Have a nice summer,

Jonatan Kolegar a Jana Bartoňová, organizers,

Jan Slovák, Director of the Department of Mathematics and Statistics

**Krein's Formula and Sturm-Liouville Operators on a Compact Interval**

Abstract:

Recalling parametrizations of self-adjoint extensions associated with a regular, symmetric, second-order differential expressions, we give a comprehensive accounting of all self-adjoint extensions of the minimal Sturm--Liouville operator in terms of Krein's formula for resolvent differences given Sturm--Liouville operators with Dirichlet boundary conditions at a and b as a convenient reference operator, and give a detailed description of the Krein extension of the minimal Sturm--Liouville operator.

**Cofibrant generation and stable independence**

Abstract:

We discuss recent joint work with Rosicky and Vasey concerning connections between stable independence notions and cofibrant generation of weak factorization systems in locally finitely presentable categories. In particular, we show that for a sufficiently nice class of morphisms M in an lfp category K, M is cofibrantly generated just in case the wide subcategory of K with morphisms precisely those in M has a stable independence relation. This result, and its consequences, cover a wide variety of examples and, in particular, provide an ideal context in which to analyze the stability of Ext-orthogonality classes of models of the sort considered in Baldwin/Eklof/Trlifaj.

You are cordially invited to the 23rd mathematical hike. It will take place on

Start at **08:41 at the bus station Židlochovice (you can join us in Brno, bus from Zvonařka, at 08:07).**

We plan a short hike, about 13.8 km. We will go to the lookout tower "Akátová věž", then through the forest to Žabčice. There's a train or bus back to Brno.

Looking forward to seeing you there,

Jonatan Kolegar a Jana Bartoňová, organizers,

Jan Slovák, Director of the Department of Mathematics and Statistics

I am suggesting the following programme:

1. Brief information on the numbers of students applying for Bc. and Mgr. programmes (Jan Paseka)

2. Brief information on the result of the accreditation of our doctoral programme and further proceedings (Martin Kolář)

3. Report on the development of the department in the in the past four years and the future plans (Jan Slovák)

4. Other issues

I am looking forward to meeting at the Assembly,

Jan Slovák

The Department of Mathematics and Statistics at Masaryk University invites applications for postdoctoral research positions within the project

- Solid background in the area of Partial Differential Equations (PDEs) and Calculus of Variations. Preference will be given to applicants with expertise in elliptic and parabolic PDEs

- Good publication record

- A PhD degree in Mathematics (or be close to obtain)

- Fluency in English, both written and spoken

- Curriculum Vitae

- List of publications

- Outline of research project

- Cover letter explaining motivation and interest

All documents should be sent directly to mkolar@math.muni.cz. In addition, the applicants should also arrange for at least 2 letters of recommendation to be sent directly to mkolar@math.muni.cz. The received applications will be continuously evaluated until the position is filled.]]>

**Assessing disparities in student and applicant ratings**

**Elliptic equations with Hardy potential and gradient-dependent nonlinearity**

**Simplicial models for (oo,2)-categories**

Abstract:

This talk will revolve around two simplicial models for(oo,2)-categories, namely Lurie's oo-bicategories and Verity's complicial model. After a brief overview and some preliminaries on the category of scaled and stratified simplicial sets, we will delve right into the construction of a model structure for "weak" oo-bicategories, which we prove to be equivalent to the one for saturated 2-trivial complicial sets (i.e. the complicial version of (oo,2)-categories). We then describe Lurie's model structure for oo-bicategories and a Quillen equivalence with another model, i.e. that of categories enriched over marked simplicial sets, which shows oo-bicategories are a model for (oo,2)-categories in the sense of Barwick-Schommer Pries. We conclude the talk with a conjecture on the equivalence between our model structure and Lurie's one, and its corollaries.

**Multiplicity results and sign changing solutions of non-local equations with concave-convex nonlinearities**