The third meeting of CRN Seminar will take place on Thursday, December 19, 2024, at 14:15–17:45 in room A.4.1 in building C-19. Agenda includes three lectures:

14:15–15:15
Integration meeting

15:15–15:55
Prof. Jarosław Harężlak (Indiana University)
Statistical regularization methods with applications in brain imaging

Abstract:

Regularization methods play a crucial role in the analysis of brain imaging data, where the number of observations is frequently much smaller than the number of covariates. This is even more crucial in multi-modal imaging, where combining data from different sources (e.g., sMRI, fMRI, and dMRI) can enhance insights into brain structure and function. In these settings, regularization helps to address the challenges posed by high-dimensional, noisy data by imposing constraints that promote stability and interpretability in model estimation. Off-the-shelf techniques such as Lasso, ridge regression, and elastic net are commonly employed to control overfitting and improve prediction accuracy, while spatial and informed regularization methods can leverage the inherent structure of imaging data, allowing for the integration of multiple imaging modalities. We describe the common regularization methods, and their extensions developed by us, including PEER (partially empirical eigenvectors for regression) and SpINNEr (Sparsity Inducing Nuclear-Norm Estimator).

16:05–16:45
Prof. Adam Nowak (Polish Academy of Sciences)
On the heat equation on a sphere and on other manifolds (in Polish)

16:55–17:35
Prof. Bartosz Trojan (Wrocław University of Science and Technology)
Compactifications of affine buildings (in Polish)

The second lecture of the CRN Seminar will take place on Tuesday, March 26, 2024, at 1:15 p.m. in room A.1.3 in building C-19 (and online). Our speaker will be

Prof. Wojciech Samotij (Tel Aviv University)

who will give a lecture

Ramsey properties of random graphs

Abstract:

The well-known theorem of Ramsey implies that every red/blue-colouring of the edges of K₆, the complete graph on six vertices, must contain a monochromatic triangle. Are there graphs that do not contain a K₆ as a subgraph and still have this property? Forty years ago, this innocent question motivated the study of Ramsey and extremal properties of random graphs, an area of research that remains very active to this day. The aim of this talk is to provide a gentle introduction to this area, answering the above question along the way.

The first lecture of the CRN Seminar will take place on Thursday, October 19, 2023, at 11:15 a.m. in room A.1.14 in building C-19 (and online). Our speaker will be

Prof. Tomasz Downarowicz

who will give a lecture

Topological normality preservation by addition

Abstract:

In this lecture, inaugural for the CRN seminar, I will present something perhaps interesting, very natural and — above all — easy to follow, namely, an answer to the question given below.

A symbolic sequence x over a finite alphabet A = {0, 1, 2, …, r – 1} is called topologically normal if it is transitive in the full shift over A (that is, every finite block of symbols occurs in x). In the shift space we introduce coordinatewise addition modulo r.

Question: What sequences y over A have the property that x + y is topologically normal for every topologically normal sequence x?

The answer is surprising, because it involves a new class of sequences that presumably none of us has ever heard about before.