School of Mathematical Sciences
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Algebra and Analysis

Our internationally leading research ranges from Motives, quadratic forms, non-associative algebras and combinatorial group theory to Banach algebras, complex analysis and complex and quasi-regular dynamics to calculus of variations, partial differential equations and geometric data analysis. 


The Algebra subgroup deals with relationships and operations and structures that underpin other areas such as geometry, mathematical physics and computer science.

Research includes:

  • Algebraic cobordism
  • Categorical representation theory
  • Combinatorial and geometric group theory
  • Commutative algebra and invariant theory
  • Milnor K -theory
  • Nonassociative algebras
  • Quadratic forms and forms of higher degree
  • Quadratic and hermitian lattices
  • Quantum groups and tensor categories

Stephen Scully, a PhD student with Vishik, was awarded the prestigious LMS Cecil King Travel Scholarship.

The University of Nottingham is part of the Applied Algebra and Geometry research network. This network brings together UK academics who are interested in applications of algebra and geometry and related fields. The scope extends to computational algebra for applications including data-science, biology, medicine, engineering and physics.


The Analysis subgroup focuses on the mathematical description of natural phenomena. Research includes: 

  • Banach algebras 
  • Calculus of variations and PDE 
  • Complex analysis  
  • Functional analysis 
  • Complex dynamics 
  • Data and image analysis 

The Analysis subgroup has resolved prominent long-standing conjectures such as those of Hayman (1959) and Wiman (1911). 

Contact us PhD projects in Algebra and Analysis Apply for a PhD View our masters courses Research events


Group members



  • Joel Feinstein
  • Matthias Kurzke
  • Jim Langley
  • Dan Nicks
  • Kewei Zhang

Thinking of joining us? 

We are keen to create an environment which supports all staff members by providing:

Childcare services

Equality and diversity networks

Women's professional development

Work-life balance



Dr Alexander Vishik


School of Mathematical Sciences

University of Nottingham
University Park

t: +44 (0) 115 95 14940

School of Mathematical Sciences

The University of Nottingham
University Park
Nottingham, NG7 2RD

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