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Program

The School will officially start on Monday morning, September 14, and will
end on Friday afternoon, September 18.

The program will consist of invited lectures, talks,
as well as sessions devoted to student presentations.

**The tentative program of the school is available here.
**

**R. Jackiw**(MIT Center for Theoretical Physics, USA):

*Appreciation of the role of topology in physics led to a vigorous collaboration between the two*(2 lectures)(public colloquium)

How topology saved the standard model

Abstract: In the sixties a few bits of topology fell on the physicists plate. Although viewed at first as a bothersome annoyance, it turned out to be a crucial ingredient, without which the standard model could not describe Nature.**S. Bellucci**(INFN - Laboratory Nazionali di Frascati, Italy):

*Graphene materials for electronic and electromagnetic applications*(2 lectures)

Abstract: Among their remarkable properties, graphene and graphene-related materials constitute an effective vehicle for the realization of new electronic devices operating at different frequencies. We will overview in lecture 1 the Synthesis and Electrical Characterization of few-layered Graphene along with some recently developed applications, such as:

- Theoretical and Experimental Characterization of a Graphene-Based Broadband Microwave Attenuator

- Bottom-up Realization and Temperature-Dependent Electrical Characterization of a Green, Low-Cost Graphene-Based Device

- Electromagnetic Characterization of Graphene and Graphene Nanoribbons via ab-Initio Permittivity Simulations.

Lecture 2 will be focused on the description of Composite and Multilayered Graphene-Based Materials for Electromagnetic Compatibility.**A. Iorio**(Charles University, Prague, Czech Republic):

*Graphene and its use to reach the unreachable*(2 lectures)

Abstract: We shall give an overview of the possible uses of graphene as a tool to probe ideas about the fundamental properties of Nature. These research lines are at different stages of development: some are one step away from experiments, some are work in progress, some are still only conjectures.**A. Marzuoli**(Pavia University, Italy):

*BF theories and graphene*(Talk 1)

Abstract: Non-Abelian Topological Quantum Field Theories (TQFT) of the BF-type are shown to be particularly suitable to model the monolayer graphene effective action. The original proposal (cf. A Marzuoli, G Palumbo, EPL 99 (2012) 1002) was motivated on the basis of the 'universality' of this theoretical background with respect to basic requirements of topological -or anyonic- quantum computing. Here I am goin to highlight the potentiality of 3D BF theory emerging from its discretized counterpart, the family of the so-called Turaev and Viro 'state sum models'.

*Colored discretizations of Topological Quantum Field Theories*(Talks 2, 3, 4)

Abstract: Aim of this series of lectures is to present a few basic features of the branch of geometric topology that deals with colored quantum invariants of knots and 3-manifolds. In particular, 3-manifolds can be presented as colored triangulations, the coloring being associated to the representation ring of SU(2,q) for a deformation parameter q equal to a complex root of unity. For a closed 3-manifold the resulting (Turaev-Viro) invariant is the square of the Reshetikhin-Turaev invariant, which in turn represents the Chern-Simon-Witten generating functional obtained within the field-theoretic path integral prescription. State sums for colored trivalent graphs (and their specialization to knots or links embedded in a 3-manifold) are associated to Wilson-line/loop expectation values of observables in standard TQFTs (the Jones polynomial of knots and its generalizations).

**J. Pachos**(University of Leeds, UK):

1.*An introduction to knots, anyons, quantum computation, topological order*(colloquium)

2.*The toric code and error correcting codes*(slides)

3.*Majorana fermions and quantum evolutions*(blackboard, 2 lectures)

4.*Topological entanglement entropy, errors and outlook*(slides)**F. Peeters**(University of Antwerp, Belgium):

*Graphene and beyond*(4 lectures)

1.*Electronic structure. Nanoengineering of graphene*

2.*Mechanical properties and strain-engineering of graphene*

3.*Functionalization of graphene*

4.*Other two-dimensional atomic layers, e.g. transition metal*dichalcogenides**J. Zanelli**(CECs Valdivia, Chile):

*Chern-Simons Supersymmetry*(2 lectures)

Abstract: Chern-Simons (CS) field theories are the simplest gauge systems that can be defined in every odd dimension and for (almost) any gauge symmetry: given the gauge group G and the spacetime dimension D the CS action is uniquely defined. Not even the spacetime metric is required, but if the gauge group is SO(D-1,2), SO(D,1) or ISO(D-1,1) --that is, D-dimensional AdS, dS or Poincare'--, the CS action describes gravity and therefore the spacetime geometry emerges from the theory (provided the topology is simple enough). Supersymmetry, on the other hand, is an assumption that seems to be at odds with the Standard Model, although a good part of the theoretical physics community believe in it nonetheless. We will see how, with the help of some insight from CS and a minimum of assumptions, a supersymmetric model can be constructed that can reasonably describe some aspects of nature, including graphene.