## Dr Robin Hillier

### Overview

Telephone: +44(0)29 2087 5554

Fax: +44(0)29 208 74199

Extension: 75554

Location: M/2.04

#### Research Interest

Operator Algebras, Algebraic and Conformal Quantum Field Theory, Noncommutative Geometry, Quantum Probability, and in particular relations between these fields.

#### Research Group

Mathematical Physics

#### Recent Significant Publications

S.Carpi, R.Hillier, Y.Kawahigashi, and R.Longo. Spectral triples and the super-Virasoro algebra. (Comm.Math.Phys. 295 (2010), 71—97.)

S.Carpi, R.Conti, R.Hillier, and M.Weiner. Representations of conformal nets, universal C*-algebras and K-theory. (Comm.Math.Phys. DOI: 10.1007/s00220-012-1561-5, 2012.)

### Publications

Superconformal nets and noncommutative geometry (with S.Carpi and R.Longo). Preprint arXiv: math.OA/1304.4062.

On super-KMS functionals for graded quantum field nets. Preprint arXiv: math.OA/1204.5078.

N=2 super-conformal nets (with S.Carpi, Y.Kawahigashi, R.Longo, and F.Xu). Preprint arXiv: math.OA/1207.2398

Conformal nets and KK-theory (with S.Carpi and R.Conti). Ann.Funct.Anal. 7, 1 (2013), 11-17.

Representations of conformal nets, universal C*-algebras and K-theory (with S.Carpi, R.Conti, and M.Weiner). Comm.Math.Phys. (2012) DOI: 10.1007/s00220-012-1561-5.

Spectral triples and the super-Virasoro algebra (with S.Carpi, Y.Kawahigashi, and R.Longo). Comm.Math.Phys. 295 (2010), 71—97.

### Research

#### Research Interests

My research interest in the past concerned the studies of conformal quantum field theory by operator algebraic methods, and in particular their representation theory and end relations to noncommutative geometry and K-theory. Moreover, I dealt with super-KMS properties for graded quantum systems, and again potential relations o noncommutative geometric invariants.

In the current two-years project I would like to intensify the K-theoretic relationships in the case of currents algebra conformal field theories, which connects to the research interests of other members of the Mathematical Physics groups of the School. Moreover, I will deal with quantum stochastic aspects of conformal field theory and noncommutative geometry.

**Major Conference Talks**

“Spectral triples and and index pairing for conformal quantum field theory” (EU-NCG Network Meeting, Cardiff, 2010)

“Some K-theory and noncommutative geometry invariants for conformal nets”

(Minicourse, Cardiff, 2011)

“K-theory aspects of conformal nets” (4th Meeting of the French-Italian Network for Noncommutative Geometry, Paris, 2011)

“Super-KMS functionals and supersymmetry” (Topology and Physics, Porto, 2012)

“Universal C*-algebras and K-theory for conformal nets” (QQ12 – satellite conference of ICMP 2012, Hamburg)

“Noncommutative geometry and quantum probability for conformal nets” (QP 33, Luminy, 2012)

### Biography

MSc – Physics, 2007 TU Darmstadt (Germany)

MSc – Mathematics, 2007, TU Darmstadt (Germany)

PhD – Mathematics, 2010, University of Rome “Tor Vergata” (Italy)

**Previous Positions**

Postdoc at University of Rome “Tor Vergata”, 2010-2012