Funding for Sheffield mathematician to pursue 'adventurous' research

Dr Haluk Sengun's research is being supported through the Engineering and Physical Sciences Research Council (EPSRC)'s New Horizons programme.

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A University of Sheffield mathematician has been awarded £200,000 in funding for "adventurous, high-risk research".

Dr Haluk Sengun's research is being supported through the Engineering and Physical Sciences Research Council (EPSRC)'s New Horizons programme.

His project, 'A torsion Jacquet-Langlands Transfer via K-theory', is being funded alongside others focussing on mathematical models to determine the best way to save the Amazon rainforest and systems of electromagnetic mirrors to protect electronic devices such as smartphones from threats.

The Langlands Programme is one of the grand mathematical theories of the 20th century that brings together several areas of mathematics – notably number theory, representation theory, arithmetic geometry and harmonic analysis.

An emerging new area in the Langlands programme is the so-called 'integral Langlands programme' which aims to extend the Langlands programme beyond its traditional 'complex' setting to an 'integral' setting.

"Instead of working with invariants that are defined over the complex numbers, we aim to work with invariants that are defined over the integers," Haluk, a lecturer in the School of Mathematics and Statistics, said.

"In this proposal, we propose to use tools and ideas from the theory of C*-algebras (an area that has been so far outside the Langlands programme) to tackle a foundational case of the problem of functoriality in the integral Langlands programme."

The theory of C*-algebras has proven itself to be a topic of fundamental role since its inception in the 1940s.

Haluk said: "With the invention of K-theory in the 1960s, C*-algebras started finding powerful applications to index theory, representation theory, dynamical systems, noncommutative geometry and mathematical physics.

"Our proposal promises to lead to new synergies between the Langlands programme and the theory of C*-algebras."

EPSRC, part of UK Research and Innovation, has allocated almost £25.5 million to 126 projects in the mathematical and physical sciences through New Horizons, which is designed to support adventurous, high-risk research.

Science Minister Amanda Solloway said: "It is critical we give the UK’s best researchers the resources to drive forward their revolutionary ideas so they can focus on identifying solutions to some of the world’s greatest challenges, such as climate change.

“This government funding will allow some of our brightest mathematicians and physicists to channel all their creative ingenuity into achieving potentially life-changing scientific breakthroughs."

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