EPSRC Grant EP/K016687/1 "Topology, Geometry and Laplacians of Simplicial Complexes"
GGA Seminars (Groups, Graphs and Analysis)
2013
Tuesday, 8 October 2013, 4pm (Durham), CM105 Norbert
Peyerimhoff On Polygonal Complexes with Planar Substructures
(joint work with Matthias Keller and Felix Pogorzelski)
Friday, 18 October 2013, 10am (Newcastle), HERB3.19 Alina
Vdovina Arithmetic groups acting on trees (joint work with Jacob
Stix)
Thursday, 7 November 2013, 2pm (Durham), CM219 Olaf Post
(Durham University) Spectral bracketing on generalised magnetic
Laplacians (joint work with Fernando Lledo)
Wednesday, 13 November 2013, 4pm (Durham), CM107 Shiping
Liu Geometric analysis aspects of infinite semiplanar graphs with
nonnegative curvature (joint work with Bobo Hua and Juergen Jost)
Friday, 15 November 2013, 3pm (Durham), CM204 Shiping Liu
Continuation of Geometric analysis aspects of infinite semiplanar
graphs with nonnegative curvature (joint work with Bobo Hua and
Juergen Jost)
Wednesday, 4 December 2013, 5pm (Durham), CM105 Stefan
Dantchev Entropy of simplicial complex (with application to shape
reconstruction) (joint work with Ioannis Ivrissimtzis)
2014
Thursday, 16 January 2014, 11am (Newcastle),
HERB3.19 Ioannis Ivrissimtzis Discrete curvatures and
applications
Wednesday, 22 January 2014, 3pm (Durham), CM105 Shiping
Liu Multi-way dual Cheeger constants and spectral clustering on
graphs
Friday, 7 February 2014, 11am (Newcastle),
HERB3.19 Pavel Zalesskii (Universidade de Brasilia) Genus
for groups
Wednesday, 12 February 2014, 3pm (Durham), CM219 Carsten
Lange (TU München) Combinatorial Ricci curvatures
Friday, 14 February 2014, 2pm (Durham),
E005 Carsten Lange (TU München) Continuation of
Combinatorial Ricci curvatures
Thursday, 20 March 2014, 4pm (Newcastle),
HERB3.19 Carsten Lange (TU München) Many polytopal
realizations of generalized associahedra
Tuesday, 24 June 2014, 5pm (Durham), CM103 Riikka
Kangaslampi (Aalto University, Helsinki) Surface subgroups of groups acting
on hyperbolic buildings, Abstract: We study surface subgroups of
groups acting simply transitively on vertex sets of certain hyperbolic
triangular buildings. The study is motivated by Gromov’s famous
surface subgroup question: Does every one-ended hyperbolic group
contain a subgroup which is isomorphic to the fundamental group of a
closed surface of genus at least 2? Earlier with Alina Vdovina and
Lisa Carbone we constructed and classified all groups acting simply
transitively on the vertices of hyperbolic triangular buildings of the
smallest non-trivial thickness. These groups gave the first examples
of cocompact lattices acting simply transitively on vertices of
hyperbolic triangular Kac-Moody buildings that are not
right-angled. In this talk I will consider surface subgroups acting on
the 23 torsion free groups we obtained. I will show that there are no
surfaces of genus 2 inside the apartments of these buildings, but,
that some of them admit non-orientable surface subgroups.
Tuesday, 16 September 2014, 10am (Durham), CM103 Shiping
Liu (Durham) Unification of Cheeger and dual Cheeger constants via
the signed Cheeger constant
Friday, 24 October 2014, 10am (Newcastle), HERB 3.19Alina
Vdovina (Newcastle)/Stefan Dantchev (Durham) Expanders and Hash
functions/Search Problems in Computational Complexity
Wednesday, 12 November 2014, 3pm (Durham), CM103 Shiping
Liu (Durham) On the Bilu-Linial Conjecture
Friday, 21 November 2014, 10am (Newcastle), HERB
3.19 Alexandre Borovik (University of Manchester) Black
box groups: back to computer science, Abstract: I will discuss our
recent results in black box group theory, a branch of computational
group theory devoted to probabilistic algorithms for finite groups. I
will mention, in particular, an effective construction of unipotent
elements in black box groups, an answer to a question by Babai and
Beals that remained open since 1991. The talk will focus on a new
approach to black boxes that brings them back into the realm of
computer science --- where they have originated in 1980-s in the
pioneering works by Laci Babai. This is joint work with Sukru
Yalcinkaya.
