Previous Special Year 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...

Using loops of contactomorphisms generated by vector fields that are positively transverse to the contact distribution, Eliashberg and Polterovich introduced the notion of orderability for contact manifolds. Recent work seems to suggest that the...

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

Consider a $Ck$ function $F : M^m \times N^n \longrightarrow \mathbb{R}$ defined on the product of the manifold $Mm$ of dimension $m$ with the compact manifold $Nn$ of dimension $n$. 

The function defined by ${\textstyle\inf_{N^n} F} : M^m...

A symplectophagy is a symplectic isotopy satisfying certain constraints reminiscent of the symplectic camel problem. In this talk, I will introduce this notion and basic examples, and present a new phenomenon of symplectic rigidity in the form of...

The transformer architecture, introduced in the 2017 paper Attention Is All You Need, forms the backbone of modern large language models (LLMs)—and gives ChatGPT its “T.” Despite the remarkable capabilities of these models, many aspects of their...

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...

Embedded contact homology (ECH) is a powerful invariant of contact 3-manifolds due to Hutchings and Taubes. It is key to the proofs of the Weinstein conjecture (existence of Reeb orbits), Arnold's chord conjecture, Irie's closing lemma...

Let $f: X \to S$ be a quasi-projective family of varieties defined over $\overline{\mathbb{Q}} \subset \mathbb{C}$. We show that the points of $S(\overline{\mathbb{Q}})$ that are Hodge generic for the variation of Hodge structures associated to $f$...

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...