Dear friends of hikes and mathematics,

you are cordially invited to the 47th mathematical hike planned on Saturday, November 9. Start at 8:44 at the train station Doubravice nad Svitavou. (train from Brno main station leaves at 8:00).

The planned route is no shorter than 12 km and no longer than 17 km and goes through the nearby forests, ending at one of the nearby train stations.

A short explanation: we organize these hikes for mathematicians (and their friends), so it is not a mathematical activity, but a time together outdoors. You can read about past hikes in the chronicle.

Have a nice autumn and we look forward to seeing you,

Pavel Francírek and Jonatan Kolegar, organizers

If you have questions, send them to This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Lectures between 21.10. - 25.10.2024, DMS building (M5 and seminar room, level2 )

Benno van den Berg, University of Amsterdam

Effective Kan Fibrations

Mon 21.10. 14:00-15:00 (seminar room, level 2)
Tue 22.10. 13:00-14:00 (seminar room, level 2)
Wed 23.10, 14-15 (M5)
Fri 25.10. 13:00-14:00 (seminar room, level 2)

Abstract: Simplicial techniques are important in homotopy theory and (higher) category theory. They are also important in type theory, because they were used by Voevodsky to construct a new model of type theory. This model validates principles like the Univalence Axiom and Higher-Inductive Types, leading to a new form of type theory, which goes by the name of Homotopy Type Theory. This model construction uses a fundamental result about simplicial sets: that it carries a Quillen model structure in which the fibrations are the Kan fibrations.

It turns out that the standard proofs of the existence of the model structure as well as the model of homotopy type theory use non-constructive principles; however, in this series of lectures I want to outline an approach that aims to give a constructive account of these results. For this, a key ingredient is the theory of algebraic weak factorisation systems, as developed by Garner, Riehl, Bourke and others; this theory is used to formulate a more explicit variant of the traditional Kan fibrations: the effective Kan fibrations, as introduced by Faber and myself. I will explain these notions and indicate how far we are in giving constructive and explicit proofs of the fundamental results in simplicial homotopy theory. I will also explain the relation to other approaches, in particular one due to Henry and Gambino.

This series of lectures will be accessible to an audience of PhD students and researchers in Mathematics with a basic training in category theory.

A delegation of mathematicians from Gadjah Mada University in Indonesia visited Brno. They also came to our department to discuss the potential of future cooperation between our organizations.

Website of the University Gadjah Mada.

Mathematics, Physics & Computer Science Seminar Series

October 9, 2024, 4pm, meeting room 300, Komenského náměstí 220/2

Tamar Ziegler

Sign patterns of the Mobius function

The Mobius function is one of the most important arithmetic functions. There is a vague yet well known principle regarding its randomness properties called the “Mobius randomness law". It basically states that the Mobius function should be orthogonal to any "structured" sequence. P. Sarnak suggested a far reaching conjecture as a possible formalization of this principle. He conjectured that "structured sequences" should correspond to sequences arising from deterministic dynamical systems. Sarnak’s conjecture follows from Chowla’s conjecture - which is the mobius version of the prime tuple conjecture. I will describe progress in recent years towards these conjectures, building on major advances dynamics, additive combinatorics, and analytic number theory.

Tamar Ziegler is an Israeli mathematician known for her work in ergodic theory, combinatorics and number theory. She received her Ph.D. from the Hebrew University in 2003 under the supervision of Hillel Furstenberg.
She was a faculty member at the Technion Institute of Technology until 2013, and is currently the Henry and Manya Noskwith Chair of Mathematics at the Einstein Institute of Mathematics at the Hebrew University.
She held visiting professorships at Stanford university in 2012-13, at MSRI in 2017, and was a distinguished visiting professor at the IAS in Princeton in 2022-23. Ziegler received the Alon Fellowship and the Ostrowski Fellowship in 2008, the Erdos Prize in 2011, the Bruno memorial award in 2015. She was the European Mathematical Society lecturer of the year in 2013, and an invited speaker at the 2014 International Congress of Mathematicians. She was elected to Academia Europaea in 2021.