Friday, 21 November 2014, 12pm (Newcastle), HERB 3.19 Dawid
Kielak (University of Bonn, Germany) Nielsen Realisation for
right-angled Artin groups, Abstract: We will introduce both the class
of right-angled Artin groups (RAAG) and the Nielsen realisation
problem. Then we will discuss some recent progress towards solving the
problem.
2015
Thursday, 22 January 2015, 3pm (Durham), CM107 Fernando
Lledo (Univ. Carlos III and ICMAT, Madrid) and Olaf Post (Durham)
Aspects of discrete magnetic Laplacians, Abstract: In the first part
of the talk we will introduce discrete magnetic Laplacians on oriented
graphs as second order operators. We will address then some group
theoretical aspects (e.g., the relation to magnetic translation
groups) and spectral aspects of these operators. In particular, we
will mention how to prove spectral bracketing results without using
metric graphs and the corresponding Kirchhoff Laplacians. Continuation
in CM105, 5pm
Tuesday, 3 February 2015, 11am (Durham), CM103 Florentin
Münch (Friedrich Schiller University Jena) Li-Yau inequality on
finite graphs via non-linear curvature dimension conditions, Abstract:
We introduce a new version of a curvature-dimension inequality for
non-negative curvature. We use this inequality to prove a logarithmic
Li-Yau inequality on finite graphs. To formulate this inequality, we
introduce a non-linear variant of the calculus of Bakry and Emery. In
the case of manifolds, the new calculus and the new
curvature-dimension inequality coincide with the common ones. In the
case of graphs, they coincide in a limit. In this sense, the new
curvature-dimension inequality gives a more general concept of
curvature on graphs and on manifolds. We show that Ricci-flat graphs
have a non-negative curvature in this sense. Moreover, a variety of
non-logarithmic Li-Yau type gradient estimates can be obtained by
using the new Bakry-Emery type calculus. Furthermore, we use these
Li-Yau inequalities to derive Harnack inequalities on
graphs. Continuation in CM204, 2.30pm
Monday, 9 March 2015, 11am-1pm (Durham), CM221 Ivan Veselic
(TU Chemnitz) Reconstruction and estimation of rigid functions
based on local data, Abstract: In many areas of mathematics and its
application in other sciences one is confronted with the task of
estimating or recosntruction a function based on partial data. Of
course, this will not work for all functions well. Thus one needs an
restriction to an adequate class of functions. This can be
mathematically modeled in many ways. Spacial statistics or complex
function theory are relevant areas of mathematics which come to ones
mind. We present several results on reconstrucion and estimation of
functions which are solutions of elliptic partial differential
equations on some subset of Euclidean space. We comment also on
analogous statements for solutions of finite difference equations on
graphs.
Tuesday, 21 April 2015, 10-12am (Durham), CM103 Christian Sadel (Institute of Science and Technology,
Klosterneuburg (Vienna), Austria) On analytic one-frequency
cocycles and relations to quasi-periodic operators (joint work with
A. Avila and S. Jitomirskaya), Abstract: Consider a quasi-one
dimensional discrete Schroedinger operator on a strip $Z x {1,...,m}$,
for instance consider such a strip embedded in $Z^2$, and take the
discrete Laplace operator and some potential. Solving the eigenvalue
equation of such an operator leads to transfer matrices (fundamental
solution). The products of such transfer matrices form a dynamical
system that contains essentially all the information about the
operator. If the potential is quasi-periodic, constructed through an
irrational rotation on the torus, i.e. $v(n,j)=f_j(n alpha+x)$ then
products of transfer matrices form a so called quasi-periodic
cocycle. It is conjectured that generically one has Cantor spectrum
for such operators. I will give an overview of these relations and
report on results going in this direction.
