...

The saying has it that if you plan a talk for graduate students, then a few professors might understand it. Therefore we suggest that you plan your talk so that even undergraduates will understand it, and then maybe most of the audience will actually do so.

...

**20182019-2019 2020 Schedule**

1712.7 | 13:15 | Shill Fan (Central China Normal University) | Stationary determinantal point processes: ψ-mixing property, correlation dimensions and g-conformal property | Let $f$ be a Borel function from the unit circle to the closed unit interval. It determines a translate invariant measure on $\{0,1\}^{\mathbb{Z}}$. We will first introduce the construction of these measures and then discuss some properties of these measures. | 22.5 | 9 | 14:15 (MA342MA341) | Juho Kontio (Research plan seminar) | Scalable non-parametric pre-screening method for searching higher-order genetic interactions underlying quantitative traits | The Gaussian process (GP) based automatic relevance determination (ARD) is known to be an efficient technique for identifying determinants of gene-by-gene interactions important to trait variation. However, the estimation of GP models is feasible only for low-dimensional datasets ($\sim$ 200 variables) which severely prevents the GP-based ARD method to be applied for high-throughput sequencing data. We have developed a non-parametric pre-screening method that transforms the input variable space via an appropriate kernel function to reduce the GP-based ARD method into a linear similarity regression problem. The proposed method preserves virtually all the major benefits of the GP-based ARD method and extends its scalability to typical high-dimensional datasets used in practice. We present several simulated test scenarios to show that the proposed method compares superiorly with existing non-parametric pre-screening methods suitable for higher-order interaction search. Methodological extensions and straightforward applications will be briefly discussed. |

7.5 | 14:15 (MA342) | Jukka Kemppainen | Scaling Limits for Continuous Time Random Walks with Heavy-Tailed Distributions | We discuss the scaling limits for continuous time random walks, when the jumps or waiting times have heavy-tailed distributions. We will outline how the probability distribution functions of the limiting processes are connected to anomalous diffusion equations. | ||||||

23.4 | 14:15 (MA342) | Xiang GAO (Hubei University, Wuhan) | On Fourier decay of some fractal measures | |||||||

17.4 | 14:15 (IT137) | Sebastian Lunz (University of Cambridge) | Adversarial Regularizers in Inverse Problems | In the past years, machine learning algorithms and in particular deep learning have been providing new tools to the inverse problems community, that have been used to greatly improve reconstruction quality. In this talk, we will give a brief overview of recent approaches to inverse problems using machine learning and will then discuss adversarial regularizers, an approach based on learning a regularization functional, in detail. As applications, we consider traditional imaging problems like computed tomography as well as single particle analysis as a novel application. | ||||||

5.2. | 12:15 (IT137) | Han Yu (University of St. Andrews) | Numbers with restricted digits and Furstenberg slicing problem | Furstenberg posed a problem on intersections between Cantor sets. In this talk, I will talk about Shmerkin-Wu's breakthrough towards this problem as well as a tiny improvement made by myself. It turns out that this tiny improvement can be used to show some intriguing results in number theory on numbers with restricted digits which I will also state in the talk. If time permits, I will briefly mention some key steps of the proofs and some potential future works. | ||||||

14.12 | 13:15 (L9) | Andreas Hauptmann (University College, London) | Learned image reconstruction for high-resolution tomographic imaging | Recent advances in deep learning for tomographic reconstructions have shown great potential to create accurate and high quality images with a considerable speed-up of reconstruction time. In this talk I will discuss two common approaches to combine deep learning methods, in particular convolutional neural networks (CNN), with model-based reconstruction techniques. I will illustrate these approaches with two conceptually different imaging modalities: For accelerated dynamic cardiovascular magnetic resonance we can train a CNN to remove noise and aliasing artefacts from an initial reconstruction to obtain clinically useful information. For the more challenging problem of limited-view photoacoustic tomography, we rather need to train a network that performs an iterative reconstruction which feeds back the model information into the reconstruction algorithm to successively negate limited-view artefacts. | ||||||

4.12 | 13:15 (MA341) | Ruxi Shi | Fuglede's spectral set conjecture on some finite abelian groups | For a locally compact abelian group $G$, Fuglede's spectral set conjecture states that a Borel set is spectral if and only if it tiles the group $G$ by translation. In the case $G=\mathbb{R}^n$, it have been studied for long time since Fuglede formulated this conjecture in 1974. It is proved to be false for $n\ge 3$ but it is still open for $n=1, 2$. Actually, Fuglede's conjecture on $\mathbb{R}$ and $\mathbb{R}^2$ is strongly related to the one on finite abelian groups, which is connected with number theory and combination. In this talks, I will present some recent results about Fuglede's spectral set conjecture on some finite abelian groups. | ||||||

