*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)

*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 Gromovâ€™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 3.19***Alina 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.

*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 Seminar***Anne 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).

*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.

*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

## Main |
## Conferences and Research Visits |
## Preprints and Publications |
## Software |
||||||