Tuesday, 11 August 2015, 3pm-4pm (Newcastle), also
Algebra-Geometry Seminar, HERB.4.TR4 Shai Evra (Hebrew University, Israel) Simplicial complexes
with large 'girth' and large chromatic number, Abstract: In 1959 Erdos
proved by random methods that there exist graphs with arbitrary large
girth and arbitrary large chromatic number. Explicit constructions
were given in 1988 by Lubotzky, Philips & Sarnak : the Ramanujan
graphs. In this talk we will study the high dimensional analogous question,
i.e., for simplical complexes instead of graphs. Here one should
explain first what is "girth" and what is "chromatic number". After
doing this, we will show how representation theory (and in particular
a quantitative form of Kazhdan property T, due to Hee Oh) leads to a
proof that the Ramanujan complexes constructed in 2005 by
Lubotzky-Samuels-Vishne give simplical complexes of large girth and
large chromatic number.
This is a joint work with Konstantin Golubev and Alex Lubotzky.
Monday, 17 August 2015, 11am-1pm (Durham), CM103 Vsevolod Chernyshev (National Research University Higher School of Economics, Moscow) Dynamics and statistics of narrow wave packets on metric and decorated graphs, Abstract: The talk will be devoted to the study of the dynamics of narrow packets on metric and decorated graphs. Let a decorated graph be a hybrid manifold obtained by gluing endpoints of a segment to a Riemannian manifold of dimension less than four. Let us consider the Cauchy problem for the time-dependent Schrodinger equation with the initial conditions have the form of narrow Gaussian packet with the support on the segment. When a packet reaches a segment's end a diverging wave front is formed on the surface. When this front reaches another point of gluing, another narrow packet starts to move along the segment, and so forth. We find an asymptotic estimate for N (t), i.e. the number of packets on the glued segment at time t for some decorated graphs. We show that N(t) could have polynomial, subexponential and exponential growth. We use the results of abstract analytic number theory. We also carried out computer experiments to learn more about the leading coefficient for some examples.
Thursday, 5 November 2015, 4pm-6pm (Newcastle), HERB 3.20 Agelos Georgakopoulos (Warwick) Square Tilings and the
Poisson Boundary
Thursday, 3 December 2015, 4pm-6pm (Newcastle), HERB 3.20 Nigel Boston (Wisconsin-Madison) Group Inequalities,
Information Inequalities, and the Entropy Region, Abstract: Given a
finite group G and subgroups G_1,...,G_n, for S a subset of
{1,...,n} let h_S be the log of the index of the intersection of the
G_i for i in S and let h = (h_S), a point in 2^n-dimensional real
space. A fundamental question is to describe the conic closure of
these points as G and its subgroups vary. This set arises in many
fields- it has alternative definitions in terms of polymatroids or
of joint entropies of discrete random variables. It interests
engineers since finding network coding capacities is a convex
optimization problem on the set. It is, however, only explicitly
known for n=2 and 3. For n=4 its boundary is curved and I will
describe work with Ting-Ting Nan that describes a little more about
this mysterious region.
