Anton Mellit

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It is no secret that Catalan numbers are ubiquitous in mathematics. Anton Mellit believes that trying to explain their mysterious appearance in seemingly unrelated places will lead to many interesting discoveries. In his ERC Consolidator Grant Project, he plans to bring together algebraic and geometric methods to attack open problems in such areas of mathematics as combinatorics (q-analogues, q,t-analogues, Macdonald polynomials), low-dimensional topology (quantum invariants of knots and 3-manifolds), algebraic geometry and mathematical physics (moduli spaces of connections and Higgs bundles). The common theme uniting these subjects in one project is that computations of certain algebraic invariants of geometric objects produces Catalan numbers and their various generalizations.