Previous Conferences & Workshops

A top degree differential form \omega on a smooth algebraic variety X over a local field K gives rise to a (real valued) measure on X(K). The Serre duality yields a natural isomorphism between 1-dimensional spaces of global top degree forms on an...

Over a high-dimensional vector space $F_p^n $over a fixed finite field $F_p$, the inverse theorem for the Gowers norm asserts that a bounded function f on this space that has a large Gowers $U^{k+1}$ norm, must necessarily correlate with a phase...

Let $f: \mathbf C^2 \rightarrow \mathbf \C^2$ be a polynomial transformation. The dynamical degree of $f$ is defined as $\lim_n (\text{deg} f^n)^{1/n}$, where $\text{deg} f^n$ is the degree of the $n$-th iterate of $f$. In 2007, Favre and Jonsson...

We will discuss stochastic quantization i.e. Langevin dynamic of the Yang-Mills model on two and three dimensional torus. This is described by a Lie algebra valued stochastic PDE driven by space-time white noise. We construct $(local)$ solution to...

I will review some recent progress on regularity properties of vortex and SQG patches. In particular, I will present an example of a vortex patch with continuous initial curvature that immediately becomes infinite but returns to $(C^2)$ class at all...

The inverse theorem for the Gowers U^{s+1}-norms has a central place in modern additive combinatorics, but all known proofs of it are difficult and most do not give effective bounds.

Over this seminar and the next, I will give an outline of a proof...

The Chowla conjecture from 1965 predicts that all autocorrelations of the Liouville function vanish. In fact, after an adaptation, the Chowla conjecture was expected to hold for all aperiodic multiplicative functions with values in the unit disc (cf...