27.9 | 14:15 (MA342) | Hua Qiu (Nanjing University) | The spectrum of the Laplacian on a family of domains in the Sierpinski gasket
| For a certain domain $\Omega$ in the Sierpinski gasket $\mathcal{SG}$ whose boundary is a line segment, a complete description of the eigenvalues of the Laplacian, with an exact count of dimensions of eigenspaces, under the Dirichlet and Neumann boundary conditions is presented. Let $\rho^\Omega(x)$ be the eigenvalue counting function of the Laplacian on $\Omega$. We prove that $\rho^\Omega(x)=g(\log x)x^{\log 3/\log5}+O(x^{\log2/\log5}\log x)$ as $x\rightarrow\infty$ for some (right-continuous, discontinuous) $\log 5$-periodic function $g:\mathbb{R}\rightarrow\mathbb{R}$ with $0<\inf_{\mathbb{R}}g<\sup_\mathbb{R}g<\infty$. Moreover, we explain that the asymptotic expansion of $\rho^\Omega(x)$ should admit a second term of order $\log2/\log5$, that becomes apparent from the experimental data. This is analogous to the conjectures of Weyl and Berry. We will also talk about some other related boundary value problems on subdomains in the Sierpinski gasket. | ||||||

14.9 | 14:15 (TA101) | Ruxi Shi | Chowla sequences in $(S^1\cup \{0\})^\mathbb{N}$}
| The Chowla sequences and Sarnak sequences taking values in $\{-1,0,1\}$ was introduced by El Houcein el Abdalaoui, Joanna Kułaga-Przymus, Mariusz Lemańczyk and Thierry De La Rue for studying Chowla's conjecture and Sarnak's conjecture from ergodic theory point of view. One of their results is that Chowla sequences are always Sarnak sequences, and consequently orthogonal to all topological dynamical systems of zero entropy. In this talk, I will explain how to generalize Chowla sequences from $\{-1,0,1\}^\mathbb{N}$ to $(S^1\cup \{0\})^\mathbb{N}$. I will also show that for almost all $\beta>1$, the sequences $(e^{2\pi i \beta^n})_{n\in \mathbb{N}}$ are Chowla sequences and consequently orthogonal to all topological dynamical systems of zero entropy | ||||||

14.9 | 13:15 (TA101) | Wen Wu (South China Unversity of Technology) | On the abelian complexity of the Rudin-Shapiro sequence | In this talk, we study the abelian complexity of the Rudin-Shapiro sequence. We show the regularity and some asymptotic property of its abelian complexity function. | ||||||

14.9 | 11:15 (SÄ105) | Amir Algom (The Hebrew University of Jerusalem) | Slicing Theorems and rigidity in the class of Bedford-McMullen carpets | Let F be a Bedford-McMullen carpet, with algebraically independent defining integer exponents. Let L be an affine line in the plane that is not parallel to the principal axis We prove that the upper-box dimension of F\cap L is bounded by max{ dim^* (F) - 1, 0}, where dim^* (F) is the star-dimension of F (which is the maximal Hausdorff dimension of a microset of F). To prove this, we first reduce the problem to that of bounding the dimension of non-principal slices in a product set of two Cantor sets. Each Cantor set is assumed to be a non-stationary deleted digit set for some integer base, and the two bases are independent. To bound the dimension of these slices , we adapt Wu's ergodic-theoretic proof of Furstenberg's slicing conjecture to this situation. Time permitting, we will explain how this slicing Theorem for products of Cantor sets can be applied to obtain various rigidity results in the class of Bedford-McMullen carpets. For example, we find explicit combinatorial upper bounds for the dimension of the intersection of two Bedford-McMullen carpets, under the assumption that all defining exponents are independent. | ||||||

14.9 | 10:15 (SÄ105) | Bing Li (South China University of Technology) | Simultaneous shrinking target problems for $\times 2$ and $\times 3$ | We consider the simultaneous shrinking target problems for ×2 and ×3. We obtain the Haisdorff dimensions of the intersection of two well approximable sets and also of the set of points whose orbits approach a given point simultaneously for these two dynamical systems. It is a joint work with Lingmin Liao. | ||||||

