Dear Friends of Hikes and Mathematics,

Extreme hike! The 31st mathematical hike is planned on August 8th. Meet at 5:50 at the Main Train Station of Brno.

We go by train, then 12 hours and 45 km to get to the train back to Brno. Evaluate your strength and join us.

All information and photos can be found at http://conference.math.muni.cz/vylety/. (in CZ)

Have a nice summer, we look forward to you joining us.

Jana Bartoňová and Jonatan Kolegar, organizers
Jan Slovák, Director of the Department of Mathematics and Statistics

Title: Geometric Approach to Segmentation in Diffusion Magnetic Resonance Imaging

Author: Sumit Kaushik

Defence: Monday, 29 June, 2020, 4pm, Meeting Room of the department

Supervisor: Jan Slovák

The anatomy of the biological structures in human brain plays an important role in study and diagnosis of medical conditions. The extraction of these structures in DMR images need appropriate methods and modelling. In this work, two standard segmentation methods are discussed. We have used deformable models and the dimensionality reduction method to project the data from high dimension to very small dimensions. On the projected lower dimensional data, we employed the classical k-means clustering for segmentation. Novelty in this work consists in exploitation of the similarity measures for the voxels based on the properties of Riemannian symmetric spaces, as well as quaternionic representation of transformations and their polar decompositions.

Video , thesis

Department of Mathematics and Statistics at the Faculty of Science MU invites applications for a postdoctoral research position within the project "Linear and nonlinear elliptic equations with singular data and related problems''.
Details here.

We will continue online on Thursday, June 18, at 1pm on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:

Alexander Campbell

The gregarious model structure for double categories

Abstract:
In this talk, I will introduce a new model structure on the category of double categories and double functors, which I will argue is the most natural analogue for double categories of Lack’s model structure for 2-categories. This “gregarious” model structure is completely characterised by the following two of its properties: every double category is fibrant, and a double functor is a trivial fibration iff it is surjective on objects, full on horizontal morphisms, full on vertical morphisms, and fully faithful on squares. Note that this model structure is preserved by all eight auto-equivalences of the category of double categories.

This model structure shares many of the excellent features of Lack’s model structure for 2-categories. For instance, it is proper, it is monoidal with respect to Bo ̈hm’s Gray tensor product for double categories, a double category is cofibrant iff its underlying categories of horizontal and vertical morphisms are free, and the double pseudofunctor classifier comonad is a cofibrant replacement comonad. Moreover, Lack’s model structure for 2- categories is created by the (homotopically fully faithful) “double category of squares” functor from the gregarious model structure for double categories.

I will also introduce the notion of double quasi-category, defined as the fibrant objects of a Cisinski model structure on the category of bisimplicial sets, which I will argue presents the correct ∞-categorical generalisation of the notion of double category. I will prove that the gregarious model structure for double categories is right-induced by Watson’s bisimplicial nerve functor from the model structure for double quasi-categories, and that this nerve functor is homotopically fully faithful.