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.
Friday 25.03.22
7:008:30 Overview
of path homology theory of digraphs (4) 
Tuesday 05.04.22 9:0010:30 Overview
of path homology theory of digraphs (5) 
Tuesday 12.04.22
9:0010:30 Overview
of path homology theory of digraphs (6) 
Tuesday 19.04.22
9:0010:30 Overview
of path homology theory of digraphs (7) 
Tuesday 26.04.22
9:0010:30 Overview
of path homology theory of digraphs (8) 
Tuesday 10.05.22
9:0010:30 Overview
of path homology theory of digraphs (9) 
Tuesday 17.05.22
9:0010:30 Overview
of path homology theory of digraphs (10) 
Tuesday 24.05.22 9:0010:30 BakryEmery
curvature on graphs as an eigenvalue problem Abstract: BakryEmery curvature is a notion of
Riccitype 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 LinYau (2010). Here, we propose the method of computing the
BakryEmery 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 BakryEmery 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.
Tuesday 16.11.21
10:1511:45 
Tuesday 23.11.21
10:1511:45 
Tuesday
30.11.21 9:1510:45 I. Parabolic mean value inequality and ondiagonal upper estimate of heat kernel 
Tuesday
07.12.21 9:1510:45 II. Tail estimate of heat semigroup and offdiagonal upper estimate of heat kernel 
Tuesday
14.12.21 9:1510:45 III. Hölder continuity and offdiagonal lower estimate of heat kernel 
Tuesday
21.12.21 10:1511:45 
Tuesday
11.01.22 10:1511:45 
Tuesday
18.01.22 10:1511:45 
Tuesday
25.01.22 10:1511:45

Tuesday
01.02.22 15:1516:45 
The seminar meets in this semester online via Zoom.
Tuesday
20.04.21 10:1511:45

Tuesday
27.04.21 10:1511:45

Tuesday
04.05.21 10:1511:45 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. 
Tuesday
18.05.21 10:1511:45

Tuesday
25.05.21 10:1511:45 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.

Tuesday 01.06.21 10:1511:45 Alexander
Bendikov (Wroclaw)

Tuesday
15.06.21 13:1514:45 Abstract:
We will talk about a version of the strong halfspace theorem between the
classes of recurrent minimal surfaces and complete minimal surfaces with
bounded curvature of R³. We also consider the ndimensional
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 ndimensional Riemannian
manifold with nonnegative Ricci curvature and whose sectional curvatures are
bounded from above. For Hsurfaces we prove that a stochastically
complete surface M cannot be in the mean convex side of a Hsurface
N embedded in R³ with bounded curvature if sup H_{M} 
< H, or dist(M, N) = 0 when sup H_{M}
 = H. Finally, we will show a maximum principle at infinity for the
case where M has nonempty 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.
Tuesday
01.12.20 10:1511:45 Abstract. We derive the parabolic L^{2}mean value inequality from the FaberKrahn 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 ondiagonal upper bound of the heat kernel, and then the lower bound of the mean exit time on any ball, and finally the offdiagonal 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 L^{1}norm (for example, on the ultrametric space), and the other is the stablelike estimate of the heat kernel corresponding to the (strongest or pointwise) jump kernel upper bound in L^{1}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 stablelike upper bound of the heat kernel. 
Tuesday 08.12.20 10:1511:45 Restriction and extension theorems for the Sobolev W^{1}_{p}(R^{n})spaces. The case 1 < p ≤ n. Abstract. Let S ½ R^{n}
be a closed nonempty set such that, for some d 2 [0; n] and " > 0, the dHausdorff 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 Calderontype maximal functions and special
sequences of Frostmantype measures. Our results extend those available in
the case p 2 (1; n] for Ahlforsregular sets S. 
Tuesday 15.12.20 10:1511:45 Regularity theory for nonlocal equations with VMO coefficients I 
Tuesday
22.12.20 10:1511:45
Simon Nowak (Bielefeld)
Regularity theory for nonlocal equations with VMO coefficients II 
Tuesday
19.01.21 15:1516:45
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. 
Tuesday 26.01.21 10:1511:45 Philipp Sürig (Bielefeld) Heat kernel's lower bounds and volume growth 
Tuesday 02.02.21 10:1511:45 Shilei Kong (Bielefeld) Nearisometries of hyperbolic graphs and biLipschitz embeddings of their boundaries 
Tuesday 09.02.21 10:1511:45 Liguang Liu (Renmin University) Hardy’s inequality and Green Function on metric measure spaces 