Tuesday, 15 December 2015, 3pm-4pm (Newcastle), HERB.3.LMR, Joint Algebra-Geometry and GGA SeminarAnne Thomas (Sydney)Affine Deligne-Lusztig varieties and the geometry of Euclidean reflection groups, Abstract: Let G be a reductive group such as SL_n over the field F=k((t)), where k is an algebraic closure of a finite field, and let W be the affine Weyl group of G(F). The associated affine Deligne-Lusztig varieties X_x(b) were introduced by Rapoport. These are indexed by elements x in W and b in G(F), and are related to many important concepts in algebraic geometry over fields of positive characteristic. Basic questions about the varieties X_x(b) which have remained largely open include when they are nonempty, and if nonempty, their dimension. For these questions, it suffices to consider elements x and b both in W. We use techniques inspired by geometric group theory and representation theory to address these questions in the case that b is a translation. Our approach is constructive and type-free, sheds new light on the reasons for existing results and conjectures, and reveals new patterns. Since we work only in the standard apartment of the affine building for G(F), which is just the tessellation of Euclidean space induced by the action of the reflection group W, our results also hold over the p-adics. We obtain an application to reflection length in W. This is joint work with Elizabeth Milicevic (Haverford) and Petra Schwer (Karlsruhe).
2016
Tuesday, 19 January 2016, 3pm-5pm (Durham), CM105 David Cushing (Durham) Calculating the star graph and links of a complex
Tuesday, 1 March 2016, 9am-11am (Newcastle), HERB
3.19 Shiping Liu (Durham) Ramanujan coverings of Graphs,
Abstract: I will talk about the article with the same title by
C. Hall, D. Puder and W. F. Sawin.
Tuesday, 8 March 2016, 4pm-6pm (Durham), CM301 Asma
Hassannezhad (Max Planck Institute Bonn) Prescribing a finite
part of the Laplace spectrum in the conformal class of a metric
Monday, 23 May 2016, 11am-1pm (Durham), CM103 (Magic room)
Michela Egidi (TU Chemnitz) Quantitative uncertainty principle on the torus, Abstract: Motivated by Logvinenko and Sereda, and Kovrijkine's results on uncertainty principle for functions on the real line, we present similar
estimates for functions on the torus [0,2Lpi] for L>0. We pay particular attention to the explicit dependance on the modal parameter and we show
that the estimates are scale-free in L. Moreover, we discuss some applications in the realm of control theory of the heat equation.
Monday, 12 September, 10am-12pm (Durham), CM103 (Magic room)Christian Rose (TU Chemnitz) Heat kernels and locally
uniform Ricci curvature integral bounds, Abstract: The aim of the talk
is to show that the heat kernel on any complete connected Riemannian
manifold admits upper heat kernel bounds for small times if the
negative part of the Ricci curvature is locally uniform L^p-small. In
the special case that the manifold under consideration is compact, we
give explicit heat kernel upper bounds and therefore bounds on the
first Betti number. Additionally, we will discuss a more general
curvature condition such that Gaussian heat kernel bounds on compact
manifolds hold.
Wednesday, 28 September, 3pm-6pm (Durham), CM103 (Magic room)William Norledge (Newcastle) Coxeter groups and Buildings,
Abstract: This talk features joint work with Anne Thomas and Alina Vdovina.
Hyperbolic buildings are certain highly symmetrical, negatively curved
polyhedral complexes which have a combinatorial description as a
"Weyl-metric space". Towards a greater understanding of locally
compact groups, lattices in the automorphism groups of hyperbolic
buildings are studied in a hope to extend the theory of Bruhat-Tits on
algebraic groups over non-Archimedean local fields, wherein such a
group is realized as a group of automorphisms of an associated
Euclidean building. During the talk we shall introduce buildings and
their natural quotients under group actions- so called "complexes of
groups". Using covering theory of complexes of groups, we will
construct maximal-index, torsion-free subgroups of uniform lattices of
certain hyperbolic buildings. We then show that these subgroups are
amalgams of surface groups over free groups. Using a construction of
Haglund, these groups are also maximal-index, torsion-free subgroups
of a certain class of Coxeter groups.
2017
Thursday, 17 August 2017, 4pm-5pm (Durham), CM301 Shiping Liu (University of Science and Technology, Hefei, China) Ollivier Ricci curvature calculation as a linear programming problem
Tuesday, 22 August 2017, 2pm-3pm (Durham), CM103 (Magic room) Rikka Kangaslampi (Aalto University, Helsinki) Cubic graphs with K ≧ 0 and girth ≧ 4
