# Welcome to listen Analysis seminar every Wednesday 14:15-15:15 @MaD380.

**Spring 2018**

14.2.2018 at 14:15 MaD380 Alex Karrila (Aalto)

Title: Branches in a uniform spanning tree and conformal invariance

Abstract: It is predicted by physicists that continuum limits of critical random models on planar lattices should be described by conformally invariant quantum field theories. The aim of this talk is to characterize the limit of a certain collection of random interfaces, on increasingly dense lattices, in terms of conformally invariant random geometry. In more detail, let $\Lambda$ be a bounded and simply connected planar domain and $\Lambda^\delta$ its natural approximation by the square grid $\delta \mathbb{Z}^2$. We consider a uniform random spanning tree of the graph $\Lambda^\delta$, and condition it on the existence of certain boundary-to-boundary branches. The weak limit of the corresponding random interfaces, as $\delta \to 0$, is a conformally invariant family of random curves called the local multiple $SLE(2)$. Partly based on joint work with Kalle Kytölä (Aalto) and Eveliina Peltola (Geneva).

21.2.2018 No seminar on the conference week.

28.2.2018 at 14:15 MaD380 Joonas Heino

Title: A characterization of solutions for parabolic p(x,t)-Laplace type equations

14.3.2018at 14:15 MaD380 Debanjan Nandi

Title: (TBA)

21.3.2018 Dimitrios Ntalampekos (UCLA)

28.3.2018 Mikko Salo

11.4.2018 Domenico La Manna (Naples)

_______________________________________________________________________

7.2.2018 at 14:15 MaD380 Laurent Dufloux (Oulu)

Title: (TBA)

31.1.2018 at 14:15 MaD380 Timo Schultz

Title: Optimal transport maps in metric measure spaces with curvature bounded below

24.1.2018 at 14:15 MaD380 Michael Seidl (Dept. of Theor. Chemistry, VU Amsterdam.)

Title: Strictly correlated electrons in quantum mechanics: Density functional theory (DFT) meets optimal transport theory (OT)

Abstract: The quantum-mechanical limit of infinitely strong repulsion between electrons ("strictly correlated electrons": SCE) provides important information for DFT (density functional theory). Nowadays, DFT is the method of choice for a wide class of electronic structure calculations (e.g.: quantum chemistry, solid state physics). Interestingly, the SCE concept has turned out to provide solutions to certain optimal transport (OT) problems in mathematics. This talk intends to highlight this connection between quantum physics (DFT) and mathematics (OT theory).

**Fall 2017**

29.11.2017 at 14:15 MaD380 Aleksis Koski

Title: Radial symmetry of p-harmonic minimizers

Abstract: Motivated by models in elasticity theory, we study the minimization of p-harmonic energy among Sobolev homeomorphisms between planar doubly connected domains. The main problem in this setting is that there is no guarantee that an energy-minimal homeomorphism exists, as the Sobolev weak limits of homeomorphisms need not be injective themselves (nor continuous when p < 2). Hence our first points of discussion will be

1) The correct notion of a minimizer

2) The regularity and properties of such a minimizer

The main topic of this talk is the radially symmetric minimization problem between planar annuli for p < 2. This talk is based on joint work with Jani Onninen (__https://arxiv.org/abs/1710.01067__).

22.11.2017 at 14:15 MaD380 Tapio Rajala

Title: Quasiconvex domains Abstract: A domain is quasiconvex if any two of its points can be connected by a curve inside the domain that has length comparable to the distance between the points. In this talk, we will study closed sets in the Euclidean space with quasiconvex complements. In particular, we will look at metrically removable sets. This is joint work with Sergei Kalmykov and Leonid Kovalev.

15.11.2017 at 14:15 MaD380 David Bate (Helsinki)

Title: Characterising rectifiable metric spaces using typical Lipschitz functions.