Wen Wu (South China University of Technology/ University of Helsinki) | Certain binary automatic sequences and their Hankel determinants | We focus on automatic sequences that are pure substitution sequences on the alphabet {0,1} or {-1,1}. For such sequences on {0,1} (resp. {-1,1}), we give a sufficient and necessary condition that ensures their Hankel determinants H_n = 1 (mod 2) (resp. H_n/2^{n-1} = 1 (mod 2)) for all positive n. Our method can be used to find all such sequences, and we shall show how it works through examples. The talk is based on an ongoing work joint with Y.-J. Guo and G.-N. Han. |

Previous years

**2008-2009 Schedule**

29.9 | Peter Hästö | Function spaces and differential equations |

13.10 | Iwona Wróbel (Technical U. Warsaw) | On the numerical range of companion matrices |

20.10 | Juri Nesterenko (Moscow State U.) | On irrationality of certain numbers |

3.11 | Esa Läärä | Analysis of the distribution of survival times of cancer patients |

24.11 | Jussi Klemelä | Non-parametric function estimation |

10.12 | Tom Hettmansperger (Pennsylvania State U.) | TBA |

9.3 | Pekka Salmi | Fourier transform, duality, quantum groups |

16.3 | Stephen Walter (McMaster U.) | Incorporating patient and physician preferences into the design and analysis of clinical studies |

30.3 | Hannu Oja (U. Tampere) | Multivariate Linear Regression Based on Spatial Signs and Ranks |

20.4 | Markku Niemenmaa | On mathematicians bank accounts and finite groups |

27.4 | Sigfired Carl (Halle-Wittenberg) | Multiple Solutions of Nonlinear Elliptic Problems |

11.5 | Keijo Väänänen | Eräiden päättymättömien tulojen aritmeettisista ominaisuuksista (On arithmetic properties of certain infinite products) |

...

Day | Time | Speaker | Title | Abstract |
---|---|---|---|---|

14.6. | 14:15 | Changhao Chen (UNSW, Sydney) | Finite field analogue of restriction theorem | I will first talk about Fourier analysis in Euclidean spaces and introduce the restriction problems, a basic problem in Fourier analysis. Then we turn to the finite field analogue of restriction problem. G. Mockenhaupt and T. Tao initially studied the finite field analogue of restriction problem. By adapting their arguments we obtain finite field analogue of restriction theorem. Furthermore, inspired by the constructions in the Euclidean setting, we show that the range of the exponentials is sharp for the finite fields setting. |

14.6. | 13:15 | Örjan Stenflo (Uppsala University) | Random iterations of homeomorphisms on the circle | TBA |

16.3. | 14:15 | Antti Kemppainen (University of Helsinki) | Conformal invariance and stochastic models of statistical physics | I will present some recent results in mathematics on conformal invariance in two-dimensional statistical physics. Stochastic models, such as the Ising model or percolation, are used as simplified models in statistical physics to describe physical phenomena, e.g. ferromagnetic material or porous medium (respectively, in these examples). Such models have also been applied to economics, biology, computer science etc. In particular, I will describe in this talk the mathematical theory related to the convergence of these models to conformally invariant scaling limits, which are Schramm-Loewner evolutions (SLE) and conformal loop ensembles (CLE) when we consider the random geometry of interfaces in these models. |

13.12 | 12:15 | Changhao Chen (UNSW, Sydney) | Patterns in random subsets of vector spaces of finite fields | Motivated by analogous results in additive combinatorics, random graphs, and recent works in fractal geometry. We show the existence of certain ''patterns" in random subsets of vector spaces over finite fields. Our random model can be consided as a discrete version of Fractal percolation. One nice thing for vector spaces over finite fields is that it is a vector space with finite vectors. The talk is based on joint work with Catherine Greenhill. |

23.11. | 14:15 | D. Gintides (National Technical University of Athens, Greece) | Solvability of the Integrodifferential Equation of Eshelby's Equivalent Inclusion Method
| In this talk we will discuss the solvability of the integrodifferential equation corresponding to the Eshelby's equivalent inclusion method in static linear elasticity and some modifications and applications of the derived equation. We consider the problem of an infinite elastic isotropic substrate which contains an isotropic inhomogeneity with arbitrary shape and any loading at infinity. We characterize the integrodifferential equation as a tensor singular integral equation of second kind. We adopt a classical matrixization procedure which provides an equivalent matrix integral equation. We compute its symbol and prove that the index is zero which means that it is of Fredholm type. Consequently, according to Noether's theory we infer existence and uniqueness. We prove equivalently that the homogeneous transmission problem has only the trivial solution. We will discuss modifications including eigenstress or body forces and anisotropies. |

29.8 | 14:15 | Ville Suomala | Point configurations in random fractal sets | Motivated by analogous results in additive combinatorics, we present various results on the existence of patterns in random fractal sets. We focus on a canonical model, the fractal percolation. |

