**November 23, 2022 from 4:30 PM at Governor's Palace, Moravské náměstí 1a, Baroque Hall**

**Taming the Monster of Independence**

**Abstract**:

Mathematicians feel that every genuine mathematical problem has a solution. Gödel's incompleteness theorem is a major challenge to this feeling, because it claims that every rich enough mathematical theory contains a statement that can not be proved or disproved by this theory. Namely: the problem is independent of present theory. The result of the last half a century showed that many problems in many subfields of Mathematics are independent of the usual axiom system mostly used by mathematicians: ZFC. The most famous one is the Continuum Hypothesis, CH. Discovering that a problem you spent a lot of time and effort with, is independent, is very frustrating for the working mathematician. This is the source of the expression ” the monster of independence” . Can the ” ugly monster of independence” be tamed? Can we still find ways of settling problems that seem to be independent? In the talk we shall explore several approaches to this challenge.**Menachem Magidor** is an Israeli mathematician who specializes in mathematical logic, in particular, set theory at the Hebrew University's Einstein Institute of Mathematics. He served as President of the Hebrew University of Jerusalem, was President of the Association for Symbolic Logic from 1996 to 1998, and is currently the President of the Division for Logic, Methodology and Philosophy of Science and Technology of the International Union for History and Philosophy of Science (DLMPST/IUHPS; 2016-2019). In 2016 he was elected an honorary foreign member of the American Academy of Arts and Sciences. In 2018 he received the Solomon Bublick Award.

The programme will involve my report on the department budgeting and evaluation, discussion, and the item "other".

**October 26**, 2022 from **4:30 PM **at **Governor's Palace, Moravské náměstí 1a, Baroque Hall**

**Expanders in higher dimensions**

Abstract:

Expander graphs have been studied in many areas of mathematics and in computer science with versatile applications, including coding theory, networking, computational complexity and geometry.

High-dimensional expanders are a generalization that has been studied in recent years and their promise is beginning to bear fruit. In the talk, I will survey some powerful local to global properties of high-dimensional expanders, and describe several interesting applications, ranging from convergence of random walks to construction of locally testable codes that prove the c3 conjecture (namely, codes with constant rate, constant distance, and constant locality).

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The PCP theorem

The PCP theorem says that any mathematical proof can be written in a special "PCP" format such that it can be verified, with arbitrarily high probability, by sampling only a few symbols in the proof. Hence the name, Probabilistically Checkable Proofs (PCPs). Alternatively and equivalently, any system of multivariate polynomial equations can be efficiently converted into another, so that if no input satisfies all equations in the former, no input satisfies even a tiny fraction of the equations in the later. Moreover, each of the new equations will involve only 3 variables.

This theorem is the key to understanding the difficulty of approximation and optimization problems; and also amazingly finds uses in modern cloud computing protocols. We will explain the context and meaning of the theorem, and outline a proof that relies on expander graphs, which are a central combinatorial object in numerous computer science and mathematical areas.

**Irit Dinur** is interested in theoretical computer science, and especially in error-correcting codes and probabilistically checkable proofs, both of which capture a certain “robustness” in computation. Currently, she is interested in connecting these to so-called high-dimensional expansion—an analogue of expander graphs that draws on group theory, topology, and combinatorics.

you are cordially invited to the 38th mathematical hike planned on Saturday,

This hike is a special one as it will be led by our colleague David Kruml through his woods. We leave Komořany following the green path and at "Panská skála" enter the woods. We continue to Viničné Šumice and go back to Brno by bus. The hike is 13 km but crossing the forest cover is more demanding. We strongly recommend proper footwear (for mud, etc.) and protective clothing.

All information and photos can be found at https://conference.math.muni.cz/vylety/index.php?id=kronika. (in CZ)

Looking forward to see you soon!

Pavel Francírek or Jonatan Kolegar, organizers

Jan Slovák, Director of the Department of Mathematics and Statistics

If you have questions, send them to francirek@math.muni.cz.

]]>the 37th mathematical hike is planned on the

Meet near the Maloměřice bridge (49.2156853N, 16.6422850E) at 06:30h.

Every participant will contribute to determine the path by a dice roll on predetermined crossroads. Thus it will be (not entirely) a random walk all day (possibility to leave anytime), our goal is to walk 40 km.

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

Have a great summer,

Pavel Francírek or Jonatan Kolegar, organizers

Jan Slovák, Director of the Department of Mathematics and Statistics

The 36th mathematical hike is planned on the

We meet at 09:34 at the train station in Dolní Loučky. We recommend going by the train that leaves Brno main train station at 8:53.

We have planned a 16 km hike to Tišnov (train station) through Deblín.

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

Looking forward to see you soon and have a wonderful spring season,

Jana Bartoňová and Jonatan Kolegar, organizers

Jan Slovák, Director of the Department of Mathematics and Statistics

by **Andrei Dikarev**

supervisor Anton Galaev, specialization Geometry, Topology, and Geometric Analysis**Thursday, 5 May, 2022, 12:00, lecture hall M4**

The dissertation and the reviews are available at https://is.muni.cz/auth/th/joca9/

**The sustainability of safety, security and privacy**

Abstract:

Now that we’re putting software and network connections into durable safety-critical goods such as cars and medical devices, we’ll have to patch vulnerabilities, as we do with phones and laptops. But we can't let vendors stop patching after three years! So in 2019, the EU passed Directive 2019/771, which gives the right to software updates for goods with digital elements, for the time period the consumer might reasonably expect. In my talk I'll describe the background, including a study we did for the European Commission in 2016, and the likely future effects. As sustainable safety, security and privacy become a legal mandate, this will create real tension with existing business models and supply chains. It will also pose a grand challenge for computer scientists. What sort of tools and methodologies should you use to write software for a car that will go on sale in 2023, if you have to support security patches and safety upgrades till 2043?

]]>Some Android mobile devices may still experience problems with the update installation. If this is the case, please contact us at it@muni.cz.

]]>The Department of Mathematics and Statistics at Masaryk University invites applications for fellowships for PhD studies, at the date depending on mutual agreement.

The main research areas of the department are:

- Category theory
- Number theory
- Ordered sets
- Semigroup theory
- Geometric complex analysis
- Lie theory and geometric theory differential equations
- Algebraic and geometric structures of Mathematical Physics
- Geometric aspects of algebraic topology
- Nonlinear differential and difference equations
- Limit periodic and almost periodic systems
- Oscillation theory for linear differential systems
- Oscillation and spectral theory for linear difference systems
- Calculus of variations and optimal control
- Mathematical modelling
- Statistics and data analysis

The fellowship for the initial year will range between 22000 - 27000 CZK per month, with a possibility of extension, conditional on the student's performance. The candidates must hold a Master degree (before starting the PhD studies), or equivalent. They should submit a letter of application accompanied by a CV including their study history and a motivation letter to Martin Kolář ( mkolar@math.muni.cz) .

They should also arrange for at least 2 letters of recommendation to be mailed directly to mkolar@math.muni.cz .

The applications will be assessed continuously. The successful applicants will be notified as soon as possible, but not later than 60 days after the submission.