Research Area(s)

• General valuation theory and field theory
• Applications of valuation theory to algebraic and arithmetic algebraic geometry: local uniformization and desingularization in arbitrary characteristic
• Model theory of valued fields (generalizations of the Ax-Kochen-Ershov Theorem and quantifier elimination), power series fields in positive characteristic
• Valuations on function fields
• Valuation theory of ordered fields with exponential functions or derivations, Hardy fields, o-minimality
• Ordered structures, lexicographic products of ordered sets
• Ultrametric spaces
• Fixed point theorems

Research