22.8 | 14:15 | Wen Wu (South China University of Technology) | On the complexity of the Cantor sequence | The k-abelian complexity, which was introduced by Karhumäki is a measure of the disorder of infinite words. This talk is concerning on the k-abelian complexity of the Cantor sequence c = 101000101 · · ·, which is a typical automatic sequence. We shall first introduce various complexity functions of infinite words, and recall the definition of automatic sequences and regular sequences. Then, we show that the k-abelian complexity function of the Cantor sequence is 3-regular, which supports a conjecture posed by Parreau, Rigo, Rowland and Vandomme. |

**2018-2019**

17.7 | 13:15 | Shill Fan (Central China Normal University) | Stationary determinantal point processes: ψ-mixing property, correlation dimensions and g-conformal property | Let $f$ be a Borel function from the unit circle to the closed unit interval. It determines a translate invariant measure on $\{0,1\}^{\mathbb{Z}}$. We will first introduce the construction of these measures and then discuss some properties of these measures. |

22.5 | 14:15 (MA342) | Juho Kontio (Research plan seminar) | Scalable non-parametric pre-screening method for searching higher-order genetic interactions underlying quantitative traits | The Gaussian process (GP) based automatic relevance determination (ARD) is known to be an efficient technique for identifying determinants of gene-by-gene interactions important to trait variation. However, the estimation of GP models is feasible only for low-dimensional datasets ($\sim$ 200 variables) which severely prevents the GP-based ARD method to be applied for high-throughput sequencing data. We have developed a non-parametric pre-screening method that transforms the input variable space via an appropriate kernel function to reduce the GP-based ARD method into a linear similarity regression problem. The proposed method preserves virtually all the major benefits of the GP-based ARD method and extends its scalability to typical high-dimensional datasets used in practice. We present several simulated test scenarios to show that the proposed method compares superiorly with existing non-parametric pre-screening methods suitable for higher-order interaction search. Methodological extensions and straightforward applications will be briefly discussed. |

7.5 | 14:15 (MA342) | Jukka Kemppainen | Scaling Limits for Continuous Time Random Walks with Heavy-Tailed Distributions | We discuss the scaling limits for continuous time random walks, when the jumps or waiting times have heavy-tailed distributions. We will outline how the probability distribution functions of the limiting processes are connected to anomalous diffusion equations. |

23.4 | 14:15 (MA342) | Xiang GAO (Hubei University, Wuhan) | On Fourier decay of some fractal measures | |

17.4 | 14:15 (IT137) | Sebastian Lunz (University of Cambridge) | Adversarial Regularizers in Inverse Problems | In the past years, machine learning algorithms and in particular deep learning have been providing new tools to the inverse problems community, that have been used to greatly improve reconstruction quality. In this talk, we will give a brief overview of recent approaches to inverse problems using machine learning and will then discuss adversarial regularizers, an approach based on learning a regularization functional, in detail. As applications, we consider traditional imaging problems like computed tomography as well as single particle analysis as a novel application. |

5.2. | 12:15 (IT137) | Han Yu (University of St. Andrews) | Numbers with restricted digits and Furstenberg slicing problem | Furstenberg posed a problem on intersections between Cantor sets. In this talk, I will talk about Shmerkin-Wu's breakthrough towards this problem as well as a tiny improvement made by myself. It turns out that this tiny improvement can be used to show some intriguing results in number theory on numbers with restricted digits which I will also state in the talk. If time permits, I will briefly mention some key steps of the proofs and some potential future works. |

14.12 | 13:15 (L9) | Andreas Hauptmann (University College, London) | Learned image reconstruction for high-resolution tomographic imaging | Recent advances in deep learning for tomographic reconstructions have shown great potential to create accurate and high quality images with a considerable speed-up of reconstruction time. In this talk I will discuss two common approaches to combine deep learning methods, in particular convolutional neural networks (CNN), with model-based reconstruction techniques. I will illustrate these approaches with two conceptually different imaging modalities: For accelerated dynamic cardiovascular magnetic resonance we can train a CNN to remove noise and aliasing artefacts from an initial reconstruction to obtain clinically useful information. For the more challenging problem of limited-view photoacoustic tomography, we rather need to train a network that performs an iterative reconstruction which feeds back the model information into the reconstruction algorithm to successively negate limited-view artefacts. |

