Special Year Research Seminar

A balanced convex domain in 𝑅 𝑛 is a compact convex set that is invariant under the (𝑍/2) 𝑛 action which flips the signs of the coordinates. In this talk, I will explain a construction of a simple symplectic embedding of a ball of capacity 4 into...

A basic object in the modern study of symplectic topology is the space 𝑀𝑔(𝐴,𝐽)

of 𝐽-holomorphic curves of genus 𝑔 representing the homology class 𝐴

in a symplectic manifold (𝑀,𝑤). In a wide variety of situations, this space is a compact manifold (or...

Locally conformally symplectic (LCS) manifolds are manifolds that are symplectic up to a locally defined positive factor. In this generalization, we still have (locally conformally) exact Lagrangians, (locally conformally) Hamiltonian vector fields...

Using Tougeron’s characterization of multisummable (in the positive real directions) series, the latter can be viewed as infinite series of convergent power series with radii of convergence shrinking to 0. In joint work with Jean-Philippe Rolin and...

The Pila–Zannier strategy has proved to be a particularly fruitful approach: first applied to reprove the Manin–Mumford conjecture, it was later exploited decisively in proofs of the André–Oort conjecture. Crucially relying on a recent counting...

Ideas from tame geometry have recently begun to find their way into quantum field theory and string theory, suggesting that consistent effective theories and their observables may admit definable descriptions of finite complexity. In this talk I...

I will discuss questions pertaining to geometric unlikely intersections and transcendence in the setting of torii in positive characteristic. This is based on work in progress joint with Anup Dixit, Philip Engel, and Ruofan Jiang. 

I'll talk about the o-minimal structures R_LN and R_{LN,exp} where one has an effective form of the finiteness property of o-minimality. Unlike the more classical structure of Pfaffian function, R_{LN,exp} contains the period integrals for aribtrary...

Since the work of Jacobi and Siegel, it is well known that Theta series of quadratic lattices produce modular forms. In a vast generalization, Kudla and Millson have proved that the generating series of special cycles in orthogonal and unitary...