# 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 large number of PhD students and post-docs. We run several weekly seminars, together with many working groups and the SMSTC graduate training programme. Edinburgh has a rich mathematical history, which has been turned into a mathematical map of Edinburgh by Sophie Powell-Hall.

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

- Algebraic Geometry related to neighbouring fields: Combinatorics, Commutative Algebra, Gauge Theory, Mathematical Physics, Homotopy theory, Symplectic Geometry
- Birational Geometry, Positivity properties of divisors
- Category Theory and its Applications
- Derived Categories and Moduli Spaces
- Derived Algebraic Geometry
- Homological Commutative Algebra
- Knots, Links and Braids
- 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. Iain Gordon was awarded the LMS Berwick Prize in 2005, was an EPSRC Leadership Fellow 2008-2013, and was an invited speaker at the 2010 International Congress of Mathematicians. Jon Pridham held an EPSRC 5-year Fellowship, ending in 2016. In 2013, Arend Bayer won an ERC starting grant. In 2015, David Jordan won an ERC starting grant and Arend Bayer won the Cambridge University Adams Prize. In 2016, Arend Bayer was awarded the Whitehead Prize of the London Mathematical Society and the Whittaker Prize of the Edinburgh Mathematical Society. Nick Sheridan and Ben Davison both hold Royal Society University Research Fellowships, and Ben Davison also holds an ERC starting grant. In 2018, Arend Bayer won an ERC consolidator grant. In 2019, the London Mathematical Society awarded a Whitehead Prize to Nick Sheridan and a Berwick Prize to Clark Barwick.

In 2018, a group at the Hodge Institute, together with researchers in Glasgow and Sheffield, was awarded the EPSRC programme grant Enhancing Representation Theory, Noncommutative Algebra and Geometry.