4.12 | 13:15 (MA341) | Ruxi Shi | Fuglede's spectral set conjecture on some finite abelian groups | For a locally compact abelian group $G$, Fuglede's spectral set conjecture states that a Borel set is spectral if and only if it tiles the group $G$ by translation. In the case $G=\mathbb{R}^n$, it have been studied for long time since Fuglede formulated this conjecture in 1974. It is proved to be false for $n\ge 3$ but it is still open for $n=1, 2$. Actually, Fuglede's conjecture on $\mathbb{R}$ and $\mathbb{R}^2$ is strongly related to the one on finite abelian groups, which is connected with number theory and combination. In this talks, I will present some recent results about Fuglede's spectral set conjecture on some finite abelian groups. |

27.9 | 14:15 (MA342) | Hua Qiu (Nanjing University) | The spectrum of the Laplacian on a family of domains in the Sierpinski gasket
| For a certain domain $\Omega$ in the Sierpinski gasket $\mathcal{SG}$ whose boundary is a line segment, a complete description of the eigenvalues of the Laplacian, with an exact count of dimensions of eigenspaces, under the Dirichlet and Neumann boundary conditions is presented. Let $\rho^\Omega(x)$ be the eigenvalue counting function of the Laplacian on $\Omega$. We prove that $\rho^\Omega(x)=g(\log x)x^{\log 3/\log5}+O(x^{\log2/\log5}\log x)$ as $x\rightarrow\infty$ for some (right-continuous, discontinuous) $\log 5$-periodic function $g:\mathbb{R}\rightarrow\mathbb{R}$ with $0<\inf_{\mathbb{R}}g<\sup_\mathbb{R}g<\infty$. Moreover, we explain that the asymptotic expansion of $\rho^\Omega(x)$ should admit a second term of order $\log2/\log5$, that becomes apparent from the experimental data. This is analogous to the conjectures of Weyl and Berry. We will also talk about some other related boundary value problems on subdomains in the Sierpinski gasket. |

14.9 | 14:15 (TA101) | Ruxi Shi | Chowla sequences in $(S^1\cup \{0\})^\mathbb{N}$}
| The Chowla sequences and Sarnak sequences taking values in $\{-1,0,1\}$ was introduced by El Houcein el Abdalaoui, Joanna Kułaga-Przymus, Mariusz Lemańczyk and Thierry De La Rue for studying Chowla's conjecture and Sarnak's conjecture from ergodic theory point of view. One of their results is that Chowla sequences are always Sarnak sequences, and consequently orthogonal to all topological dynamical systems of zero entropy. In this talk, I will explain how to generalize Chowla sequences from $\{-1,0,1\}^\mathbb{N}$ to $(S^1\cup \{0\})^\mathbb{N}$. I will also show that for almost all $\beta>1$, the sequences $(e^{2\pi i \beta^n})_{n\in \mathbb{N}}$ are Chowla sequences and consequently orthogonal to all topological dynamical systems of zero entropy |

14.9 | 13:15 (TA101) | Wen Wu (South China Unversity of Technology) | On the abelian complexity of the Rudin-Shapiro sequence | In this talk, we study the abelian complexity of the Rudin-Shapiro sequence. We show the regularity and some asymptotic property of its abelian complexity function. |

14.9 | 11:15 (SÄ105) | Amir Algom (The Hebrew University of Jerusalem) | Slicing Theorems and rigidity in the class of Bedford-McMullen carpets | Let F be a Bedford-McMullen carpet, with algebraically independent defining integer exponents. Let L be an affine line in the plane that is not parallel to the principal axis We prove that the upper-box dimension of F\cap L is bounded by max{ dim^* (F) - 1, 0}, where dim^* (F) is the star-dimension of F (which is the maximal Hausdorff dimension of a microset of F). To prove this, we first reduce the problem to that of bounding the dimension of non-principal slices in a product set of two Cantor sets. Each Cantor set is assumed to be a non-stationary deleted digit set for some integer base, and the two bases are independent. To bound the dimension of these slices , we adapt Wu's ergodic-theoretic proof of Furstenberg's slicing conjecture to this situation. Time permitting, we will explain how this slicing Theorem for products of Cantor sets can be applied to obtain various rigidity results in the class of Bedford-McMullen carpets. For example, we find explicit combinatorial upper bounds for the dimension of the intersection of two Bedford-McMullen carpets, under the assumption that all defining exponents are independent. |

14.9 | 10:15 (SÄ105) | Bing Li (South China University of Technology) | Simultaneous shrinking target problems for $\times 2$ and $\times 3$ | We consider the simultaneous shrinking target problems for ×2 and ×3. We obtain the Haisdorff dimensions of the intersection of two well approximable sets and also of the set of points whose orbits approach a given point simultaneously for these two dynamical systems. It is a joint work with Lingmin Liao. |