### Department of Mathematics and Systems Analysis

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

Marti Prats**Minimizers for the thin one-phase free boundary problem***** Today * ** Wednesday 29 January 2020, 12:15, M3 (M234)

We will give an overview of the literature on the non-negative minimizers for the one-phase free boundary problem of Alt and Caffarelli. This functional contains two competing terms, the standard Dirichlet energy and the measure of the set where the function is positive. Every minimizer is harmonic in its positive phase and vanishes elsewhere. Many questions arise regarding the regularity of the free boundary of such a minimizer, some of them still open.
We will also discuss how these ideas can be brought to the thin one-phase free boundary problem, where the first term is a weighted Dirichlet energy related to the Poisson extension used to compute the fractional Laplacian, and the second competing term is only evaluated in a hyperplane. Minimizers of such a functional will have vanishing fractional Laplacian in the hyperplane's positive phase. This intrinsic nonlocallity will make some arguments to vary substantially.

Seminar on analysis and geometry

Dario Gasbarra (University of Helsinki)**TBA***** ** Tuesday 04 February 2020, 16:15, M2 (M233)

Algebra and discrete mathematics seminar

Prashanta Garain**TBA**

Wednesday 05 February 2020, 12:15, M3 (M234)

Seminar on analysis and geometry

Alex Engström**TBA**

Tuesday 11 February 2020, 16:15, M2 (M233)

Algebra and discrete mathematics seminar

Matias Vestberg**TBA**

Wednesday 12 February 2020, 12:15, M3 (M234)

We will give an overview of the literature on the non-negative minimizers for the one-phase free boundary problem of Alt and Caffarelli. This functional contains two competing terms, the standard Dirichlet energy and the measure of the set where the function is positive. Every minimizer is harmonic in its positive phase and vanishes elsewhere. Many questions arise regarding the regularity of the free boundary of such a minimizer, some of them still open.
We will also discuss how these ideas can be brought to the thin one-phase free boundary problem, where the first term is a weighted Dirichlet energy related to the Poisson extension used to compute the fractional Laplacian, and the second competing term is only evaluated in a hyperplane. Minimizers of such a functional will have vanishing fractional Laplacian in the hyperplane's positive phase. This intrinsic nonlocallity will make some arguments to vary substantially.

Seminar on analysis and geometry

Peter Lindqvist (NTNU)**TBA**

Wednesday 26 February 2020, 12:15, M3 (M234)

We will give an overview of the literature on the non-negative minimizers for the one-phase free boundary problem of Alt and Caffarelli. This functional contains two competing terms, the standard Dirichlet energy and the measure of the set where the function is positive. Every minimizer is harmonic in its positive phase and vanishes elsewhere. Many questions arise regarding the regularity of the free boundary of such a minimizer, some of them still open.
We will also discuss how these ideas can be brought to the thin one-phase free boundary problem, where the first term is a weighted Dirichlet energy related to the Poisson extension used to compute the fractional Laplacian, and the second competing term is only evaluated in a hyperplane. Minimizers of such a functional will have vanishing fractional Laplacian in the hyperplane's positive phase. This intrinsic nonlocallity will make some arguments to vary substantially.

Seminar on analysis and geometry

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

Monday 02 March 2020, 15:15, M205

Aalto Stochastics & Statistics Seminar

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 (ICTP Trieste)**TBA**

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

Seminar on analysis and geometry

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