# Welcome to the Hodge Institute

We are the algebra, geometry, number theory and topology research groups in the School of Mathematics at the University of Edinburgh. Together we have 15 permanent faculty, and a number of PhD students and post-docs. We run several weekly seminars, together with many working groups and the SMSTC graduate training programme.

In general, our work traverses algebraic geometry, algebraic number theory, algebraic topology, category theory, noncommutative algebra, representation theory. Specific research interests include:

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- Algebraic Geometry related to neighbouring fields: Combinatorics, Commutative Algebra, Gauge Theory, Mathematical Physics, Homotopy theory, Symplectic Geometry
- Algebraic Surgery Theory
- Birational Geometry, Positivity properties of divisors
- Category Theory and its Applications
- Derived Categories and Moduli Spaces
- Derived Algebraic Geometry
- Geometry of Algebraic Numbers
- Homological Commutative Algebra
- Knots and Links
- Noncommutative Algebraic Geometry
- Noncommutative Ring Theory
- Representation Theory related to: Combinatorics, Lie theory, Mathematical Physics
- Topology of Manifolds
- Toric and tropical geometry

Agata Smoktunowicz has won a European Mathematical Society Prize, the Whitehead Prize of the London Mathematical Society, the Whittaker Prize of the Edinburgh Mathematical Society and the Wacław Sierpiński Prize of the Polish Academy of Sciences, and also gave an invited lecture at the 2006 International Congress of Mathematicians. She was awarded an ERC advanced investigator grant in 2013. Andrew Ranicki won the Junior Whitehead Prize (1983) and the Senior Berwick Prize (1994) of the London Mathematical Society. Iain Gordon was awarded the Berwick Prize of the London Mathematical Society in 2005, was an EPSRC Leadership Fellow 2008-2013, and was an invited speaker at the 2010 International Congress of Mathematicians. Jon Pridham has an EPSRC 5-year Fellowship. In 2013, Arend Bayer won an ERC starting grant and Michael Wemyss was awarded a 5-year Early Career Fellowship by EPSRC. In 2015, David Jordan won an ERC starting grant and Arend Bayer won the Cambridge University Adams Prize.