# Faculty Research Profiles

Local analytic geometry, singularities, local algebra

My main research interests are in (real and complex) local analytic geometry. More specifically, I study algebraic aspects of the local geometry of analytic mappings, as well as algebro-geometric and differential properties of subanalytic sets, and analytic invariants. I am also interested in discrete mathematics. Particularly, extremal graph theory, long cycles and paths, and the combinatorics of desingularization.

### Tatyana Barron

Analysis on manifolds, complex geometry, symplectic geometry, automorphic forms, quantization

### Dan Christensen

Algebraic topology, homotopy type theory, derived categories, modular representation theory, mathematical physics, algebraic and scientific computation

### Graham Denham

Algebraic combinatorics; arrangements of hyperplanes and subspaces; configuration spaces; combinatorial aspects of rational homotopy theory

See my personal webpage (above) for details

### Ajneet Dhillon

Algebraic geometry, moduli of bundles, algebraic stacks

### Matthias Franz

Transformation groups, toric topology, homological algebra, computer algebra

### Chris Hall

Number Theory, Arithmetic Geometry

### John Jardine

Homotopy theory and its applications, algebraic geometry, category theory

See Personal Webpage.

### Masoud Khalkhali

Noncommutative geometry, mathematical physics, noncommutative spectral geometry and geometric analysis, cyclic cohomology, operator algebras, quantum groups and Hopf algebras.

### Nicole Lemire

Birational invariant theory, multiplicative invariants, algebraic groups, Galois cohomology, Lie theory, representation theory, lattices, essential dimension, vector bundles over curves

### Ján Mináč

Class field theory, Galois cohomology, absolute Galois groups, group cohomology, motivic cohomology, anabelian geometry, Langlands program

### Martin Pinsonnault

Symplectic geometry, Gromov-Witten invariants, Hamiltonian groups actions, low dimensional topology

My main interest is in symplectic topology and geometric topology. Currently, my research focuses on the homotopy theoretic, geometric, and algebraic properties of symplectomorphism groups. Symplectic geometry was initially developped as the mathematical framework of classical physics. It evolved into an independent field of research, very topological in nature, at the crossroads of differential topology, algebraic geometry, dynamics, and gauge theory. Nowadays most of the new developments involve Gromov's theory of $J$-holomorphic curves, Hofer geometry, Donaldson's theory of topological Lefschetz fibrations, and Floer homology theory.

### Lex Renner

Algebraic groups and monoids, group actions in algebraic geometry, invariant theory, reflection groups

### David Riley

Associative algebra, Lie algebra, and group theory; the relationship between identities, gradings, and actions.

The specific branch of Noncommutative Algebra that I study is sometimes called Combinatorial Algebra. The term derives from its ancestor, Combinatorial Group Theory, which traditionally focuses on such topics as groups presented by generators and relators, growth in groups, the Burnside Problem, as well as computational and algorithmic problems. Similar problems are now studied for infinite-dimensional associative algebras, Lie algebras, and Jordan algebras. I served as Department Chair during the period 2006-2011 and was appointed Faculty Scholar in 2010. Before joining Western University in 1999, I held various positions at the University of Alabama, the University of Alberta, the University of Oxford, and the Università degli Studi di Palermo. I have also made extended research visits to the University of Auckland, the Vrije Universiteit Brussel, Lunds Universitet, the University of New Brunswick, and the Università di Milano-Bicocca.

### Rasul Shafikov

Holomorphic mappings, CR geometry, analytic continuation, biholomorphic equivalence of domains and real submanifolds

### Gordon Sinnamon

Hardy inequalities, Fourier inequalities, function spaces, positive operators