### Department of Mathematics and Systems Analysis

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* Dates within the next 7 days are marked by a star.

Kim Myyryläinen (Aalto University)**What is...Bounded Mean Oscillation (BMO)?***** ** Tuesday 25 February 2020, 14:15, M2 (M233)

The space of bounded mean oscillation (BMO) consists of functions whose mean oscillation over cubes is uniformly bounded. The mean oscillation tells that how much function differs in average from its integral average. One of the most important theorems concerning BMO (the John-Nirenberg inequality) states that the logarithmic blowup is the worst possible behaviour for a BMO function. It also implies that BMO is a substitute for the space of bounded functions in the sense that every BMO function is locally exponentially integrable. As one application of BMO, many interesting linear operators in harmonic analysis fail to map bounded functions to bounded functions but instead map bounded functions to BMO.

What is...? Seminar

Tuomas Hytönen (University of Helsinki)**Commutators and Jacobians***** ** Tuesday 25 February 2020, 15:15, U5

The commutator of two objects A and B is the expression AB-BA, a measure of the extent to which A and B fail to commute. Probably the most famous instance arises from the uncertainty principle in Quantum Mechanics, when A and B are the position and momentum operators, or (in a common representation of these operators) multiplication by x and differentiation in x, respectively. The commutators featuring in this talk are distant cousins of the Heisenberg commutator: again, one of the operators is multiplication by a function, while the other one is an (singular) integral operator. Among other things, such commutators have am interesting connection to a distinguished nonlinear partial differential equation, the prescribed Jacobian problem.

Department Colloquium

Peter Lindqvist (NTNU)**The time derivative in some Evolutionary p-Laplace Equations: a problematic quantity***** ** Wednesday 26 February 2020, 12:15, M3 (M234)

Seminar on analysis and geometry

Konstantin Avrachenkov (INRIA Sophia Antipolis)**Hedonic coalitional game approach to network partitioning**

Monday 02 March 2020, 15:15, M205

The traditional methods for detecting community structure in a network are based on selecting dense subgraphs inside the network. Here we propose to use the methods of coalitional game theory that highlight not only the link density but also the mechanisms of cluster formation. Specifically, we propose an approach which is based on hedonic coalitional games. This approach allows to find clusters with various resolution. Furthermore, the modularity-based approach and its generalizations as well as ratio cut and normalized cut methods can be viewed as particular cases of the hedonic games. Finally, for methods based on potential hedonic games we suggest a very efficient computational scheme using Gibbs sampling.
Bio: Konstantin Avrachenkov received the masters degree in control theory from St. Petersburg State Polytechnic University in 1996, the Ph.D. degree in mathematics from the University of South Australia in 2000, and the Habilitation (Doctor of Science) degree from the University of Nice Sophia Antipolis in 2010. Currently, K. Avrachenkov is Director of Research at Inria Sophia Antipolis. His main research interests are Markov chains, Markov decision processes, stochastic games and singular perturbations. He applies these methodological tools to the modelling and control of telecommunication systems and to design data mining and machine learning algorithms. He has won 5 best paper awards. He is an Associate Editor
of the International Journal of Performance Evaluation, Probability in the Engineering and InformationalSciences, ACM TOMPECS and Stochastic Models.

Aalto Stochastics & Statistics Seminar

Carlos Mudarra**TBA**

Wednesday 04 March 2020, 12:15, M3 (M234)

Seminar on analysis and geometry

Lauri Hitruhin**TBA**

Wednesday 11 March 2020, 12:15, M3 (M234)

Seminar on analysis and geometry

Sari Rogovin**Poincaré inequalities and a general quasihyperbolic growth condition**

Wednesday 18 March 2020, 12:15, M3 (M234)

Seminar on analysis and geometry

Emanuel Carneiro**TBA**

Wednesday 25 March 2020, 12:15, M3 (M234)

Seminar on analysis and geometry

Lauri Viitasaari**TBA**

Wednesday 08 April 2020, 12:15, M3 (M234)

Seminar on analysis and geometry

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