15.11.2017 **at 15:15** MaD380 Tuomas Orponen (Helsinki)

Title: Sharpening Marstrand‘s projection theorem

8.11.2017 at 14:15 MaD380 Clifford Gilmore (Helsinki)

Title: Growth rates of frequently hypercyclic harmonic functions

Abstract:The notion of frequent hypercyclicity stems from ergodic theory and wasintroduced by Bayart and Grivaux (2004). Many natural continuous linear operators are frequently hypercyclic, for instance the differentiation operator on the space of entire functions. We consider the partial differential operator acting on the space of harmonic functions on R^n and we identify sharp growth rates, in terms of the L^2-norm on spheres, of its frequently hypercyclic vectors. This answers a question posed by Blasco, Bonilla and Grosse-Erdmann (2010). This is joint work with Eero Saksman and Hans-Olav Tylli.

1.11.2017 at 14:15 MaD380 Luca Rondi (Trieste)

Title: Stability for the direct electromagnetic scattering problem

Abstract:I discuss the scattering problem for time-harmonic electromagnetic waves, due to the presence of scatterers and of inhomogeneities in the medium. I show a stability result for the solution to the corresponding exterior boundary value problem, with respect to variations of the scatterer and of the inhomogeneity, under minimal regularity assumptions for both of them. For example, both obstacles and screen-type scatterers are allowed at the same time. As a consequence, one can obtain bounds on solutions to these scattering problems which are uniform with respect to extremely general classes of admissible scatterers and inhomogeneities. In order to prove such a stability result, two key ingredients were developed: the first one is Mosco convergence for H(curl) spaces; the second one is a higher integrability property of solutions to Maxwell equations in nonsmooth domains. This is a joint work with Hongyu Liu and Jingni Xiao (Hong Kong Baptist University)

25.10.2017 at 14:15 MaD380 Thomas Singer (Aalto)

18.10.2017 at 14:15 MaD380 Panu Lahti

Title: BV functions and fine potential theory for p=1 in metric spaces

Abstract: We consider functions of bounded variation and some topics in fine potential theory in the case p=1, such as a Cartan property and questions related to the fine topology. We do this in the setting of a metric space that is equipped with a doubling measure and supports a Poincaré inequality.

11.10.2017 at 14:15 MaD380 Angel Arroy

Title: Mean value properties in metric measure spaces

4.10.2017 at 14:15 MaD380 Daniel Campbell (Charles University)

Title: Sobolev homeomorphisms and monotone maps and their approximation

27.9. at 14:15 MaD380 Lauri Hitruhin (Helsinki)

Title: Stretching multifractal spectra of mappings with integrable distortion

Abstract: We present sharp bounds for the stretching multifractal spectra of planar mappings with p-integrable distortion. That is, we find the maximal size of sets in which a mapping with p-integrable distortion can satisfy some specific stretching conditions. We will also mention how finding the sharp multifractal spectra gives sharp area contraction results.

### 20.9. at 14:15 MaD380 Ville Tengvall

Title: Mappings of finite distortion: size of the branch set

### 23.8. at 14:15 MaD380 Eemeli Blåsten (HKUST)

Title: The planar inverse boundary value problem for L^p potentials with p>4/3

Abstract: I will talk about recent work with Leo Tzou and Jenn-Nan Wang. Based on the method of Bukhgeim, we show that Schrödinger operators with two different L^p-potential with p>4/3 always produce different Cauchy data at the boundary. This is an improvement over the previous result of L^2 potentials. What made this possible comes from an earlier interesting result by Sun-Uhlmann, Päivärinta-Serov: the difference of two potentials with the same Cauchy data is actually smoother than either potential is a-priori.

### 6.9. at 14:15 MaD380 Nicola Fusco (University of Naples)

Title: Evolution of material voids by surface diffusion

Abstract: We consider the evolution by surface diffusion of material voids in a linearly elastic solid. We prove short time existence and asymptotic stability when the initial configuration is close to a stable critical point for the energy. Similar results are also obtained for the evolution by surface diffusion of epitaxially thin films.

### 13.9. at 14:15 MaD380 Joonas Ilmavirta

Title: Spectral rigidity and tensor tomography

Abstract: Can you reconstruct a Riemannian manifold up to isometry from the knowledge of the spectrum of the Laplace-Beltrami operator? This question is wide open. An easier version of this problem is spectral rigidity: Is an isospectral deformation necessarily trivial? We will discuss this problem and its connection to geodesic X-ray tomography of tensor fields.