### Department of Mathematics and Systems Analysis

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

Aleksis Koski (University of Jyväskylä)**Sobolev homeomorphic extensions***** ** Wednesday 21 November 2018, 12:15, M3 (M234)

In the mathematical theory of nonlinear elasticity one typically represents elastic bodies as domains in Euclidean space, and the main object of study are deformations (mappings) between two such bodies. The class of acceptable deformations one considers usually consists of Sobolev homeomorphisms between the respective domains, for example, with some given boundary values. It is hence a fundamental question in this theory to ask whether a given boundary map admits a homeomorphic extension in the Sobolev class or not. We share some recent developments on this subject, including sharp existence results and counterexamples.

Seminar on Analysis and Geometry

Negin Karimi**Generalized regenerating codes and security of distributed storage system***** ** Wednesday 21 November 2018, 15:15, M3 (M234)

Traditional regenerating codes are efficient tools to optimize both storage and repair bandwidth in storing data across a distributed storage system, particularly in comparison to erasure codes and data replication. In traditional regenerating codes, the collection of any k nodes can reconstruct the information file and is called the reconstruction set, N_R. Also, a failed node can be regenerated from any d surviving nodes. These collections of d nodes are called the regeneration sets, N_H. The number of reconstruction sets and the number of regeneration sets satisfies N_R= C_n^k and N _H=C_{n-1}^d, where C_n^k denotes "n choose k". In generalized regenerating codes, we will have, 1 \le N_R \le C^k_n and 1 \le N_H \le C_{n-1}^d. In this talk, I address the problem of secure generalized regenerating codes and present a coding scheme by focusing on the features of the generalized regenerating codes that protect data in the distributed storage system in presence of an active omniscient adversary.

ANTA seminar

Prof Tuomo Kuusi (University of Helsinki)**Quantitative Stochastic Homogenization and Large-Scale Regularity**

Tuesday 27 November 2018, 15:15, E

One of the principal difficulties in stochastic homogenization is transferring quantitative ergodic information from the coefficients to the solutions, since the latter are nonlocal functions of the former. In our recent book, jointly with S. Armstrong and J.-C. Mourrat, we have addressed this problem from a new perspective. Essentially, we use recently developed regularity theory for stochastic homogenization to accelerate the weak convergence of the energy density, flux and gradient of the solutions as we pass to larger and larger length scales, until it saturates at the CLT scaling. I will discuss our approach and give, at the same time, an informal introduction to our book.

Department Colloquium

Carlos Mudarra (Complutense University of Madrid)**Smooth and nonsmooth Whitney's extension theorems for convex functions**

Wednesday 28 November 2018, 12:15, M3 (M234)

Seminar on analysis and geometry

Eveliina Peltola (University of Geneva)**Crossing Probabilities of Multiple Ising Interfaces**

Monday 03 December 2018, 15:15, M3 (M234)

Aalto stochastics and statistics seminar / Ilmonen, Kytölä, Leskelä

Michele Miranda (University of Ferrara)**TBA**

Wednesday 05 December 2018, 12:15, M3 (M234)

Seminar on analysis and geometry

Antti Pöllänen (Aalto)**Optimization of dense Wi-Fi networks via Markov chain models**

Monday 10 December 2018, 15:15, TBA

MSc thesis presentation.

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