearly under the assumption of linear metric
subregularity. Linear metric subregularity is in any case necessary for linearly
convergent fixed point sequences, so the result is tight. To show this, we develop a
theory of fixed point mappings that violate the usual assumptions of
nonexpansiveness and firm nonexpansiveness in p-uniformly convex spaces.

This is joint work with Florian Lauster

12:30 PM → 2:00 PM Discussion & Lunch Break

2:00 PM → 2:50 PM Research Talk Shin-ichi Ohta (Osaka University)

Title: A generalization of Grünbaum’s inequality in RCD(0,N)-spaces

Abstract:

We generalize an important inequality in convex geometry, Grünbaum’s inequality, to curved spaces of nonnegative Ricci curvature. Cheeger-Gromoll-type splitting theorems will play a key role. This is joint work with Victor-Emmanuel Brunel and Jordan Serres (CREST/ENSAE).

3:00 PM → 3:30 PM Discussion & Coffee Break

3:30 PM → 4:20 PM Research Talk Jun Masamune (Tohoku University)

Title: Recent progress on the essential selfadjointness of the Laplacians on Riemannian manifolds and weighted graphs.

Abstract:

The first step in the spectral analysis of the Laplacians on Riemannian manifolds and weighted graphs
is to determine its selfadjoint realization and the problem of its uniqueness has received an active interest in the last years.
I will review the recent progress made on this research topic mainly from the collaborative effort with
A. Inoue, S. Ku, and R. Wojciechowski.

Friday, November 29

10:00 AM → 10:50 AM Research Talk Shinpei Baba (University of Osaka)

Title: Riemann surfaces and representations of surface groups into $PSL(2, C)$.

Abstract:

By the uniformization theorem, a Riemann surface corresponds to a discrete torsion-free subgroup of $PSL(2, R)$ isomorphic to the surface group, the fundamental group of the surface. Moreover, by Bers' simultaneous uniformization theorem, a pair of Riemann surface structures of opposite orientations corresponds a "typical" discrete torsion-free surface subgroup of $PSL(2, C)$. In a similar spirit, we discuss some correspondences between complex projective structures on Riemann surfaces and more general representations of the surface group into $PSL(2, C)$

11:00 AM → 11:30 AM Discussion & Coffee Break

11:30 AM → 12:20 PM Research Talk Hisashi Kasuya (University of Osaka)

Title: Higgs bundles and flat bundles on Sasakian manifolds

Abstract:

Hitchin, Corlette and Simpson established the correspondence between flat bundles and Higgs bundles on compact Kähler manifolds. This correspondence is called the non-abelian Hodge correspondence. Sasakian geometry is an odd-dimensional analogy of Kähler geometry. In the joint works with I. Biswas, we investigate the non-abelian Hodge correspondence on compact Sasakian manifolds. In this talk, we give some applications of this correspondence to classifications of Sasakian manifolds and a detailed description of the correspondence at the live of moduli space.

12:30 PM → 2:00 PM Discussion & Lunch Break

2:00 PM → 2:50 PM Research Talk Benjamin Eltzner (University of Göttingen)

Title: Diffusion Means on Compact Symmetric Spaces

Abstract:

On manifold data spaces, we introduce a new family of location statistics describing centers of isotropic diffusion for different diffusion times. In contrast to the situation in Euclidean data, these diffusion means on manifolds do not generally coincide for different diffusion times. In the limit of vanishing diffusion time, diffusion means can be shown to converge to the intrinsic mean in general. For diverging diffusion time, we show for the circle and spheres of arbitrary dimension that diffusion means converge to the extrinsic mean in the canonical embedding into Euclidean space. The generalization of this result to real projective spaces leads to a conjecture for all compact symmetric spaces. We point out questions concerning the Nash embedding and the Laplace-Beltrami operator which connect our conjecture to differential geometry.

3:00 PM → 3:30 PM Discussion & Coffee Break

5:30 PM → 8:30 PM Conference Dinner

Saturday, November 30

10:00 AM → 11:00 AM Departure