EPSRC Grant EP/K016687/1 "Topology, Geometry and Laplacians of Simplicial Complexes"
Some pre-grant papers (since 2011)
B. Hua, J. Jost and Sh. Liu, Geometric analysis aspects
of infinite semiplanar graphs with nonnegative curvature, J. Reine
Angew. Math. 700 (2015), pp. 1-36.
J. Jost and Sh. Liu, Ollivier's Ricci curvature, local
clustering and curvature dimension inequalities on graphs,
Discrete Comput. Geom. 51 (2014), pp. 300-322.
I. Ivrissimtzis and N. Peyerimhoff, Spectral representations
of vertex transitive graphs, Archimedean solids and finite Coxeter
groups, Groups Geom. Dyn. 7 (3) (2013), pp. 591-615.
Y. Yang, N. Peyerimhoff and I. Ivrissimtzis, Linear
Correlations between Spatial and Normal Noise in Triangle Meshes,
IEEE TVCG 19 (1) (2013), pp. 45-55.
J. Stix and A. Vdovina, Simply transitive quaternionic
lattices of rank 2 over F_q(t) and a non-classical fake quadric,
arXiv:1304.5549, April 2013.
S. Dantchev and I. Ivrissimtzis, Efficient construction of the Cech complex, Computers & Graphics 36 (6) (2012), pp. 708-713.
L. Carbone, R. Kangaslampi and A. Vdovina, Groups
acting simply transitively on vertex sets of hyperbolic triangular
buildings, LMS J. Comput. Math. 15 (2012), pp. 101-112.
Y. Yang and I. Ivrissimtzis, A logistic model for the
degradation of triangle mesh normals, Curves and surfaces, Lecture
Notes in Comput. Sci. 6920 (2012), pp. 697-710, Springer.
F. Bauer, J. Jost and Sh. Liu, Ollivier-Ricci curvature
and the spectrum of the normalized graph Laplace operator,
Math. Res. Lett. 19 (6) (2012), pp. 1185-1205.
R. J. Blok, C. G. Hoffman and A. Vdovina, Expander
graphs from Curtis-Tits groups, J. Combin. Theory
Ser. A 119 (3) (2012), pp. 521-525.
N. Barker, N. Boston, N. Peyerimhoff and
A. Vdovina, New examples of Beauville surfaces,
Monatsh. Math. 166 (3-4) (2012), pp. 319-327.
G. Daskalopoulos, Ch. Mese and A. Vdovina, Superrigidity of hyperbolic buildings, Geom. Funct. Anal. 21 (4) (2011), pp. 905-919.
N. Peyerimhoff and A. Vdovina, Cayley graph expanders and groups of finite width, J. Pure Appl. Algebra 215 (11) (2011), pp. 2780-2788.
M. Keller and N. Peyerimhoff, Cheeger constants, growth
and spectrum of locally tessellating planar graphs,
Math. Z. 268 (3-4) (2011), pp. 871-886.
Papers supported by the grant (since September 2013)
S. Dantchev and I. Ivrissimtzis, Simplicial Complex Entropy, in Lecture Notes in Comput. Sci., Mathematical methods for curves and surfaces, Volume 10521, pp. 96-107, Springer, Berlin, 2017.
O. Kharlampovich, A. Mohjeri, A. Taam, A. VdovinaQuadratic equations in hyperbolic groups are NP-complete, Transactions of the American Mathematical Society 369 (2017), pp. 6207-6238.
B. Hua, Sh. Liu, Ch. XiaLiouville theorems for f-harmonic maps into Hadamard spaces, Pacific Journal of Mathematics 290 (2017), pp. 381-402.
Sh. Liu, F. Münch, N. Peyerimhoff, Bakry-Emery curvature and diameter bounds on graphs , arXiv:1608.07778, August 2016.
M. Egidi, Sh. Liu, F. Münch, N. PeyerimhoffRicci curvature and eigenvalue estimates for the magnetic Laplacian on manifolds , arXiv:1608.01955, August 2016.
D. Cushing, Sh. Liu, N. PeyerimhoffBakry-Ă‰mery curvature functions of graphs, arXiv:1606.01496, June 2016.
Sh. Liu, F. Münch, N. PeyerimhoffCurvature and higher order Buser inequalities for the graph connection Laplacian, arXiv:1512.08134, December 2015, MPIM preprint 2016(3).
J. Gu, J. Jost, Sh. Liu, P. F. StadlerSpectral classes of
regular, random, and empirical
graphs,
arXiv:1406.6454, June 2014, Linear Algebra and its
Applications 489 (2016), pp. 30-49.
C. Lange, Sh. Liu, N. Peyerimhoff, O. Post, Frustration index and Cheeger inequalities for discrete and continuous magnetic Laplacians,
arXiv:1502.06299, Calculus of Variations and Partial Differential Equations 54 (2015), pp. 4165-4196.
J. Stix and A. Vdovina, Series of p-groups with Beauville structure, arxiv:1405.3872, May 2014, Monatshefte für Mathematik, Online First 5 August 2015, DOI 10.1007/s00605-015-0805-9, pp.1-10.
N. Barker, A. J. Duncan, D. M. Robertson, The power conjugacy problem in Higman-Thompson groups,
arXiv:1503.01032, March 2015.
Sh. Liu, Multi-way dual cheeger constants and spectral
bounds of graphs, Advances in Mathematics 268 (2015), pp. 306-338.
J. Gu, B. Hua, Sh. Liu, Spectral distances on graphs, arxiv:1402.6041, Discrete Applied Mathematics 190/191 (2015), pp. 56-74.
Sh. Liu, N. Peyerimhoff, A. Vdovina, Signatures, lifts, and eigenvalues of graphs, arXiv:1412.6841, December 2014.
F. M. Atay, Sh. Liu, Cheeger constants, structural balance, and spectral clustering analysis for signed graphs, arXiv:1411.3530, MPI MiS Preprint 111/2014, November 2014.
R. Kangaslampi and A. Vdovina, Hyperbolic triangular buildings without periodic planes of genus two, arxiv:1409.1401, October 2014, To appear in Experimental Mathematics.
I. Ivrissimtzis, A Geometric Approach for the Computation of Principal Directions in Point Sets, http://diglib.eg.org/EG/DL/LocalChapterEvents/TPCG/CGVC14/, Proceedings of Computer Graphics & Visual Computing (CGVC), DOI
10.2312/cgvc.20141210, September 2014.
L. Bromberg, V. Shpilrain and A. Vdovina, Navigating in the Cayley graph of $SL_2(F_p)$ and applications to hashing, arxiv:1409.4478, September 2014, to appear in Semigroup Forum.
Sh. Liu, N. Peyerimhoff, Eigenvalue ratios of nonnegatively curved graphs, arxiv:1406.6617, June 2014.
Sh. Liu, An optimal dimension-free upper bound for eigenvalue ratios, arxiv:1405.2213, May 2014.
W. Li, J. Gu, Sh. Liu, Y. Zhu, S. Dheng, L. Zhao, J. Han, X. Cai,
Optimal Transport in Worldwide Metro Networks, arxiv:1403.7844, March 2014.
N. Barker, N. Boston, N. Peyerimhoff and A. Vdovina, An
infinite family of 2-groups with mixed beauville structures,
International Mathematics Research Notices 2015 (11) (2015), pp. 3598-3618, first published online March 27, 2014, DOI:
10.1093/imrn/rnu045.