We organise a seminar in cooperation with the group Graph limits and inhomogeneous random graphs from the Institute of Mathematics of the Czech Academy of Sciences.
The seminars themselves are located either at the Institute of Mathematics, or at the Institute of Computer Science. Please check the location of each seminar!
Friday 1.3.2019 at 10:00 MI, room modrá posluchárna by Ferenc Bencs (Central European University and Hungarian Academy of Sciences): Local spectral measures of the Young-lattice
Abstract: In this talk we will examine the local spectral measure of the Young-lattice as a graph, that is a graph on the irreducible representation of all the symmetric groups. This graph has been thoroughly investigated and it was observed by Stanley, that the local spectral measure of the vertex corresponding to the empty partition is the normal distribution. Building on these techniques, we will show that from any vertex of the n^{th} level the local spectral measure is absolutely continuous with respect to the Lebesgue-measure, moreover, its density function is a "polynomial perturbation" of the density function of the normal distribution, where the polynomial depends only on the character table of the n^{th} symmetric group. In this talk we will examine the local spectral measure of the Young-lattice as a graph, that is a graph on the irreducible representation of all the symmetric groups. This graph has been thoroughly investigated and it was observed by Stanley, that the local spectral measure of the vertex corresponding to the empty partition is the normal distribution. Building on these techniques, we will show that from any vertex of the n^{th} level the local spectral measure is absolutely continuous with respect to the Lebesgue-measure, moreover, its density function is a "polynomial perturbation" of the density function of the normal distribution, where the polynomial depends only on the character table of the n^{th} symmetric group.
Friday 15.2.2019 at 10:00 MI, room modrá posluchárna: Christos Pelekis (Czech Academy of Sciences): Projection inequalities for antichains
Abstract: An antichain in the unit n-cube is a set that does not contain two distinct elements such that one is coordinate-wise dominating the other. I will show that the Hausdorff dimension of an antichain is at most n-1 and that its (n-1)-dimensional Hausdorff measure is at most n. Both bounds are best possible, and the latter is obtained as a corollary of the following statement, which may be of independent interest: the (n-1)-dimensional Hausdorff measure of an antichain is is less than or equal to the sum of the (n-1)-dimensional Hausdorff measures of its n orthogonal projections onto the facets of the unit n-cube containing the origin. This is joint work with Konrad Engel, Themis Mitsis and Christian Reiher. |
Friday 25.1.2019 at 10:00 MI, room "modrá posluchárna": Mate Vizer (Hungarian Academy of Sciences): Geometry of permutation limits
Abstract: We initiate a limit theory of permutation valued processes, building on the recent theory of permutons. We apply this to study the asymptotic behaviour of random sorting networks. Despite main conjectures concerning random sorting networks were recently solved, the techniques developed might be independent of interest. Joint work with M. Rahman and B. Virag |