SFB 1283, project
A3
IRTG 2235, area D
The seminar meets in this semester online via Zoom. Time is given in Central European Time Zone.
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Friday 25.03.22
7:00-8:30 Overview
of path homology theory of digraphs (4) |
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Tuesday 05.04.22 9:00-10:30 Overview
of path homology theory of digraphs (5) |
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Tuesday 12.04.22
9:00-10:30 Overview
of path homology theory of digraphs (6) |
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Tuesday 19.04.22
9:00-10:30 Overview
of path homology theory of digraphs (7) |
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Tuesday 26.04.22
9:00-10:30 Overview
of path homology theory of digraphs (8) |
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Tuesday 10.05.22
9:00-10:30 Overview
of path homology theory of digraphs (9) |
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Tuesday 17.05.22
9:00-10:30 Overview
of path homology theory of digraphs (10) |
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Tuesday 24.05.22 9:00-10:30 Bakry-Emery
curvature on graphs as an eigenvalue problem Abstract: Bakry-Emery curvature is a notion of
Ricci-type curvature (or more precisely, lower Ricci curvature bound)
motivated from Bochner's formula in Riemannian geometry. It has been
introduced and developed in the setting of weighted graphs by Elworthy
(1989), Schmuckenschlager (1996) and Lin-Yau (2010). Here, we propose the method of computing the
Bakry-Emery curvature: in short, this curvature is the smallest eigenvalue of
a symmetric matrix, which we called "curvature matrix". We then use
this formulation to analyze Bakry-Emery curvature as a function of the
dimension parameter. As an application, we could simply derive the curvature
of Cartesian products. This talk is based on a joint work with David
Cushing (Newcastle), Shiping Liu (USTC) and Norbert Peyerimhoff (Durham). |
The seminar meets in this semester online via Zoom. Time is given in Central European Time Zone.
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Tuesday 16.11.21
10:15-11:45 |
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Tuesday 23.11.21
10:15-11:45 |
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Tuesday
30.11.21 9:15-10:45 I. Parabolic mean value inequality and on-diagonal upper estimate of heat kernel |
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Tuesday
07.12.21 9:15-10:45 II. Tail estimate of heat semigroup and off-diagonal upper estimate of heat kernel |
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Tuesday
14.12.21 9:15-10:45 III. Hölder continuity and off-diagonal lower estimate of heat kernel |
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Tuesday
21.12.21 10:15-11:45 |
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Tuesday
11.01.22 10:15-11:45 |
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Tuesday
18.01.22 10:15-11:45 |
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Tuesday
25.01.22 10:15-11:45
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Tuesday
01.02.22 15:15-16:45 |
The seminar meets in this semester online via Zoom.
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Tuesday
20.04.21 10:15-11:45
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Tuesday
27.04.21 10:15-11:45
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Tuesday
04.05.21 10:15-11:45 Abstract. We establish an almost sharp Liouville principle for the weak solutions to the aforementioned differential inequality on geodesically complete noncompact Riemannian manifolds for the following range of parameters: m > 1 while p and q are arbitrary real. The results is entirely new for negative p and q, even in the Euclidean spaces. |
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Tuesday
18.05.21 10:15-11:45
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Tuesday
25.05.21 10:15-11:45 Abstract. In my talk I will touch on such topics as shape of the spectrum
of Cayley and Schreier graphs of finitely generated groups, type of spectral
measures, the question of A.Valette "Can one hear the shape of a
group", and the relation to the random Schrödinger operator.
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Tuesday 01.06.21 10:15-11:45 Alexander
Bendikov (Wroclaw)
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Tuesday
15.06.21 13:15-14:45 Abstract:
We will talk about a version of the strong half-space theorem between the
classes of recurrent minimal surfaces and complete minimal surfaces with
bounded curvature of R³. We also consider the n-dimensional
case and show that any minimal hypersurface immersed with bounded curvature
in M×R+ equals some slice M×{s}
provided M is a complete, recurrent n-dimensional Riemannian
manifold with non-negative Ricci curvature and whose sectional curvatures are
bounded from above. For H-surfaces we prove that a stochastically
complete surface M cannot be in the mean convex side of a H-surface
N embedded in R³ with bounded curvature if sup |HM |
< H, or dist(M, N) = 0 when sup |HM
| = H. Finally, we will show a maximum principle at infinity for the
case where M has non-empty boundary. This is a joint work with G.P. Bessa and L.P. Jorge (Federal University of Ceará - Brazil). |
The seminar meets in this semester online via Zoom.
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Tuesday
01.12.20 10:15-11:45 Abstract. We derive the parabolic L2-mean value inequality from the Faber-Krahn inequality, the generalized capacity condition, and the integrated jump kernel upper bound, for any regular Dirichlet form without a killing part on the doubling space. As an application, we obtain first the on-diagonal upper bound of the heat kernel, and then the lower bound of the mean exit time on any ball, and finally the off-diagonal upper bound of the heat kernel. Our result covers two extreme cases: one is the weak upper estimate of the heat kernel corresponding to the (weakest) jump kernel upper bound in L1-norm (for example, on the ultra-metric space), and the other is the stable-like estimate of the heat kernel corresponding to the (strongest or pointwise) jump kernel upper bound in L1-norm (on the general metric space), and therefore unifies the existent achievements in this direction. We also obtain the localized lower bound of heat kernel under the Poincare inequality, the generalized capacity condition, and the (weakest) integrated jump kernel upper bound. If the Poincare inequality is replaced by the full lower bound of the jump kernel, then we can obtain the full lower bound of heat kernel, which matches the aforementioned stable-like upper bound of the heat kernel. |
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Tuesday 08.12.20 10:15-11:45 Restriction and extension theorems for the Sobolev W1p(Rn)-spaces. The case 1 < p ≤ n. Abstract. Let S ½ Rn
be a closed nonempty set such that, for some d 2 [0; n] and " > 0, the d-Hausdorff content We also discus new tools and methods which are keystones for that
extension problem. More precisely, we give new modifications of the classical
Whitney Extension Operator, consider new Calderon-type maximal functions and special
sequences of Frostman-type measures. Our results extend those available in
the case p 2 (1; n] for Ahlfors-regular sets S. |
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Tuesday 15.12.20 10:15-11:45 Regularity theory for nonlocal equations with VMO coefficients I |
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Tuesday
22.12.20 10:15-11:45
Simon Nowak (Bielefeld)
Regularity theory for nonlocal equations with VMO coefficients II |
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Tuesday
19.01.21 15:15-16:45
Abstract. We discuss regenerative properties of a directed acyclic random graph on the line and the algorithm for simulating the growth rate of its maximal paths. We also comment on various directions of generalisations, with introducing random weights of edges, replacing the line by a partially ordered set, etc. |
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Tuesday 26.01.21 10:15-11:45 Philipp Sürig (Bielefeld) Heat kernel's lower bounds and volume growth |
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Tuesday 02.02.21 10:15-11:45 Shilei Kong (Bielefeld) Near-isometries of hyperbolic graphs and bi-Lipschitz embeddings of their boundaries |
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Tuesday 09.02.21 10:15-11:45 Liguang Liu (Renmin University) Hardy’s inequality and Green Function on metric measure spaces |