Previous Conferences & Workshops

We prove a level raising mod $p = 2$ theorem for elliptic curves over $\mathbb Q$, generalizing theorems of Ribet and Diamond-Taylor. As an application, we show that the 2-Selmer rank can be arbitrary in level raising families. We will begin by...

Let $A$ be an affine variety inside a complex $N$ dimensional vector space which either has an isolated singularity at the origin or is smooth at the origin. The intersection of $A$ with a very small sphere turns out to be a contact manifold called...

Problems analogous to Bloch's conjecture, and some tentative methods of attacking them, will be discussed.

In this talk, we will discuss the local geometry of the closure of orbit space that parametrising smooth Fano manifolds inside certain Chow/Hilbert scheme. In particular, we will discuss the separatedness of the moduli of smoothable $K$-polystable $...

For a finitely presented group, the Word Problem asks for an algorithm which declares whether or not words on the generators represent the identity. The Dehn function is the time-complexity of a direct attack on the Word Problem by applying the...

The study of Cayley graphs of finite groups is related to the investigation of pseudo-random graphs and to problems in Combinatorial Number Theory, Geometry and Information Theory. I will discuss this topic, describing the motivation and focusing on...

The Parallel Repetition Theorem upper-bounds the value of a repeated (tensored) two prover game in terms of the value of the base game and the number of repetitions. In this work we give a simple transformation on games -- "fortification" -- and...

We will discuss the boundedness of log general type pairs, with the aim on proving the moduli of KSBA stable varieties is bounded.

Finding large cliques in random graphs and the closely related "planted" clique variant, where a clique of size \(k\) is planted in a random \(G(n,1/2)\) graph, have been the focus of substantial study in algorithm design. Despite much effort, the...

Start with a compact Riemann surface \(X\) and a complex reductive group \(G\), like \(\mathrm{GL}(n,\mathbb C)\). According to Hitchin-Simpson's ``non abelian Hodge theory", the pair \((X,G)\) comes with two new complex manifolds: the character...