Previous Special Year Seminar

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...

Let A be a simple abelian variety, and X and Y be two subvarieties. We say X and Y are in the Bezout range if \dim X + \dim Y >= \dim A, and outside of the Bezout range otherwise. It is known that two varieties in the Bezout range in A always...

A category of motives is an axiomatic framework in which several cohomology theories from algebraic geometry are represented. While Morel and Voevodsky's classical framework of motivic homotopy theory focused on $A^1$-invariant cohomology theories...

I will discuss how the Lang–Trotter conjecture for pairs of elliptic curves implies new cases of the Zilber–Pink conjecture for curves in $\mathcal{A}_3$. Unlike previous results for curves in $\mathcal{A}_g$, our result does not rely on any...

Around 1921 Polya asked about the algebraicity of the indefinite integral of an algebraic function, in terms of the integrality of the coefficients in a power-series expansion. Polya nicely answered the special case of rational functions, using...